(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 9.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 4190568, 69552] NotebookOptionsPosition[ 4055730, 66994] NotebookOutlinePosition[ 4186206, 69410] CellTagsIndexPosition[ 4186124, 69405] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell["Computable Geographic Data and Knowledge Engineering", "Title", CellChangeTimes->{{3.448190122176695*^9, 3.44819012385317*^9}, { 3.485609127497636*^9, 3.485609133015955*^9}, {3.514308355088097*^9, 3.514308374696691*^9}, 3.5146594348020153`*^9, 3.5146601881617107`*^9, { 3.58328790287073*^9, 3.583287912851458*^9}, {3.583288155850483*^9, 3.58328817010365*^9}, {3.5832883767200403`*^9, 3.58328838810998*^9}, { 3.5832885513742743`*^9, 3.583288552085997*^9}, 3.591403975523428*^9}], Cell["Christopher Haydock", "Subtitle", CellChangeTimes->{{3.485609136120798*^9, 3.4856091511532907`*^9}, { 3.4856091945334663`*^9, 3.485609199379443*^9}, {3.4951031489375*^9, 3.49510314984375*^9}, {3.495106455296875*^9, 3.495106455453125*^9}, { 3.5143083846926413`*^9, 3.514308395249558*^9}, 3.5443793532699003`*^9, { 3.583287917812069*^9, 3.583287923051011*^9}}], Cell["Applied New Science LLC", "Subsubtitle", CellChangeTimes->{ 3.483202458953512*^9, {3.495105345328125*^9, 3.495105347890625*^9}, { 3.49510644571875*^9, 3.495106448390625*^9}, {3.5143083980990458`*^9, 3.514308409442589*^9}, {3.583287928170907*^9, 3.583287933658478*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Story", "Section", CellChangeTimes->{ 3.483202458955147*^9, {3.514308340990994*^9, 3.514308352103572*^9}, { 3.591411595534037*^9, 3.591411596242832*^9}}], Cell[TextData[{ StyleBox["BEGINNING:", FontWeight->"Bold"], " Disappointed, frustrated, stressed computable knowledge engineers leave \ too many great technology ideas on the table, others struggle to create \ viable knowledge businesses.\n", StyleBox["MIDDLE:", FontWeight->"Bold"], "\n", StyleBox["\[Bullet] Very brief history of NKS and Mathematica \ entrepreneurship.", FontWeight->"Bold"], "\n\tEpigraph: Intelligence equals computation\nAbout 3 decades ago Stephen \ Wolfram discovered elementary rule 30, a very simple 1 byte program that \ counterintuitively generated complex random output. This discovery has lead \ to important theoretical results such as the Principle of Computational \ Equivalence and Computational Irreducibility as well as practical \ applications such as Wolfram Alpha. Stephen Wolfram is the true hero of this \ story who created the company Wolfram Research and the Mathematica \ Computation System that has transformed this somewhat disturbing discovery \ into today\[CloseCurlyQuote]s computable knowledge with all its present \ challenges and opportunities. Thus entrepreneurship has long played an \ important role. The signs are that it will continue in this role, for \ example: Wolfram Alpha Pro and apps offer a low consumer price point for \ customized computable knowledge. The EnterpriseCDF 4 figure price point \ offers a solution in any market niche that can generate at least strong 4 \ figure revenue stream.\n", StyleBox["\[Bullet] How do we get more entrepreneurs creating successful \ computable knowledge businesses?", FontWeight->"Bold"], "\n\tEpigraph: Management, market, capital, technology\nCreate opportunities \ for computable knowledge experts to collaborate and learn from people with \ the skills and attitudes needed start a business, such as sales, networking, \ creativity and comfort with failure. Business accelerators do this in a wide \ variety of industries. For example, Space Tango and the Silicon Valley Space \ Center \[OpenCurlyDoubleQuote]LaunchPad\[CloseCurlyDoubleQuote] program help \ startups in the NewSpace industry. There\[CloseCurlyQuote]s great potential \ to expand Mathematica\[CloseCurlyQuote]s geodetic and geospatial computable \ data into small-sat earth imagery. To the extent that Wolfram Research \ resembles more an academic institution doing computable data basic research, \ a better model for helping startups might be university business incubators \ such as MIT\[CloseCurlyQuote]s Deshpande Center for Technological Innovation \ or UCSD\[CloseCurlyQuote]s von Liebig Entrepreneurism Center. Wolfram \ Research might also adopt some enterprise inovation practices pioneered by \ companies such as ?What If! and IDEO.\n", StyleBox["\[Bullet] Could Wolfram Research collaborate with external \ partners on Mathematica development?", FontWeight->"Bold"], "\n\tEpigraph: Natural language programming\nThe Wolfram Alpha Participate \ website recruits data curation volunteers and invites experts to suggest data \ sources, review new project proposals, and join internal discussions. Thus \ there is external collaboration on the first of the four major components of \ the Wolfram Alpha computable knowledge engine:\n\tData Curation Pipeline\n\t\ Algorithms and Models\n\tLinguistic Analysis\n\tPresentation Technology\n\ Especially in the areas of algorithms and models and presentation technology, \ new computable knowledge may depend on significant Mathematica development. \ Although the Mathematica provides state-of-the-art high-precision geodesy \ computation that supports all standard datums and projections, it is for \ example not nearly as easy as it could be to create computable geographic \ knowledge that combines 3D geodetic elevation data and 2D cartographic \ images. The barriers are even more dramatic for computable lighting \ knowledge. Mathematica can easily display luminous intensity functions, for \ example for linear fluorescent tubes. But what my customers want to see is \ something more like a virtual light meter computable document that shows the \ lighting levels (illuminance) on the merchandise on display in their retail \ store and compares it with that available with a proposed new LED lighting \ installation. This requires internal Mathematica luminous flux computations, \ but output that effectively simulates a photographic process of converting \ these fluxes into image pixel brightness levels.\n", StyleBox["\[Bullet] Are we software developers or service providers?", FontWeight->"Bold"], "\n\tEpigraph: Designed by Apple in California\nAs software developers it\ \[CloseCurlyQuote]s very easy to loose ourselves in the fun of creating code \ that does something and all the possible ways of expanding its functionality. \ But we only deserve to exist if we are solving a problem or in some way \ improving the lives of our potential customers. I\[CloseCurlyQuote]ve \ already mentioned that retail business owners would want to know how new \ lighting would improve their customers shopping experience, but don\ \[CloseCurlyQuote]t care that I\[CloseCurlyQuote]ve created virtual light \ meter computable documents. Similarly a customers of time series satellite \ imagery won\[CloseCurlyQuote]t have any interest in how computable geographic \ knowledge works or even care that their using computable knowledge, but \ rather they will want to know its impact on the service that they are \ providing such as natural resource management, real estate site selection, \ construction planning and project management, insurance risk modeling and \ damage assessment, humanitarian aid emergency response, location-based \ services and navigation, agriculture crop intelligence, etc.\n", StyleBox["\[Bullet] Who is your networking target?", FontWeight->"Bold"], "\n\tEpigraph: Never thank your audience\nThere are many networking \ opportunities at this 2013 Wolfram Technology Conference. Presumably all of \ us will have as our first priority to connect with potential customers and \ make the conversation be about them and their less-than-ideal present \ situation, not ourselves or our situation. In the case of my lighting \ business startup this would be:\n\tRetail business owners seeking dramatic \ improvements in their customers\[CloseCurlyQuote] shopping experience.\nOr \ for computable geographic knowledge business it might be:\n\tRepresentatives \ of any of the above mentioned satellite imagery industries whose customers \ would benefit from the low cost and unprecedented spacial and temporal \ resolution resulting from the NewSpace revolution.\nI propose that beyond \ this customer networking we all do a little networking around the objective \ of broadly accelerating the applications of computable knowledge technology. \ Who are the heros who can help make this happy ending come about? These \ additional targets of our networking could assist with some of the steps I\ \[CloseCurlyQuote]m proposing this afternoon or ones that you in the audience \ come up with during the question and answer period.\n", StyleBox["\[Bullet] How do we powerfully present ourselves and our \ commitment to advancing computable knowledge technology?", FontWeight->"Bold"], "\n\tEpigraph: Winning presence for business presenters\nThis is perhaps the \ most important step presented here because we must move from known computable \ knowledge applications to innovations with which most of us have little prior \ experience. Under such circumstances the world will want to know that we\ \[CloseCurlyQuote]re trustworthy, confident enough to proceed, and resilient \ enough to learn from the inevitable setbacks. Everything thus depends on how \ we present ourselves. The presentation keys are\n\tConnection, Message, \ Dynamism\nor equivalently\n\tAppreciation, Story, Change\nConnection \ (appreciation) releases our passion and authentic selves. The message (story) \ describes the desirable change that the main character, our audience, will \ experience. Dynamism (change) captures our audiences attention and aligns \ the heart, mind, and body, it\[CloseCurlyQuote]s being ourselves!\n", StyleBox["ENDING:", FontWeight->"Bold"], " Productive, powerful, excited engineers and business people participate in \ a vibrant field of seed, startup, and early-growth firms that commercialize \ computable knowledge technology." }], "Text", CellChangeTimes->{{3.495209008234375*^9, 3.49520915653125*^9}, 3.495209919765625*^9, 3.4952106014375*^9, {3.4952106824375*^9, 3.495210832234375*^9}, 3.514307848543872*^9, {3.514308058576482*^9, 3.514308065607885*^9}, {3.51430841745117*^9, 3.514308419642997*^9}, { 3.5149152616687326`*^9, 3.514915280523456*^9}, {3.514915328702818*^9, 3.5149153375415287`*^9}, 3.514915444638068*^9, {3.591411611874284*^9, 3.591411657600564*^9}, {3.5914117106736107`*^9, 3.591411930277309*^9}, { 3.5914119785556097`*^9, 3.5914120199400063`*^9}, {3.591412126504105*^9, 3.5914121932930183`*^9}, {3.5914122459131947`*^9, 3.591412247707507*^9}, { 3.591412779322204*^9, 3.5914128228243*^9}, {3.591412853775423*^9, 3.591412861836858*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Intelligence equals computation", "Section", CellChangeTimes->{ 3.483202458955147*^9, {3.514308340990994*^9, 3.514308352103572*^9}, { 3.591405948643826*^9, 3.5914059559289083`*^9}, {3.591406033787633*^9, 3.591406057581025*^9}, {3.591406453743795*^9, 3.59140645986895*^9}}], Cell["\<\ \[OpenCurlyDoubleQuote][The NKS principle of computational equivalence \ implies] there is no bright line that identifies \ \[OpenCurlyQuote]intelligence\[CloseCurlyQuote]; it is all just computation. \ [\[Ellipsis]] That\[CloseCurlyQuote]s the philosophical underpinning that \ makes possible the idea that building a Wolfram Alpha isn\[CloseCurlyQuote]t \ completely crazy.\[CloseCurlyDoubleQuote] \t\[LongDash]Stephen Wolfram, Talking about Computing and Philosophy \ [Recording: 51:33\[Dash]53:23] - \ http://blog.stephenwolfram.com/2011/05/talking-about-computing-and-philosophy/\ \>", "Text", CellChangeTimes->{{3.5914132151232*^9, 3.5914132715957117`*^9}, { 3.5914133344834127`*^9, 3.591413354400099*^9}, {3.5914228299173737`*^9, 3.591422871366782*^9}, {3.591423018943591*^9, 3.59142302506455*^9}, { 3.591423068960944*^9, 3.5914230968863287`*^9}}], Cell["\<\ \[OpenCurlyDoubleQuote]It is the very ubiquity of computational \ irreducibility that forces there to be only small islands of computational \ reducibility\[LongDash]which can readily be identified even from quite vague \ linguistic input.\[CloseCurlyDoubleQuote] \t\[LongDash]Stephen Wolfram, First killer NKS app - \ http://blog.wolfram.com/2009/05/14/7-years-of-nksand-its-first-killer-app/\ \>", "Text", CellChangeTimes->{{3.495209008234375*^9, 3.49520915653125*^9}, 3.495209919765625*^9, 3.4952106014375*^9, {3.4952106824375*^9, 3.495210832234375*^9}, 3.514307848543872*^9, {3.514308058576482*^9, 3.514308065607885*^9}, {3.51430841745117*^9, 3.514308419642997*^9}, { 3.5149152616687326`*^9, 3.514915280523456*^9}, {3.514915328702818*^9, 3.5149153375415287`*^9}, 3.514915444638068*^9, 3.591413197025092*^9, { 3.591413239476994*^9, 3.591413242119398*^9}, {3.59142311689476*^9, 3.5914231202465353`*^9}, {3.591423290815443*^9, 3.591423291274763*^9}, { 3.591423465976153*^9, 3.591423466517939*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Management, market, capital, technology", "Section", CellChangeTimes->{ 3.483202458955147*^9, {3.514308340990994*^9, 3.514308352103572*^9}, 3.591406376911138*^9, {3.5914064717248793`*^9, 3.5914064763971453`*^9}}], Cell["\<\ \[OpenCurlyDoubleQuote]But now we\[CloseCurlyQuote]ve just got too many \ opportunities, and I\[CloseCurlyQuote]ve decided we\[CloseCurlyQuote]re just \ leaving too many great ideas\[LongDash]and great technology prototypes\ \[LongDash]on the table.\[CloseCurlyDoubleQuote] \t\[LongDash]Stephen Wolfram, Talking about the Computational Future at SXSW \ 2013 - http://blog.stephenwolfram.com/2013/03/talking-about-the-computational-\ future-at-sxsw-2013/\ \>", "Text", CellChangeTimes->{{3.59141367131279*^9, 3.591413694569254*^9}, { 3.591423125844306*^9, 3.591423128286275*^9}, 3.59142333372537*^9, { 3.5914234550253077`*^9, 3.5914234857409573`*^9}}], Cell[CellGroupData[{ Cell["Business accelerators", "Subsection", CellChangeTimes->{ 3.483202458956058*^9, {3.514309203943825*^9, 3.514309209861143*^9}, 3.5914135450807037`*^9}], Cell["\<\ \[Bullet] Space Tango - http://www.spacetango.com/ The Space Tango accelerator and community of entrepreneurs helps new and \ growing businesses develop innovations, novel applications and diverse \ NewSpace markets. \[Bullet] Silicon Valley Space Center Accelerator Program \ \[OpenCurlyDoubleQuote]LaunchPad\[CloseCurlyDoubleQuote] - http://www.svsc.org/ The accelerator \[OpenCurlyDoubleQuote]LaunchPad\[CloseCurlyDoubleQuote] \ program advises, mentors, and co-founds NewSpace start-ups. \[OpenCurlyDoubleQuote]We will help you set realistic expectations for \ building a company stemming from our collected industry and incorporation \ experience. Basically we\[CloseCurlyQuote]ll lend you our perspective on \ whether your business idea and future vision makes sense in the current \ market, and suggest any changes to the idea or to your expectations - helping \ you create a successful outlook.\[CloseCurlyDoubleQuote]\[LongDash]SVSC Vision\ \>", "Text", CellChangeTimes->{{3.495209008234375*^9, 3.49520915653125*^9}, 3.495209919765625*^9, 3.4952106014375*^9, {3.4952106824375*^9, 3.495210832234375*^9}, 3.514307848543872*^9, {3.514308058576482*^9, 3.514308065607885*^9}, {3.51430841745117*^9, 3.514308419642997*^9}, { 3.5149152616687326`*^9, 3.514915280523456*^9}, {3.514915328702818*^9, 3.5149153375415287`*^9}, 3.514915444638068*^9, {3.591413780637989*^9, 3.5914138752101917`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["University business incubators", "Subsection", CellChangeTimes->{ 3.483202458956058*^9, {3.514309203943825*^9, 3.514309209861143*^9}, 3.591413556054227*^9}], Cell["\<\ \[Bullet] Deshpande Center for Technological Innovation MIT - \ http://deshpande.mit.edu/ MIT researchers develop innovative technologies in the lab and bring them to \ the marketplace in the form of breakthrough products and new companies. \[OpenCurlyDoubleQuote]By showing these very talented researchers how to \ commercialize their innovations so they have a real-world impact, the MIT \ Deshpande Center is helping them become change makers\[LongDash]people who \ don\[CloseCurlyQuote]t just leave things at the idea stage but push ahead and \ actually make their ideas happen.\[CloseCurlyDoubleQuote]\[LongDash]Gururaj \ \[OpenCurlyDoubleQuote]Desh\[CloseCurlyDoubleQuote] Deshpande \[Bullet] von Liebig Entrepreneurism Center UCSD - \ http://www.jacobsschool.ucsd.edu/vonliebig/ The center\[CloseCurlyQuote]s technology and business advisors guide faculty \ and student inventors through the technology assessment, proof-of-concept and \ early stages of the commercialization process. \[Bullet] Stevens Institute for Innovation USC - http://stevens.usc.edu/ The institute promotes creative thinking and breakthrough research for \ societal impact, beyond traditional academic means. \[OpenCurlyDoubleQuote]Innovation can come from the arts and social sciences \ as well as engineering or medicine. It can take the shape of new products or \ services; new ventures, ranging from venture-backed startups to non-profits; \ as well as new organizational models. Innovation can be any groundbreaking \ approach or advancement that changes the way we live, work, and play.\ \[CloseCurlyDoubleQuote]\[LongDash]Stevens Center Mission\ \>", "Text", CellChangeTimes->{{3.495209008234375*^9, 3.49520915653125*^9}, 3.495209919765625*^9, 3.4952106014375*^9, {3.4952106824375*^9, 3.495210832234375*^9}, 3.514307848543872*^9, {3.514308058576482*^9, 3.514308065607885*^9}, {3.51430841745117*^9, 3.514308419642997*^9}, { 3.5149152616687326`*^9, 3.514915280523456*^9}, {3.514915328702818*^9, 3.5149153375415287`*^9}, 3.514915444638068*^9, {3.591413920792048*^9, 3.5914139547448483`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Enterprise innovation", "Subsection", CellChangeTimes->{ 3.483202458956058*^9, {3.514309203943825*^9, 3.514309209861143*^9}, 3.591413571525646*^9}], Cell["\<\ \[Bullet] ?What If! - http://www.whatifinnovation.com/ ?What If! invents new products, brands, services, and business models, and \ helps their industry partners build in-house innovation capabilities. \[OpenCurlyDoubleQuote]We strongly believe that developing innovation metrics \ is a journey much like innovation itself. Many companies try to measure too \ much too soon, often killing fragile innovation efforts before they ever \ really have a chance to succeed. We find that early on companies should focus \ on more forward-looking, leading indicators or proxies for innovation that \ will tell them whether they are executing on the right \ activities\[LongDash]for example, training people, delivering on some \ projects, etc. Only down the road can you rely on more backward-looking, \ lagging indicators to measure the commercial success of your innovation \ efforts.\[CloseCurlyDoubleQuote]\[LongDash]Client Questions, Answered \[Bullet] IDEO - http://www.ideo.com/ [pronounced \ \[OpenCurlyDoubleQuote]eye-dee-oh\[CloseCurlyDoubleQuote]] In public and private sector organizations IDEO builds creative culture and \ the internal systems required to sustain innovation and launch new ventures. \[OpenCurlyDoubleQuote]Design thinking is a human-centered approach to \ innovation that draws from the designer\[CloseCurlyQuote]s toolkit to \ integrate the needs of people, the possibilities of technology, and the \ requirements for business success.\[CloseCurlyDoubleQuote]\[LongDash]Tim \ Brown, president and CEO\ \>", "Text", CellChangeTimes->{{3.495209008234375*^9, 3.49520915653125*^9}, 3.495209919765625*^9, 3.4952106014375*^9, {3.4952106824375*^9, 3.495210832234375*^9}, 3.514307848543872*^9, {3.514308058576482*^9, 3.514308065607885*^9}, {3.51430841745117*^9, 3.514308419642997*^9}, { 3.5149152616687326`*^9, 3.514915280523456*^9}, {3.514915328702818*^9, 3.5149153375415287`*^9}, 3.514915444638068*^9, {3.591413980036086*^9, 3.591414009540189*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Miscellaneous", "Subsection", CellChangeTimes->{ 3.483202458956058*^9, {3.514309203943825*^9, 3.514309209861143*^9}, 3.591413582323719*^9}], Cell["\<\ \[Bullet] International Space Station (ISS) Center for the Advancement of \ Science in Space (CASIS) - http://www.iss-casis.org/Home.aspx CASIS manages the International Space Station U.S. National Laboratory. They \ select research and funding projects, connect investors to scientists with \ great ideas, make access to the station faster and easier, and drive \ scientific inquiry toward developing groundbreaking new technologies and \ products that will tangibly affect our lives. \[Bullet] Space Angels Network - http://www.spaceangelsnetwork.com/ Space Angels Network is the leading source of capital for aerospace and \ aviation startups. \[OpenCurlyDoubleQuote]Visionary \[OpenCurlyQuote]astropreneurs\ \[CloseCurlyQuote] can apply to present their ventures and capture the \ interest of our global network of investors who are looking for the next big \ opportunity in aerospace.\[CloseCurlyDoubleQuote]\[LongDash]Astropreneurs \ Wanted! \[Bullet] Virgin Unite - http://www.virgin.com/unite \[OpenCurlyDoubleQuote]Hello, we\[CloseCurlyQuote]re Virgin Unite, the \ non-profit foundation of the Virgin Group. We unite great people and \ entrepreneurial ideas, reinventing how we live and work to help make people\ \[CloseCurlyQuote]s lives better. We believe business can and must be a force \ for good in the world\[LongDash]and that this is also good for business!\ \[CloseCurlyDoubleQuote]\[LongDash]Virgin Unite UK Registered Charity \[Bullet] Unreasonable Institute - http://unreasonableinstitute.org/ \[OpenCurlyDoubleQuote]The Unreasonable Institute gives an \ \[OpenCurlyQuote]unreasonable advantage\[CloseCurlyQuote] to entrepreneurs \ creating solutions to the world\[CloseCurlyQuote]s biggest social and \ environmental problems. We do this by bringing entrepreneurs together to live \ under the same roof for 5 weeks, where they connect with mentors, investors, \ and a lasting global network of support. Our goal: help each of these \ ventures scale up to meaningfully impact the lives of over 1 million people.\ \[CloseCurlyDoubleQuote]\[LongDash]Unreasonable Institute 501(c)3 Non-Profit \ Organization \[Bullet] Space Frontier Foundation NewSpace Business Plan Competition - \ http://newspacebpc.com/ \[OpenCurlyDoubleQuote]The NewSpace BPC is the world\[CloseCurlyQuote]s first \ professional business plan competition focused on the burgeoning NewSpace \ industry. The competition aims to assist and showcase new startups and \ expanding firms who can demonstrate both the ability to provide a return on \ investment and the capacity to contribute to opening the space frontier.\ \[CloseCurlyDoubleQuote]\[LongDash]What is the NewSpace BPC? \[Bullet] SpaceFlorida - http://www.spaceflorida.gov/home Florida aerospace economic development agency supports talent development, \ enhances infrastructure, supports governments and organizations that improve \ the state\[CloseCurlyQuote]s competitive business climate, and helps attract, \ retain, and expand aerospace or related supply chain businesses.\ \>", "Text", CellChangeTimes->{{3.495209008234375*^9, 3.49520915653125*^9}, 3.495209919765625*^9, 3.4952106014375*^9, {3.4952106824375*^9, 3.495210832234375*^9}, 3.514307848543872*^9, {3.514308058576482*^9, 3.514308065607885*^9}, {3.51430841745117*^9, 3.514308419642997*^9}, { 3.5149152616687326`*^9, 3.514915280523456*^9}, {3.514915328702818*^9, 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$CellContext`xy$[$CellContext`m$/2, (-$CellContext`n$)/ 2]}]]], $CellContext`cr$ = N[(Part[ $CellContext`xy$[($CellContext`m$ - 1)/2, 0], 2] + Part[ $CellContext`xy$[0, ($CellContext`n$ - 1)/2], 1])/2]}, With[{$CellContext`mr$ = $CellContext`m$ + 2 Ceiling[Max[ Part[ $CellContext`\[Phi]\[Lambda]$[$CellContext`pr$, \ $CellContext`pr$], 1], Part[ $CellContext`\[Phi]\[Lambda]$[-$CellContext`pr$, \ $CellContext`pr$], 1]] - ($CellContext`m$ - 1)/ 2], $CellContext`nr$ = $CellContext`n$ + 2 Ceiling[Max[ Part[ $CellContext`\[Phi]\[Lambda]$[$CellContext`pr$, \ $CellContext`pr$], 2], Part[ $CellContext`\[Phi]\[Lambda]$[$CellContext`pr$, \ -$CellContext`pr$], 2]] - ($CellContext`n$ - 1)/2]}, With[{$CellContext`fr$ = N[ Max[ Abs[{ $CellContext`xy$[$CellContext`mr$/2, $CellContext`nr$/2], $CellContext`xy$[$CellContext`mr$/2, (-$CellContext`nr$)/ 2]}]]]}, With[{$CellContext`frstep$ = $CellContext`fr$/ 2^($CellContext`nx$ - 1), $CellContext`halfnumber$ = Ceiling[2^($CellContext`nx$ - 1) ($CellContext`cr$/$CellContext`fr$)]}, With[{$CellContext`ilo$ = 1 + 2^($CellContext`nx$ - 1) - $CellContext`halfnumber$, $CellContext`ihi$ = 1 + 2^($CellContext`nx$ - 1) + $CellContext`halfnumber$, $CellContext`imr$ = 1 + ($CellContext`mr$ - $CellContext`m$)/2, $CellContext`inr$ = 1 + ($CellContext`nr$ - $CellContext`n$)/2}, With[{$CellContext`a$ = Apply[Append, Transpose[{ Apply[Join, Array[N[ $CellContext`xy$[#, #2]]& , {$CellContext`m$, \ $CellContext`n$}, {{(-($CellContext`m$ - 1))/2, ($CellContext`m$ - 1)/ 2}, {(-($CellContext`n$ - 1))/2, ($CellContext`n$ - 1)/ 2}}]], Apply[Join, Rescale[ Part[$CellContext`averagedelevationgeodeticpixels, Span[$CellContext`imr$, -$CellContext`imr$], Span[$CellContext`inr$, -$CellContext`inr$]], \ $CellContext`averagedelevationrange]]}], {1}], $CellContext`plotzrange$ = Apply[{ Min[#, -$CellContext`\[Epsilon]$], #2}& , Rescale[ ({ Min[#], Max[#]}& )[ Part[$CellContext`simulatedcartographicelevation, Span[$CellContext`ilo$, $CellContext`ihi$], Span[$CellContext`ilo$, $CellContext`ihi$]]], \ $CellContext`averagedelevationrange]]}, With[{$CellContext`trx$ = N[ Max[ Part[ $CellContext`xy$[($CellContext`m$ - 1)/ 2, ($CellContext`n$ - 1)/2], 1], Part[ $CellContext`xy$[(-($CellContext`m$ - 1))/ 2, ($CellContext`n$ - 1)/2], 1]]], $CellContext`try$ = N[ Max[ Part[ $CellContext`xy$[($CellContext`m$ - 1)/ 2, ($CellContext`n$ - 1)/2], 2], Part[ $CellContext`xy$[($CellContext`m$ - 1)/ 2, (-($CellContext`n$ - 1))/2], 2]]]}, With[{$CellContext`ixlo$ = 1 + Floor[($CellContext`pr$ - $CellContext`trx$) (1024/( 2 $CellContext`pr$))], $CellContext`ixhi$ = Ceiling[($CellContext`pr$ + $CellContext`trx$) (1024/( 2 $CellContext`pr$))], $CellContext`iylo$ = 1 + Floor[($CellContext`pr$ - $CellContext`try$) (1024/( 2 $CellContext`pr$))], $CellContext`iyhi$ = Ceiling[($CellContext`pr$ + $CellContext`try$) (1024/( 2 $CellContext`pr$))]}, With[{$CellContext`f$ = Function[$CellContext`t, N[1/(1 + Exp[(-8) $CellContext`t])]]}, If[$CellContext`g$$, $CellContext`t$$ = 0]; If[$CellContext`g$$, Show[ Graphics3D[{}, Axes -> False, Boxed -> False, PlotRange -> Append[$CellContext`pr$ {{-1, 1}, {-1, 1}}, $CellContext`plotzrange$], BoxRatios -> {5, 5, 2 First[ Differences[$CellContext`plotzrange$]]}, ViewVector -> {$CellContext`vc$ + { 2 $CellContext`pr$, 2 $CellContext`pr$, 5/ 2} $CellContext`vp$, $CellContext`vc$}, ViewAngle -> $CellContext`va$, ImageSize -> {640, 480}], ListPlot3D[$CellContext`a$, PlotStyle -> Texture[ ImageTake[ $CellContext`RecoloredDelisPattern[], \ {$CellContext`ixlo$, $CellContext`ixhi$}, {$CellContext`iylo$, \ $CellContext`iyhi$}]], Mesh -> None]], Piecewise[{{ ImageCompose[{$CellContext`schematicscene2matchterrain, $CellContext`f$[ Rescale[$CellContext`t$$, {0, 1}, {-1, 1}]]}, {$CellContext`schematicscene1earth3D, $CellContext`f$[ Rescale[$CellContext`t$$, {0, 1}, { 1, -1}]]}], $CellContext`t$$ <= 1}, { ImageCompose[{$CellContext`schematicscene2matchterrain, 1}, {$CellContext`schematicscene1earth3D, $CellContext`f$[ Rescale[$CellContext`t$$, {1, 3/2}, {-1, 1}]]}], Inequality[1, Less, $CellContext`t$$, LessEqual, 3/2]}, { ImageCompose[{$CellContext`schematicscene2matchterrain, 1}, {$CellContext`schematicscene1earth3D, $CellContext`f$[ Rescale[$CellContext`t$$, {3/2, 2}, {1, -1}]]}], 3/2 < $CellContext`t$$}}]]]]]]]]]]]]], "Specifications" :> {{{$CellContext`g$$, True, "earth 3D"}, { True, False}}, {{$CellContext`t$$, 0, "details"}, 0, 2, Enabled -> Dynamic[ Not[$CellContext`g$$]]}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{685., {293., 298.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`averagedelevationgeodeticpixels = \ CompressedData[" 1:eJwNVXk41OsfZRjDGGMWY8kliiJFbpqkeD+2JNIio641JrQgFZGyhkqFqweJ qPy4SaFE2d6vhMmStVD34kayVfb1ys8f57/zPOc8z3nOOapuvodPkISEhKRX wVzFw0unXZ+YycKhwpkKNQUZaDGdqZK3pUOzNVOr2YQNefY6+8LdOaA42nR7 dogJQe6ceRU2DVaYzPzrLZLQl0Fv61MnQadZ1Gy/3RLafS/BZl/5R2ThlG9i 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The proposed Earth 3D framework generates 3D graphics from ", StyleBox["Mathematica", FontSlant->"Italic"], "\[CloseCurlyQuote]s built-in geographic data. This 3D graphic displays \ elevation and terrain imagery in a cartographic coordinates, which are \ especially suitable if the field of view is small compared to the earth\ \[CloseCurlyQuote]s curvature. 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The opaque fleur-de-lis pattern \ within the larger partially transparent pattern designates the selected \ terrain region. The cartographic coordinate mesh on the fleur-de-lis pattern \ aligns with the selected terrain region. Above the opaque fleur-de-lis \ pattern a 3D elevation cutout shows the elevation of the selected terrain \ region and also has a cartographic coordinate mesh. The red outline that \ roughly follows the boundary of the elevation cutout is precisely the \ boundary of the earth 3D graphic as can be confirmed by scanning the animate \ view point between 1 and 2, which transiently overlays the scene 1 earth 3D \ graphic. The earth 3D boundary and its red outline follow lines of constant \ latitude and longitude and are thus aligned with geodetic coordinates. The \ schematic exaggerates the difference between cartographic and geodetic \ coordinates so that the difference is plainly visible throughout the entire \ series of animated images. 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t-1.79032\\t-2.0782\\t-2.24048\\t-2.3406\\t-2.67237\\t-3.0483\\t-3.3346\\t-3.\ 63279\\t-4.05177\\t-4.6097\\t-5.12982\\t-5.38178\\t-5.38088\\t-5.27259\\t-5.\ 14627\\t-5.08441\\t-5.14331\\t-5.1437\\t-5.01341\\t-4.94254\\t-4.82145\\t-4.\ 71848\\t-4.68594\\t-4.68589\\t-4.62723\\t-4.47337\\t-4.36116\\t-4.10996\\t-3.\ 80068\\t-3.48892\\t-3.16971\\t-2.83342\\t-2.55625\\t-2.41095\\t-2.43107\\t-2.\ 48847\\t-2.53571\\t-2.55679\\t-2.42814\\t-2.27433\\t-2.08092\\t-1.81853\\t-1.\ 61538\\t-1.51938\\t-1.38947\\t-1.1549\\t-0.923757\\t-0.827686\\t-0.652512\\t-\ 0.426626\\t-0.346817\\t-0.360532\\t-0.471107\\t-0.734679\\t-1.00626\\n5.7112\\\ t5.6686\\t5.68232\\t5.69611\\t5.66113\\t5.74793\\t5.92602\\t6.06058\\t6.06846\ \\t6.00902\\t5.8297\\t5.48141\\t5.0276\\t4.56624\\t4.20611\\t4.09208\\t4.\ 02483\\t3.84377\\t3.70725\\t3.7544\\t3.97699\\t4.25266\\t4.51423\\t4.68518\\\ t4.83054\\t4.96128\\t5.00969\\t5.05015\\t5.22923\\t5.35597\\t5.40002\\t5.\ 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2.18204\\t-2.45296\\t-2.6744\\t-2.83159\\t-3.05967\\t-3.36115\\t-3.66552\\t-3.\ 94192\\t-4.20093\\t-4.50378\\t-4.76178\\t-4.69444\\t-4.53118\\t-4.51809\\t-4.\ 45855\\t-4.36018\\t-4.2881\\t-4.21676\\t-4.15328\\t-4.13302\\t-4.19803\\t-4.\ 22653\\t-4.19192\\t-4.16781\\t-4.20053\\t-4.06773\\t-3.85033\\t-3.68733\\t-3.\ 51977\\t-3.24807\\t-2.98051\\t-2.7639\\t-2.54824\\t-2.35684\\t-2.23456\\t-2.\ 25603\\t-2.34844\\t-2.60189\\t-2.74752\\t-2.69621\\t-2.67293\\t-2.603\\t-2.\ 23648\\t-1.77969\\t-1.62264\\t-1.66438\\t-1.59381\\t-1.46684\\t-1.35531\\t-1.\ 2839\\t-1.08309\\t-0.771595\\t-0.635974\\t-0.769303\\t-0.980171\\n5.11367\\t5.\ 1522\\t5.16582\\t5.24666\\t5.36084\\t5.58158\\t5.81459\\t5.83744\\t5.86637\\\ t6.01853\\t5.9355\\t5.52503\\t5.1396\\t4.83306\\t4.39639\\t3.98772\\t3.64878\\\ t3.41994\\t3.34192\\t3.42055\\t3.6431\\t4.0236\\t4.35524\\t4.52702\\t4.60201\\\ t4.64026\\t4.69559\\t4.91648\\t5.10393\\t5.08218\\t5.00879\\t5.1402\\t5.42123\ 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64217\\t-1.60703\\t-1.46699\\t-1.39049\\t-1.40155\\t-1.30595\\t-1.0336\\t-0.\ 720544\\t-0.562239\\t-0.656944\\t-0.848204\\n4.87065\\t5.05041\\t5.08947\\t5.\ 10428\\t5.11898\\t5.36569\\t5.70149\\t5.82703\\t5.9239\\t6.07474\\t5.96205\\\ t5.6245\\t5.40886\\t5.19622\\t4.71558\\t4.14057\\t3.69767\\t3.43411\\t3.31589\ \\t3.37953\\t3.60566\\t3.96758\\t4.23664\\t4.39002\\t4.40936\\t4.43617\\t4.\ 60312\\t4.93123\\t5.09083\\t5.04462\\t4.93953\\t4.99342\\t5.23374\\t5.32179\\\ t5.21436\\t5.12398\\t4.97386\\t4.74658\\t4.56819\\t4.40373\\t4.05817\\t3.\ 70642\\t3.42146\\t3.29946\\t3.30717\\t3.30265\\t3.29635\\t3.37917\\t3.52943\\\ t3.5172\\t3.40841\\t3.43128\\t3.40316\\t3.19826\\t2.75605\\t2.04332\\t1.3414\\\ t0.856426\\t0.441718\\t0.107251\\t-0.0144392\\t-0.0591974\\t-0.131012\\t-0.\ 25359\\t-0.425577\\t-0.582137\\t-0.795821\\t-1.15808\\t-1.45851\\t-1.66103\\t-\ 2.05224\\t-2.60382\\t-3.02113\\t-3.20702\\t-3.30248\\t-3.36517\\t-3.52005\\t-\ 3.7168\\t-3.98226\\t-4.19143\\t-4.38063\\t-4.59807\\t-4.62147\\t-4.61943\\t-4.\ 67\\t-4.46511\\t-4.16927\\t-4.03523\\t-4.05976\\t-3.93534\\t-3.60433\\t-3.\ 33515\\t-3.25535\\t-3.29486\\t-3.3693\\t-3.51412\\t-3.58845\\t-3.59614\\t-3.\ 6131\\t-3.6402\\t-3.53038\\t-3.30806\\t-3.1249\\t-2.90006\\t-2.57323\\t-2.\ 31674\\t-2.22256\\t-2.19399\\t-2.19414\\t-2.21906\\t-2.24934\\t-2.44179\\t-2.\ 63616\\t-2.63783\\t-2.5202\\t-2.45148\\t-2.22284\\t-1.87539\\t-1.6413\\t-1.\ 49704\\t-1.3099\\t-1.32756\\t-1.33633\\t-1.10518\\t-0.798696\\t-0.565359\\t-0.\ 418724\\t-0.448368\\t-0.557817\\n4.67034\\t4.95266\\t5.05622\\t5.05024\\t5.\ 02195\\t5.28047\\t5.67583\\t5.87601\\t5.96882\\t6.03779\\t5.92034\\t5.74087\\\ t5.67096\\t5.46271\\t4.92279\\t4.34642\\t3.91331\\t3.58551\\t3.35683\\t3.\ 39656\\t3.62574\\t3.93283\\t4.19335\\t4.34302\\t4.40968\\t4.50199\\t4.72918\\\ t4.99714\\t5.05266\\t5.02105\\t4.9377\\t4.97023\\t5.16534\\t5.22063\\t5.08195\ 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42696\\t-1.27864\\t-1.28426\\t-1.21302\\t-0.873759\\t-0.578487\\t-0.478436\\t-\ 0.38928\\t-0.314763\\t-0.307775\\n4.34724\\t4.70839\\t4.89731\\t5.02832\\t5.\ 1324\\t5.32628\\t5.68805\\t5.87098\\t5.87582\\t5.91341\\t5.89605\\t5.89206\\\ t5.92269\\t5.67802\\t5.05618\\t4.43389\\t3.96159\\t3.54187\\t3.29263\\t3.\ 46425\\t3.73305\\t4.01344\\t4.24924\\t4.36628\\t4.45962\\t4.6646\\t4.98001\\\ t5.15554\\t5.07547\\t5.04418\\t5.07424\\t5.09205\\t5.24827\\t5.25372\\t5.\ 11115\\t5.11245\\t5.22237\\t5.17295\\t4.95105\\t4.62133\\t4.16798\\t3.66022\\\ t3.25448\\t3.0653\\t2.96359\\t2.83422\\t2.69123\\t2.68946\\t2.78814\\t2.82183\ \\t2.80538\\t2.82395\\t2.73933\\t2.5106\\t2.16402\\t1.6869\\t1.24563\\t0.\ 942481\\t0.622671\\t0.309484\\t0.0729206\\t-0.104218\\t-0.276546\\t-0.391941\\\ t-0.593239\\t-0.849243\\t-1.14136\\t-1.46877\\t-1.88836\\t-2.3948\\t-2.89674\\\ t-3.32668\\t-3.58481\\t-3.7653\\t-3.94184\\t-4.00854\\t-4.00814\\t-4.08296\\t-\ 4.2098\\t-4.34115\\t-4.58944\\t-4.81341\\t-4.82132\\t-4.73197\\t-4.56403\\t-4.\ 31393\\t-4.05809\\t-3.89635\\t-3.75417\\t-3.43941\\t-3.03269\\t-2.79894\\t-2.\ 67758\\t-2.63015\\t-2.63507\\t-2.72086\\t-2.90031\\t-2.98524\\t-3.07925\\t-3.\ 2936\\t-3.39024\\t-3.31411\\t-3.24276\\t-3.0869\\t-2.77123\\t-2.54456\\t-2.\ 47126\\t-2.54494\\t-2.67059\\t-2.69611\\t-2.62564\\t-2.65601\\t-2.65918\\t-2.\ 47976\\t-2.26277\\t-2.11649\\t-2.04283\\t-1.85433\\t-1.66144\\t-1.48541\\t-1.\ 31067\\t-1.20236\\t-1.03109\\t-0.660778\\t-0.401073\\t-0.32991\\t-0.237236\\t-\ 0.0922869\\t-0.0565898\\n3.99185\\t4.42057\\t4.67577\\t4.88669\\t5.09674\\t5.\ 26117\\t5.50591\\t5.59794\\t5.61496\\t5.69178\\t5.84406\\t6.01644\\t6.13632\\\ t5.92046\\t5.29499\\t4.53125\\t3.97823\\t3.58741\\t3.40775\\t3.61943\\t3.\ 87068\\t4.09583\\t4.29196\\t4.36689\\t4.46849\\t4.76574\\t5.14021\\t5.26989\\\ t5.23566\\t5.31021\\t5.40524\\t5.3435\\t5.34248\\t5.33659\\t5.20906\\t5.1436\\\ 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22389\\t-0.960626\\t-0.578342\\t-0.243936\\t-0.101027\\t-0.01198\\t0.145343\\\ t0.231125\\n3.7821\\t4.29323\\t4.62021\\t4.84897\\t4.9841\\t5.0713\\t5.20253\\\ t5.19445\\t5.19432\\t5.35053\\t5.63892\\t5.91229\\t6.07484\\t5.98464\\t5.\ 47855\\t4.7195\\t4.10079\\t3.73754\\t3.60317\\t3.704\\t3.85864\\t4.00222\\t4.\ 2079\\t4.33335\\t4.52899\\t4.92968\\t5.26098\\t5.36555\\t5.41669\\t5.60939\\\ t5.72835\\t5.60553\\t5.45382\\t5.39416\\t5.28497\\t5.10834\\t5.07908\\t5.\ 04714\\t4.85427\\t4.55438\\t4.13832\\t3.63463\\t3.23381\\t3.02212\\t2.82228\\\ t2.63385\\t2.48237\\t2.43348\\t2.3038\\t2.12382\\t2.10876\\t2.30316\\t2.38445\ \\t2.25058\\t2.05956\\t1.74148\\t1.30253\\t0.909966\\t0.701699\\t0.578347\\t0.\ 366061\\t0.107072\\t-0.2808\\t-0.604684\\t-0.867179\\t-1.10981\\t-1.3942\\t-1.\ 71066\\t-2.20328\\t-2.72557\\t-3.09162\\t-3.37736\\t-3.71469\\t-4.04679\\t-4.\ 2587\\t-4.24228\\t-4.10509\\t-3.9711\\t-3.8368\\t-3.80416\\t-4.01517\\t-4.\ 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00917082\\t-0.0234587\\t-0.0328174\\t0.0879541\\n3.8079\\t4.2869\\t4.51567\\\ t4.67566\\t4.83001\\t4.9206\\t4.82608\\t4.68665\\t4.663\\t4.77955\\t4.9775\\\ t5.17543\\t5.19285\\t5.03486\\t4.81469\\t4.45693\\t4.08482\\t3.87696\\t3.\ 80993\\t3.8442\\t3.99814\\t4.23522\\t4.41982\\t4.49042\\t4.68231\\t5.07936\\\ t5.33749\\t5.38401\\t5.46432\\t5.65532\\t5.83886\\t5.89887\\t5.75896\\t5.\ 59013\\t5.41087\\t5.13247\\t4.94731\\t4.87289\\t4.68112\\t4.33948\\t3.92836\\\ t3.50208\\t3.03889\\t2.50083\\t2.16057\\t2.17422\\t2.2187\\t2.10046\\t2.04027\ \\t2.03995\\t2.10676\\t2.11044\\t1.90782\\t1.74424\\t1.77298\\t1.72066\\t1.\ 3857\\t1.03685\\t0.81193\\t0.548417\\t0.155413\\t-0.316396\\t-0.801288\\t-1.\ 02277\\t-1.16118\\t-1.39971\\t-1.59399\\t-1.75771\\t-2.08413\\t-2.54085\\t-2.\ 90571\\t-3.27578\\t-3.73911\\t-4.13747\\t-4.33948\\t-4.29943\\t-4.1488\\t-3.\ 98303\\t-3.89521\\t-3.85853\\t-3.90864\\t-4.11552\\t-4.23166\\t-4.18194\\t-4.\ 15029\\t-4.14296\\t-4.14961\\t-3.92519\\t-3.45603\\t-3.0095\\t-2.62471\\t-2.\ 19814\\t-1.91109\\t-1.87588\\t-1.89221\\t-2.05488\\t-2.39456\\t-2.55718\\t-2.\ 56364\\t-2.66443\\t-2.83297\\t-2.93873\\t-3.05879\\t-3.0716\\t-2.98067\\t-2.\ 80682\\t-2.67157\\t-2.62514\\t-2.5985\\t-2.48564\\t-2.34723\\t-2.21722\\t-1.\ 98804\\t-1.69464\\t-1.54935\\t-1.56312\\t-1.66907\\t-1.70755\\t-1.62789\\t-1.\ 48261\\t-1.25871\\t-0.95154\\t-0.660888\\t-0.472354\\t-0.274829\\t-0.120188\\\ t-0.107923\\t-0.125652\\t-0.0950683\\n3.57912\\t4.01202\\t4.13401\\t4.32071\\\ t4.6703\\t4.82383\\t4.64652\\t4.49029\\t4.55528\\t4.65331\\t4.74109\\t4.77778\ \\t4.74018\\t4.58649\\t4.45515\\t4.27211\\t4.04564\\t3.89954\\t3.88547\\t3.\ 89989\\t4.02248\\t4.26175\\t4.46213\\t4.56103\\t4.70769\\t4.96996\\t5.14789\\\ t5.23145\\t5.27622\\t5.39046\\t5.58008\\t5.72348\\t5.72641\\t5.64443\\t5.\ 50179\\t5.27391\\t5.031\\t4.87133\\t4.64213\\t4.29074\\t3.89852\\t3.51365\\t3.\ 03129\\t2.5021\\t2.13468\\t2.12608\\t2.13426\\t2.04324\\t2.08458\\t2.32835\\\ t2.42705\\t2.35593\\t2.17468\\t2.0004\\t1.92781\\t1.77422\\t1.45639\\t1.19079\ \\t1.05907\\t0.720238\\t0.133381\\t-0.484355\\t-1.01592\\t-1.30802\\t-1.45288\ \\t-1.47869\\t-1.50597\\t-1.58609\\t-1.90992\\t-2.39598\\t-2.82465\\t-3.22214\ \\t-3.6889\\t-4.07333\\t-4.26353\\t-4.29006\\t-4.21125\\t-3.95406\\t-3.84813\\\ t-3.86367\\t-3.94393\\t-4.08305\\t-4.20588\\t-4.20878\\t-4.13961\\t-4.03069\\\ t-3.88305\\t-3.64244\\t-3.28256\\t-2.94722\\t-2.58279\\t-2.12347\\t-1.79874\\\ t-1.7898\\t-1.8684\\t-2.08873\\t-2.41654\\t-2.54644\\t-2.5739\\t-2.67599\\t-2.\ 86565\\t-2.93114\\t-2.96055\\t-2.92126\\t-2.82016\\t-2.62887\\t-2.44408\\t-2.\ 32222\\t-2.26104\\t-2.206\\t-2.13902\\t-2.06009\\t-1.84109\\t-1.55046\\t-1.\ 43988\\t-1.44431\\t-1.56825\\t-1.58873\\t-1.45898\\t-1.25124\\t-0.969522\\t-0.\ 613357\\t-0.407666\\t-0.382342\\t-0.242336\\t-0.0499035\\t0.0499623\\t0.\ 011533\\t-0.00707536\\n3.13489\\t3.5848\\t3.79737\\t4.04134\\t4.43314\\t4.\ 52929\\t4.37328\\t4.28177\\t4.44057\\t4.54536\\t4.51609\\t4.40257\\t4.31198\\\ t4.23635\\t4.16158\\t4.06913\\t3.94291\\t3.79468\\t3.72798\\t3.7546\\t3.897\\\ t4.10601\\t4.28808\\t4.45119\\t4.65225\\t4.88179\\t5.06688\\t5.11901\\t5.\ 12711\\t5.18145\\t5.30705\\t5.43973\\t5.5331\\t5.52893\\t5.5098\\t5.39186\\t5.\ 13711\\t4.87067\\t4.61772\\t4.309\\t3.95439\\t3.53787\\t3.11273\\t2.68329\\t2.\ 37075\\t2.30439\\t2.20395\\t2.07434\\t2.17617\\t2.50291\\t2.61952\\t2.63277\\\ t2.6341\\t2.50947\\t2.25166\\t1.98799\\t1.64584\\t1.40296\\t1.31353\\t0.\ 887892\\t0.189841\\t-0.480664\\t-1.0397\\t-1.4448\\t-1.63024\\t-1.53691\\t-1.\ 37966\\t-1.47578\\t-1.90138\\t-2.42639\\t-2.8259\\t-3.12536\\t-3.49003\\t-3.\ 85904\\t-4.11982\\t-4.27041\\t-4.22744\\t-3.96228\\t-3.78443\\t-3.80247\\t-3.\ 90855\\t-4.06881\\t-4.20699\\t-4.18169\\t-4.03421\\t-3.79607\\t-3.47185\\t-3.\ 16195\\t-2.97066\\t-2.78308\\t-2.48492\\t-2.06487\\t-1.68281\\t-1.53198\\t-1.\ 55582\\t-1.85897\\t-2.22788\\t-2.43148\\t-2.50346\\t-2.62766\\t-2.77347\\t-2.\ 77358\\t-2.71434\\t-2.61065\\t-2.42797\\t-2.17231\\t-1.94285\\t-1.80026\\t-1.\ 81348\\t-1.87058\\t-1.89452\\t-1.82512\\t-1.64539\\t-1.37231\\t-1.26542\\t-1.\ 33287\\t-1.40934\\t-1.3995\\t-1.23006\\t-0.953126\\t-0.562926\\t-0.072921\\t0.\ 146351\\t0.0545684\\t0.120981\\t0.296404\\t0.390748\\t0.306481\\t0.274044\\n2.\ 85111\\t3.21308\\t3.50158\\t3.80629\\t4.12428\\t4.16871\\t4.08956\\t4.11332\\\ t4.27851\\t4.37844\\t4.3061\\t4.12931\\t4.00469\\t3.91462\\t3.81798\\t3.74191\ \\t3.69279\\t3.58954\\t3.50629\\t3.54656\\t3.71503\\t3.86225\\t3.97638\\t4.\ 10793\\t4.3673\\t4.66038\\t4.90489\\t5.0116\\t5.0623\\t5.11063\\t5.2146\\t5.\ 26128\\t5.24826\\t5.25126\\t5.36882\\t5.41809\\t5.18291\\t4.78639\\t4.53368\\\ t4.35378\\t4.08081\\t3.65456\\t3.20547\\t2.88697\\t2.66164\\t2.54453\\t2.\ 39138\\t2.26414\\t2.37408\\t2.71267\\t2.83154\\t2.87256\\t3.04681\\t3.00329\\\ t2.72145\\t2.38893\\t2.01936\\t1.76903\\t1.62281\\t1.12539\\t0.392394\\t-0.\ 32964\\t-0.861935\\t-1.3107\\t-1.56468\\t-1.45861\\t-1.25644\\t-1.4281\\t-1.\ 9355\\t-2.44587\\t-2.72368\\t-2.88294\\t-3.20326\\t-3.61305\\t-3.87508\\t-4.\ 02194\\t-3.98223\\t-3.76222\\t-3.61235\\t-3.6506\\t-3.73349\\t-3.91677\\t-4.\ 04099\\t-3.96679\\t-3.81481\\t-3.56131\\t-3.1028\\t-2.70619\\t-2.56282\\t-2.\ 45051\\t-2.26002\\t-1.99009\\t-1.63456\\t-1.37332\\t-1.33985\\t-1.56331\\t-1.\ 92863\\t-2.24635\\t-2.38068\\t-2.45814\\t-2.53277\\t-2.43428\\t-2.30039\\t-2.\ 19693\\t-2.00173\\t-1.68285\\t-1.40484\\t-1.32791\\t-1.44675\\t-1.50599\\t-1.\ 48532\\t-1.4566\\t-1.35815\\t-1.12343\\t-0.97905\\t-1.0502\\t-1.13036\\t-1.\ 1284\\t-0.917658\\t-0.624703\\t-0.176608\\t0.411508\\t0.69559\\t0.532217\\t0.\ 465938\\t0.578643\\t0.63093\\t0.545221\\t0.561605\\n2.7215\\t2.98699\\t3.\ 21563\\t3.5215\\t3.85876\\t3.98036\\t3.96988\\t3.97913\\t4.04661\\t4.0992\\t4.\ 04852\\t3.83569\\t3.72608\\t3.73677\\t3.6281\\t3.43636\\t3.37329\\t3.34791\\\ t3.32672\\t3.34603\\t3.45855\\t3.57408\\t3.66931\\t3.79337\\t4.05699\\t4.\ 41969\\t4.75097\\t4.93453\\t5.03922\\t5.10978\\t5.2034\\t5.18882\\t5.20269\\\ t5.21321\\t5.32334\\t5.36942\\t5.14915\\t4.77322\\t4.47101\\t4.33517\\t4.\ 14538\\t3.73217\\t3.27724\\t2.97546\\t2.83268\\t2.81176\\t2.77603\\t2.70795\\\ t2.77275\\t3.00519\\t3.03311\\t3.01403\\t3.2078\\t3.27561\\t3.09471\\t2.80835\ \\t2.49222\\t2.20953\\t1.95755\\t1.3949\\t0.590703\\t-0.17322\\t-0.688086\\t-\ 1.08503\\t-1.3812\\t-1.36153\\t-1.21082\\t-1.32581\\t-1.82457\\t-2.32383\\t-2.\ 51756\\t-2.61869\\t-2.91137\\t-3.31051\\t-3.51582\\t-3.50552\\t-3.43727\\t-3.\ 36268\\t-3.31678\\t-3.37735\\t-3.40742\\t-3.52755\\t-3.61194\\t-3.6309\\t-3.\ 59099\\t-3.37305\\t-2.87695\\t-2.42089\\t-2.22149\\t-2.14195\\t-2.03608\\t-1.\ 86455\\t-1.55149\\t-1.33376\\t-1.31986\\t-1.46472\\t-1.77123\\t-2.11098\\t-2.\ 23578\\t-2.18944\\t-2.18431\\t-2.07312\\t-1.88758\\t-1.83575\\t-1.70032\\t-1.\ 35817\\t-1.08086\\t-1.02356\\t-1.07229\\t-1.10382\\t-1.01745\\t-0.994372\\t-0.\ 948421\\t-0.82648\\t-0.72471\\t-0.83086\\t-0.932281\\t-0.873171\\t-0.629743\\\ t-0.267213\\t0.165888\\t0.634533\\t0.901296\\t0.753131\\t0.593029\\t0.630446\\\ t0.705216\\t0.680851\\t0.774819\\n2.5348\\t2.81992\\t3.03379\\t3.34353\\t3.\ 68072\\t3.82654\\t3.80724\\t3.76414\\t3.74323\\t3.74685\\t3.64201\\t3.38005\\\ t3.31074\\t3.45817\\t3.50279\\t3.37042\\t3.26593\\t3.18634\\t3.13386\\t3.\ 09933\\t3.21214\\t3.37078\\t3.49197\\t3.68639\\t4.06586\\t4.51153\\t4.83805\\\ t5.06532\\t5.22007\\t5.25102\\t5.26429\\t5.31588\\t5.39981\\t5.44494\\t5.\ 43857\\t5.32119\\t5.12142\\t4.84549\\t4.49165\\t4.23057\\t4.00357\\t3.6416\\\ t3.25988\\t3.0691\\t3.01107\\t3.05105\\t3.11194\\t3.12596\\t3.16032\\t3.24216\ 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21462\\t4.05056\\t4.08374\\t4.202\\t4.28677\\t4.22399\\t3.92025\\t3.43595\\t2.\ 84786\\t2.42572\\t2.22075\\t1.90318\\t1.30702\\t0.737143\\t0.348721\\t-0.\ 0618767\\t-0.334064\\t-0.321256\\t-0.174441\\t-0.110402\\t-0.0369623\\t0.\ 00942319\\t-0.189362\\t-0.384003\\t-0.493856\\t-0.604309\\t-0.73505\\t-0.\ 759014\\t-0.711134\\t-0.716841\\t-0.95301\\t-1.31212\\t-1.60373\\t-1.75053\\t-\ 1.87631\\t-2.0949\\t-2.32975\\t-2.55052\\t-2.72088\\t-2.59211\\t-2.07322\\t-1.\ 55736\\t-1.23856\\t-1.02212\\t-0.897764\\t-0.880064\\t-1.06572\\t-1.30764\\t-\ 1.30471\\t-1.04404\\t-0.850025\\t-0.754897\\t-0.572634\\t-0.338394\\t-0.\ 229957\\t-0.195728\\t-0.0567768\\t0.0944281\\t0.0558307\\t-0.121367\\t-0.\ 0931725\\t0.101957\\t0.178871\\t0.174644\\t0.167045\\t0.157758\\t0.127023\\t0.\ 0893116\\t0.142246\\t0.381041\\t0.571608\\t0.719818\\t0.934327\\t1.09533\\t1.\ 18538\\t1.42224\\t1.47899\\t1.3364\\t1.35544\\t1.56048\\n2.23722\\t2.51912\\\ 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t4.81873\\t4.72651\\t4.51594\\t4.52261\\t4.65902\\t4.73749\\t4.69932\\t4.\ 55794\\t4.21405\\t3.74644\\t3.22018\\t2.79386\\t2.46869\\t2.00849\\t1.59284\\\ t1.38906\\t1.14374\\t0.917926\\t0.916112\\t1.05811\\t1.15105\\t1.14091\\t1.\ 08652\\t0.933894\\t0.743924\\t0.615277\\t0.535074\\t0.456349\\t0.443717\\t0.\ 465899\\t0.35278\\t0.178488\\t-0.000691262\\t-0.330386\\t-0.85144\\t-1.31554\\\ t-1.57816\\t-1.75948\\t-1.94406\\t-2.10521\\t-2.03617\\t-1.71904\\t-1.17472\\\ t-0.61637\\t-0.392699\\t-0.579411\\t-0.754908\\t-0.753882\\t-0.609517\\t-0.\ 509455\\t-0.435109\\t-0.350486\\t-0.372399\\t-0.487112\\t-0.548629\\t-0.\ 516028\\t-0.343507\\t-0.163877\\t-0.11237\\t-0.157895\\t-0.172086\\t0.0765849\ \\t0.375638\\t0.437403\\t0.433462\\t0.454014\\t0.336535\\t0.234057\\t0.20675\\\ t0.242453\\t0.269037\\t0.399849\\t0.737348\\t1.15031\\t1.32943\\t1.5126\\t1.\ 81096\\t2.0102\\t1.96924\\t1.89354\\t1.87341\\n2.0569\\t2.26819\\t2.4731\\t2.\ 4859\\t2.26333\\t1.95284\\t1.74016\\t1.79936\\t1.88858\\t1.77651\\t1.53691\\\ t1.47405\\t1.72413\\t2.06023\\t2.21462\\t2.30094\\t2.39686\\t2.37636\\t2.\ 38464\\t2.57008\\t2.69969\\t2.67133\\t2.6628\\t2.97504\\t3.37743\\t3.70131\\\ t4.01302\\t4.37252\\t4.64455\\t4.66977\\t4.46546\\t4.29221\\t4.35933\\t4.4487\ \\t4.41008\\t4.4055\\t4.4898\\t4.62202\\t4.64443\\t4.58453\\t4.52045\\t4.\ 52701\\t4.51153\\t4.60854\\t4.77626\\t4.80895\\t4.71612\\t4.71616\\t4.87937\\\ t4.9504\\t4.8287\\t4.82452\\t4.96349\\t5.09157\\t5.20431\\t5.10087\\t4.71625\\\ t4.20163\\t3.57572\\t3.01232\\t2.69204\\t2.39301\\t2.11487\\t1.93261\\t1.\ 66259\\t1.45856\\t1.49531\\t1.57646\\t1.58875\\t1.59612\\t1.50715\\t1.3173\\\ t1.15718\\t1.0918\\t0.994358\\t0.908277\\t0.927962\\t0.952975\\t0.786361\\t0.\ 65338\\t0.54366\\t0.166668\\t-0.472923\\t-1.00327\\t-1.20443\\t-1.25802\\t-1.\ 38221\\t-1.51724\\t-1.43398\\t-1.19141\\t-0.807548\\t-0.40263\\t-0.253584\\t-\ 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t1.38633\\t1.24759\\t1.22656\\t1.27555\\t1.27454\\t1.2882\\t1.43954\\t1.7592\\\ t2.03118\\t2.17012\\t2.31787\\t2.41805\\t2.48688\\t2.622\\t2.74127\\t2.73607\\\ t2.80839\\t3.13268\\t3.56128\\t3.85622\\t3.99573\\t4.06761\\t4.07674\\t3.9943\ \\t4.00894\\t4.03737\\t4.13561\\t4.25794\\t4.33873\\t4.30318\\t4.22274\\t4.\ 22237\\t4.36529\\t4.48673\\t4.58637\\t4.73301\\t4.8852\\t4.9217\\t4.93957\\t4.\ 99926\\t5.015\\t4.96382\\t4.97609\\t5.05776\\t5.03346\\t5.06083\\t5.3037\\t5.\ 70395\\t6.01707\\t5.95863\\t5.69226\\t5.36266\\t4.81287\\t4.0802\\t3.65987\\\ t3.4001\\t3.06484\\t2.66309\\t2.40096\\t2.39115\\t2.43881\\t2.40318\\t2.30368\ \\t2.19257\\t2.10809\\t2.11231\\t2.11491\\t2.11001\\t2.04577\\t1.91513\\t1.\ 8935\\t1.92023\\t1.84983\\t1.57491\\t1.17507\\t0.736568\\t0.258837\\t-0.\ 248555\\t-0.549201\\t-0.556787\\t-0.585647\\t-0.813778\\t-0.960145\\t-0.\ 961912\\t-0.91746\\t-0.706152\\t-0.534594\\t-0.551721\\t-0.700908\\t-0.673405\ 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t-0.414419\\t-0.356906\\t-0.155807\\t0.0790336\\t0.204903\\t0.172456\\t0.\ 210993\\t0.437555\\t0.627484\\t0.607453\\t0.554087\\t0.519937\\t0.593618\\t0.\ 750216\\t0.970291\\t1.01916\\t0.792928\\t0.57788\\t0.555438\\t0.549839\\t0.\ 423223\\t0.253792\\t0.205735\\t0.285852\\t0.42569\\t0.687635\\t0.969718\\t1.\ 29098\\t1.71403\\t2.04049\\t2.1123\\n0.0822265\\t0.0274832\\t-0.145464\\t-0.\ 383412\\t-0.63806\\t-0.721267\\t-0.712957\\t-0.551088\\t-0.27258\\t-0.109824\\\ t-0.141876\\t-0.0654887\\t0.276438\\t0.641174\\t0.952202\\t1.28854\\t1.47877\\\ t1.63044\\t1.83445\\t2.14022\\t2.73523\\t3.44135\\t3.76822\\t3.82883\\t3.\ 98945\\t4.19147\\t4.31635\\t4.36597\\t4.23256\\t3.93713\\t3.68903\\t3.51681\\\ t3.40349\\t3.40452\\t3.43199\\t3.44058\\t3.42957\\t3.47326\\t3.60337\\t3.\ 67232\\t3.75588\\t4.0208\\t4.29955\\t4.48854\\t4.70079\\t4.8829\\t4.93774\\t5.\ 02627\\t5.20726\\t5.47432\\t5.64222\\t5.64177\\t5.79822\\t6.20966\\t6.45651\\\ t6.36919\\t6.16715\\t6.00915\\t5.90813\\t5.69268\\t5.38094\\t5.19663\\t5.\ 09571\\t4.91032\\t4.69992\\t4.57459\\t4.5345\\t4.39939\\t4.25908\\t4.27972\\\ t4.20043\\t3.98057\\t3.68213\\t3.41104\\t3.11874\\t2.78814\\t2.49369\\t2.\ 21721\\t1.95583\\t1.60638\\t1.2446\\t0.998892\\t0.753699\\t0.412209\\t0.\ 202909\\t-0.00477492\\t-0.403686\\t-0.714391\\t-0.694706\\t-0.601539\\t-0.\ 554636\\t-0.399351\\t-0.131091\\t0.0119958\\t0.00447163\\t-0.141931\\t-0.\ 238594\\t-0.188014\\t-0.0858701\\t-0.0467558\\t0.156334\\t0.363585\\t0.389158\ \\t0.207463\\t0.172438\\t0.373254\\t0.560154\\t0.599332\\t0.62609\\t0.642726\\\ t0.713274\\t0.822988\\t0.871308\\t0.713903\\t0.471264\\t0.391821\\t0.47205\\\ t0.561287\\t0.499695\\t0.435105\\t0.470484\\t0.527074\\t0.594799\\t0.746589\\\ t0.960024\\t1.17216\\t1.52839\\t1.95649\\t2.26434\\n-0.253744\\t-0.281073\\t-\ 0.388499\\t-0.530774\\t-0.711177\\t-0.87512\\t-0.971257\\t-0.919635\\t-0.\ 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t-0.383783\\t-0.406985\\t-0.359949\\t-0.31842\\t-0.440681\\t-0.562618\\t-0.\ 520154\\t-0.403747\\t-0.36336\\t-0.382004\\t-0.323197\\t-0.189488\\t-0.\ 0484988\\t0.0954892\\t0.160082\\t0.10786\\t0.158669\\t0.586825\\t1.09468\\t1.\ 44588\\t1.7171\\t1.8404\\t1.94718\\t2.19787\\t2.51522\\t2.93303\\t3.21828\\t3.\ 2334\\t3.10871\\t3.08845\\t3.04195\\n-0.854974\\t-0.678189\\t-0.482024\\t-0.\ 252181\\t-0.0783685\\t0.123243\\t0.348216\\t0.509797\\t0.673093\\t0.823081\\\ t0.949873\\t1.12823\\t1.28066\\t1.42672\\t1.60326\\t1.63115\\t1.57025\\t1.\ 66624\\t1.88346\\t2.0603\\t2.22787\\t2.36707\\t2.46265\\t2.55065\\t2.78027\\\ t3.24737\\t3.83871\\t4.21327\\t4.28352\\t4.21892\\t4.16528\\t4.09004\\t3.\ 97602\\t4.01883\\t4.28299\\t4.60383\\t4.6892\\t4.63227\\t4.61976\\t4.57919\\\ t4.55531\\t4.66355\\t4.82874\\t4.85651\\t4.8619\\t4.96272\\t5.0243\\t4.84202\\\ t4.71178\\t4.84774\\t5.08286\\t5.20146\\t5.26961\\t5.16248\\t5.06035\\t5.\ 11899\\t5.28334\\t5.47616\\t5.69558\\t5.87159\\t5.89794\\t5.90006\\t5.96738\\\ t5.99211\\t5.87987\\t5.81826\\t5.66515\\t5.25494\\t4.83978\\t4.61574\\t4.\ 55204\\t4.45843\\t4.30777\\t4.10461\\t3.84344\\t3.51226\\t3.17022\\t2.81204\\\ t2.42614\\t1.86539\\t1.40312\\t1.14981\\t0.782129\\t0.194807\\t-0.101085\\t-0.\ 152717\\t-0.27842\\t-0.333415\\t-0.214345\\t-0.133261\\t-0.0166705\\t0.206948\ \\t0.304445\\t0.143728\\t-0.014461\\t-0.107961\\t-0.24844\\t-0.44629\\t-0.\ 599118\\t-0.533469\\t-0.465493\\t-0.421058\\t-0.399958\\t-0.400603\\t-0.\ 386337\\t-0.385761\\t-0.385537\\t-0.354968\\t-0.331247\\t-0.378236\\t-0.31784\ \\t-0.122809\\t0.0377597\\t0.0436492\\t0.172362\\t0.580472\\t0.984826\\t1.\ 29872\\t1.51272\\t1.65979\\t1.81657\\t2.1468\\t2.53671\\t2.97316\\t3.24156\\\ t3.15239\\t3.03773\\t3.07972\\t3.09941\\n-0.817664\\t-0.634794\\t-0.49873\\t-\ 0.312202\\t-0.00602621\\t0.334587\\t0.565316\\t0.848597\\t1.24061\\t1.47222\\\ t1.57555\\t1.62309\\t1.583\\t1.58937\\t1.69079\\t1.69304\\t1.67069\\t1.81227\\\ t2.03773\\t2.26905\\t2.41086\\t2.46915\\t2.53541\\t2.70255\\t3.05606\\t3.4873\ \\t3.93378\\t4.26451\\t4.45817\\t4.60945\\t4.648\\t4.53237\\t4.37551\\t4.\ 35083\\t4.52907\\t4.8779\\t5.02299\\t4.97124\\t4.9202\\t4.85804\\t4.76906\\t4.\ 83386\\t4.94059\\t4.9619\\t5.02607\\t5.13692\\t5.01262\\t4.69301\\t4.54117\\\ t4.76723\\t5.02156\\t5.1986\\t5.25838\\t5.15875\\t4.96934\\t4.94493\\t5.10774\ \\t5.45364\\t5.79203\\t5.96489\\t5.9666\\t6.03367\\t6.14025\\t6.10803\\t5.\ 87526\\t5.74311\\t5.58396\\t5.20106\\t4.77671\\t4.55318\\t4.5264\\t4.47701\\\ t4.24106\\t3.83643\\t3.40002\\t3.04401\\t2.80863\\t2.58218\\t2.23176\\t1.\ 66259\\t1.15916\\t0.906491\\t0.673808\\t0.286942\\t0.0126909\\t-0.155285\\t-0.\ 271997\\t-0.284616\\t-0.159613\\t-0.0419978\\t0.022419\\t0.138534\\t0.252378\\\ t0.236083\\t0.140317\\t-0.0511709\\t-0.367315\\t-0.59507\\t-0.68053\\t-0.\ 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t4.05961\\t4.11535\\t4.31706\\t4.35298\\t4.37668\\t4.44551\\t4.46418\\t4.\ 42765\\t4.2449\\t3.98168\\t3.91467\\t4.09547\\t4.20245\\t4.27792\\t4.37074\\\ t4.23957\\t3.99908\\t3.9832\\t4.13647\\t4.25297\\t4.32492\\t4.38086\\t4.4157\\\ t4.42372\\t4.45193\\t4.37268\\t4.06244\\t3.77272\\t3.68771\\t3.57756\\t3.3911\ \\t3.20063\\t2.94172\\t2.69878\\t2.62348\\t2.6449\\t2.71746\\t2.57218\\t2.\ 08618\\t1.60244\\t1.21795\\t0.805617\\t0.407737\\t0.212306\\t0.0644863\\t-0.\ 186061\\t-0.370388\\t-0.389761\\t-0.387652\\t-0.389146\\t-0.453881\\t-0.\ 678843\\t-0.768002\\t-0.617595\\t-0.462699\\t-0.37911\\t-0.352704\\t-0.461741\ \\t-0.45643\\t-0.248876\\t0.0507179\\t0.128879\\t0.0706357\\t0.077228\\t0.\ 300235\\t0.535368\\t0.573972\\t0.500552\\t0.451487\\t0.362791\\t0.280835\\t0.\ 369076\\t0.460385\\t0.496608\\t0.6009\\t0.762802\\t0.9582\\t1.21193\\t1.44212\ \\t1.57331\\t1.67796\\t1.76039\\t1.95941\\t2.31557\\t2.65415\\t2.68784\\t2.\ 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t4.7399\\t4.86995\\t4.93174\\t4.74493\\t4.62783\\t4.66562\\t4.7145\\t4.76043\\\ t4.83031\\t4.82621\\t4.85277\\t4.79246\\t4.64572\\t4.50369\\t4.49141\\t4.\ 54718\\t4.48192\\t4.34645\\t4.31466\\t4.39349\\t4.29688\\t3.94927\\t3.53385\\\ t3.2965\\t3.17612\\t3.15611\\t3.24148\\t3.30647\\t3.35318\\t3.56053\\t3.78748\ \\t4.01327\\t4.14895\\t3.9787\\t3.88288\\t4.03481\\t4.262\\t4.40873\\t4.6843\\\ t5.01736\\t5.1379\\t5.1399\\t5.06813\\t4.93614\\t4.5689\\t4.07146\\t3.6093\\\ t3.2736\\t2.99821\\t2.76941\\t2.52677\\t2.1996\\t1.81241\\t1.38176\\t1.14108\\\ t1.11528\\t1.01549\\t0.933626\\t0.922895\\t0.718562\\t0.366485\\t0.21857\\t0.\ 134037\\t-0.0540032\\t-0.344184\\t-0.612945\\t-0.918607\\t-1.33108\\t-1.72045\ \\t-1.97895\\t-2.10472\\t-2.05021\\t-1.95817\\t-2.009\\t-2.23267\\t-2.23278\\\ t-2.01022\\t-1.99324\\t-2.12194\\t-2.05033\\t-1.84352\\t-1.5813\\t-1.26644\\t-\ 1.10322\\t-1.11252\\t-1.15265\\t-1.01299\\t-0.70645\\t-0.422759\\t-0.381255\\\ 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t1.3229\\t1.12184\\t1.06574\\t0.964639\\t0.882063\\t0.865139\\t0.66473\\t0.\ 327906\\t0.136427\\t-0.0703198\\t-0.498033\\t-0.877989\\t-1.04575\\t-1.29664\\\ t-1.75256\\t-2.12237\\t-2.32294\\t-2.43899\\t-2.43414\\t-2.3545\\t-2.33644\\t-\ 2.46176\\t-2.42136\\t-2.28742\\t-2.28196\\t-2.2642\\t-2.16662\\t-2.01048\\t-1.\ 7774\\t-1.49195\\t-1.30998\\t-1.24878\\t-1.28685\\t-1.30393\\t-1.11961\\t-0.\ 787194\\t-0.652001\\t-0.657963\\t-0.558132\\t-0.270067\\t0.0912733\\t0.246253\ \\t0.317036\\t0.421892\\t0.549637\\t0.661099\\t0.782156\\t0.966087\\t1.23787\\\ t1.63993\\t1.96456\\t2.11933\\t2.15896\\t1.96757\\t1.61195\\t1.37158\\t1.\ 31799\\t1.27103\\t1.19182\\t1.228\\t1.18454\\t1.02705\\t1.13117\\n1.56005\\t1.\ 93492\\t2.37543\\t2.6516\\t2.72973\\t2.8019\\t3.01883\\t3.36137\\t3.6558\\t3.\ 85685\\t3.93155\\t4.00843\\t4.32698\\t4.73039\\t5.04549\\t5.11822\\t4.89494\\\ t4.74428\\t4.89713\\t5.04576\\t4.98558\\t4.83691\\t4.67054\\t4.5087\\t4.31301\ 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55942\\t5.64053\\t5.63102\\t5.4962\\t5.31753\\t5.05952\\t4.5826\\t4.05934\\t3.\ 65972\\t3.28808\\t2.88772\\t2.54661\\t2.38779\\t2.32097\\t2.08429\\t1.64797\\\ t1.13418\\t0.688724\\t0.453356\\t0.360116\\t0.22534\\t-0.0426684\\t-0.347153\\\ t-0.553654\\t-0.760806\\t-1.08819\\t-1.45089\\t-1.85397\\t-2.33369\\t-2.88006\ \\t-3.46364\\t-3.79157\\t-3.84848\\t-3.84858\\t-3.91313\\t-3.97094\\t-3.95457\ \\t-3.84184\\t-3.66784\\t-3.52952\\t-3.37078\\t-3.24024\\t-3.15797\\t-3.06093\ \\t-2.86674\\t-2.6294\\t-2.51714\\t-2.61269\\t-2.49782\\t-1.99992\\t-1.54814\\\ t-1.33979\\t-1.25216\\t-1.28563\\t-1.21979\\t-1.17204\\t-1.33526\\t-1.54847\\\ t-1.65192\\t-1.52261\\t-1.3233\\t-1.17858\\t-0.92666\\t-0.521507\\t-0.19065\\\ t0.00405725\\t0.127016\\t0.219049\\t0.443773\\t0.504992\\t0.337734\\t0.214355\ \\t0.270786\\t0.295461\\t0.211804\\t0.219434\\t0.403928\\n1.32453\\t1.61963\\\ t1.84332\\t1.98351\\t2.21327\\t2.44313\\t2.69739\\t3.01969\\t3.21457\\t3.\ 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t-0.788638\\t-0.863839\\t-0.963319\\t-1.05882\\t-0.987483\\t-0.821926\\t-0.\ 738114\\t-0.623524\\t-0.424065\\t-0.285967\\t-0.199499\\t0.0346228\\t0.333725\ \\t0.515587\\t0.50952\\t0.458246\\t0.566345\\t0.779482\\t0.856158\\t0.930525\\\ t1.00658\\t1.0723\\t1.23309\\n1.64412\\t1.69715\\t1.77078\\t1.97137\\t2.25132\ \\t2.44242\\t2.50207\\t2.61487\\t2.87055\\t3.02488\\t3.12894\\t3.38515\\t3.\ 7589\\t4.10624\\t4.37008\\t4.47291\\t4.342\\t3.99243\\t3.74021\\t3.64765\\t3.\ 69868\\t3.77926\\t3.83861\\t3.98664\\t4.11429\\t4.04867\\t4.04281\\t4.06797\\\ t3.97453\\t3.936\\t4.10056\\t4.2772\\t4.40091\\t4.46597\\t4.31318\\t3.99222\\\ t4.00988\\t4.2306\\t4.24516\\t4.25974\\t4.43263\\t4.45921\\t4.33212\\t4.39872\ \\t4.55896\\t4.61904\\t4.68371\\t4.82629\\t4.93805\\t4.97793\\t4.9151\\t4.\ 92889\\t5.0933\\t5.26886\\t5.28376\\t5.15516\\t4.93112\\t4.64677\\t4.34567\\\ t3.98793\\t3.53916\\t3.0307\\t2.57606\\t2.18743\\t1.81582\\t1.42456\\t1.04309\ 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t0.426774\\t0.727758\\t1.11612\\t1.4534\\t1.7392\\t2.12114\\t2.58903\\t3.\ 02515\\t3.35392\\t3.79221\\t4.44768\\t5.1004\\t5.73876\\t6.26489\\t6.57598\\\ t6.66296\\t6.62775\\t6.49865\\t6.34734\\t6.15366\\t5.87088\\t5.78047\\t5.\ 81882\\t5.66546\\t5.37934\\t5.17111\\t5.04382\\t5.09243\\t5.35626\\t5.66399\\\ t5.99245\\t6.35864\\t6.60197\\t6.55081\\t6.25661\\t5.77976\\t5.36796\\t5.\ 07211\\t4.83843\\t4.64234\\t4.52147\\t4.39983\\t4.35158\\t4.37104\\t4.44617\\\ t4.46057\\t4.411\\t4.29813\\t4.08299\\t3.8626\\t3.75952\\t3.69265\\t3.58382\\\ t3.57138\\t3.48256\\t3.04674\\t2.5533\\t2.29512\\t2.16699\\t2.1285\\t2.04242\\\ t1.82864\\t1.60905\\t1.41845\\t1.32296\\t1.25148\\t1.12464\\t0.827072\\t0.\ 372134\\t-0.0438956\\t-0.385815\\t-0.822899\\t-1.16908\\t-1.23861\\t-1.36124\\\ t-1.61339\\t-1.78763\\t-1.8257\\t-1.82997\\t-1.94986\\t-2.22105\\t-2.42052\\t-\ 2.49845\\t-2.51651\\t-2.37366\\t-2.2062\\t-2.29772\\t-2.55373\\t-2.68644\\t-2.\ 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t1.20798\\t1.24016\\t1.17093\\t1.15253\\t1.25416\\t1.28221\\t1.21528\\t1.\ 33336\\t1.5569\\t1.63401\\t1.59929\\t1.59531\\t1.57782\\t1.64254\\t1.78318\\\ t1.85874\\t1.81315\\t1.95983\\t2.33169\\t2.68844\\t2.77796\\t2.68441\\t2.\ 56489\\t2.4954\\t2.41874\\t2.43752\\t2.64137\\t2.89584\\t3.13968\\t3.22035\\\ t3.11236\\t2.89584\\t2.5801\\t2.24767\\t1.93945\\t1.62745\\t1.3177\\t1.13506\\\ t1.12263\\t1.1436\\t0.95465\\t0.747538\\t0.58268\\t0.290215\\t-0.119757\\t-0.\ 538591\\t-0.858967\\t-1.04662\\t-1.19073\\t-1.5041\\t-1.81658\\t-1.95906\\t-1.\ 99922\\t-2.07135\\t-2.07021\\t-1.98721\\t-1.90374\\t-2.03144\\t-2.31809\\t-2.\ 39845\\t-2.30251\\t-2.21115\\t-2.21083\\t-2.01597\\t-1.66474\\t-1.45751\\t-1.\ 33044\\t-1.09198\\t-0.808905\\t-0.574308\\t-0.44001\\t-0.335672\\t-0.313578\\\ t-0.19536\\t0.191192\\t0.515022\\t0.709704\\t0.791051\\t0.820782\\t1.01605\\\ t1.29295\\t1.38646\\t1.37566\\t1.50746\\t1.76093\\t1.93078\\n-2.58969\\t-2.\ 6116\\t-2.50616\\t-2.33021\\t-2.2259\\t-2.15862\\t-2.11368\\t-2.06758\\t-1.\ 93397\\t-1.7092\\t-1.49382\\t-1.29916\\t-1.22024\\t-1.34135\\t-1.43453\\t-1.\ 23104\\t-0.810678\\t-0.41138\\t0.00768603\\t0.302361\\t0.439214\\t0.509522\\\ t0.592182\\t0.717312\\t0.848089\\t0.938055\\t0.841463\\t0.707634\\t0.782061\\\ t0.985413\\t1.28898\\t1.70935\\t1.9532\\t1.93206\\t1.81709\\t1.79412\\t1.\ 64918\\t1.36214\\t1.12189\\t0.978811\\t0.783652\\t0.667599\\t0.754608\\t0.\ 989639\\t1.1\\t1.16109\\t1.22185\\t1.25697\\t1.19912\\t1.19353\\t1.37432\\t1.\ 58828\\t1.59563\\t1.45272\\t1.41625\\t1.39972\\t1.44121\\t1.50168\\t1.51797\\\ t1.57249\\t1.8662\\t2.24506\\t2.52602\\t2.5886\\t2.53153\\t2.43685\\t2.30656\\\ t2.22976\\t2.17666\\t2.22982\\t2.41195\\t2.70132\\t2.86377\\t2.8278\\t2.64503\ \\t2.30045\\t1.94307\\t1.6898\\t1.47801\\t1.27142\\t1.06798\\t1.04435\\t0.\ 991302\\t0.73268\\t0.456754\\t0.30675\\t0.10855\\t-0.212065\\t-0.601669\\t-0.\ 875826\\t-1.02503\\t-1.16907\\t-1.40339\\t-1.66491\\t-1.90032\\t-2.10293\\t-2.\ 33829\\t-2.48214\\t-2.43248\\t-2.28252\\t-2.31865\\t-2.52532\\t-2.60239\\t-2.\ 52622\\t-2.39357\\t-2.25284\\t-2.00449\\t-1.66257\\t-1.41335\\t-1.31398\\t-1.\ 12334\\t-0.793176\\t-0.490276\\t-0.350762\\t-0.328235\\t-0.368462\\t-0.285662\ \\t-0.0388195\\t0.217466\\t0.451697\\t0.605897\\t0.743133\\t1.06152\\t1.35105\ \\t1.331\\t1.22573\\t1.30943\\t1.52163\\t1.63642\\n-2.9434\\t-2.90152\\t-2.\ 70012\\t-2.45048\\t-2.31849\\t-2.28785\\t-2.24558\\t-2.23501\\t-2.16553\\t-1.\ 97998\\t-1.70321\\t-1.41471\\t-1.2916\\t-1.34052\\t-1.38101\\t-1.21007\\t-0.\ 833367\\t-0.471318\\t-0.11935\\t0.154526\\t0.304959\\t0.335428\\t0.432704\\t0.\ 665393\\t0.995042\\t1.16978\\t1.08281\\t0.876377\\t0.781699\\t0.867159\\t1.\ 16775\\t1.63559\\t1.9629\\t2.00289\\t1.92005\\t1.8124\\t1.63606\\t1.36688\\t1.\ 08344\\t0.839659\\t0.624311\\t0.539923\\t0.670431\\t0.901702\\t1.03768\\t1.\ 21054\\t1.37179\\t1.32454\\t1.25074\\t1.33237\\t1.46933\\t1.54416\\t1.42991\\\ t1.28241\\t1.23164\\t1.31086\\t1.32143\\t1.23748\\t1.18228\\t1.31024\\t1.\ 59606\\t1.86673\\t2.06511\\t2.26041\\t2.38801\\t2.34451\\t2.21986\\t2.18201\\\ t2.04442\\t1.87381\\t1.90734\\t2.22362\\t2.4346\\t2.43881\\t2.27293\\t2.00401\ \\t1.71119\\t1.54033\\t1.37874\\t1.17817\\t0.935341\\t0.87006\\t0.800214\\t0.\ 564823\\t0.226256\\t0.0545466\\t-0.0555302\\t-0.276224\\t-0.599637\\t-0.\ 794056\\t-0.872623\\t-1.05737\\t-1.33619\\t-1.62338\\t-1.94854\\t-2.30594\\t-\ 2.59137\\t-2.82626\\t-2.8351\\t-2.68756\\t-2.7235\\t-2.92892\\t-3.00597\\t-2.\ 92524\\t-2.73288\\t-2.52769\\t-2.34387\\t-2.04311\\t-1.65073\\t-1.40251\\t-1.\ 21643\\t-0.937244\\t-0.657528\\t-0.546503\\t-0.481018\\t-0.45558\\t-0.403953\\\ t-0.281751\\t-0.123865\\t0.0619433\\t0.313866\\t0.630431\\t1.06752\\t1.35828\\\ t1.24652\\t1.05294\\t1.07015\\t1.25843\\t1.4339\\n-3.05388\\t-2.93525\\t-2.\ 67598\\t-2.39494\\t-2.30089\\t-2.39803\\t-2.45689\\t-2.3819\\t-2.24324\\t-2.\ 09761\\t-1.86024\\t-1.5984\\t-1.43008\\t-1.32272\\t-1.24031\\t-1.08451\\t-0.\ 737063\\t-0.347655\\t-0.0625429\\t0.0707745\\t0.142024\\t0.299446\\t0.497674\\\ t0.768027\\t1.13102\\t1.36188\\t1.33312\\t1.14216\\t0.912564\\t0.808834\\t1.\ 05179\\t1.50438\\t1.83028\\t1.88596\\t1.87135\\t1.7289\\t1.4779\\t1.21157\\t1.\ 02071\\t0.776619\\t0.611982\\t0.589114\\t0.750111\\t0.971998\\t1.10683\\t1.\ 26255\\t1.44447\\t1.35003\\t1.2902\\t1.42451\\t1.48356\\t1.34457\\t1.19575\\\ t1.12641\\t1.09857\\t1.16464\\t1.1006\\t0.932522\\t0.777263\\t0.830133\\t1.\ 00134\\t1.23226\\t1.46834\\t1.73282\\t1.97049\\t2.04451\\t2.0902\\t2.10522\\\ t1.96771\\t1.64369\\t1.48536\\t1.64573\\t1.79328\\t1.79335\\t1.71005\\t1.\ 59891\\t1.48016\\t1.41867\\t1.25606\\t0.986527\\t0.704817\\t0.522846\\t0.\ 412165\\t0.202976\\t-0.0624093\\t-0.176332\\t-0.203871\\t-0.338703\\t-0.\ 623567\\t-0.73123\\t-0.706413\\t-0.888944\\t-1.27953\\t-1.67924\\t-2.08793\\t-\ 2.51299\\t-2.80703\\t-3.00356\\t-3.01796\\t-3.01437\\t-3.14394\\t-3.32789\\t-\ 3.37924\\t-3.33854\\t-3.11664\\t-2.90973\\t-2.80678\\t-2.53114\\t-2.03867\\t-\ 1.64772\\t-1.39947\\t-1.16681\\t-0.973308\\t-0.831636\\t-0.691374\\t-0.607305\ \\t-0.579525\\t-0.509693\\t-0.438472\\t-0.267193\\t0.0851509\\t0.513782\\t0.\ 96443\\t1.23819\\t1.13833\\t0.854807\\t0.827393\\t0.983873\\t1.22296\\n-2.\ 99216\\t-2.83386\\t-2.59783\\t-2.37923\\t-2.36072\\t-2.55427\\t-2.63854\\t-2.\ 44952\\t-2.15678\\t-2.00474\\t-1.9062\\t-1.75441\\t-1.60221\\t-1.40497\\t-1.\ 17172\\t-0.986436\\t-0.677083\\t-0.217101\\t0.081661\\t0.0945838\\t0.149686\\\ t0.464014\\t0.748042\\t0.963101\\t1.18474\\t1.37476\\t1.3908\\t1.27681\\t1.\ 01828\\t0.814616\\t0.981928\\t1.3613\\t1.62636\\t1.68697\\t1.70924\\t1.603\\\ t1.35804\\t1.13353\\t1.01297\\t0.848384\\t0.742625\\t0.737801\\t0.851906\\t0.\ 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724802\\t0.979364\\n-2.83913\\t-2.7214\\t-2.56979\\t-2.47955\\t-2.51211\\t-2.\ 68622\\t-2.72311\\t-2.4625\\t-2.12888\\t-1.9618\\t-1.94219\\t-1.86035\\t-1.\ 68672\\t-1.39936\\t-1.07291\\t-0.84351\\t-0.565724\\t-0.144534\\t0.148611\\t0.\ 208584\\t0.328836\\t0.65253\\t0.902508\\t1.0324\\t1.17148\\t1.25136\\t1.26833\ \\t1.22977\\t1.05083\\t0.911841\\t1.03648\\t1.30766\\t1.49462\\t1.57951\\t1.\ 66223\\t1.6168\\t1.43662\\t1.25879\\t1.21178\\t1.07841\\t0.835537\\t0.704938\\\ t0.69909\\t0.790805\\t1.00652\\t1.31256\\t1.50378\\t1.50936\\t1.54751\\t1.\ 62189\\t1.65032\\t1.47387\\t1.27957\\t1.15658\\t1.00288\\t0.809288\\t0.590199\ \\t0.299614\\t0.0957451\\t0.0690169\\t0.184781\\t0.347406\\t0.511048\\t0.\ 67504\\t0.86444\\t1.06708\\t1.21769\\t1.26589\\t1.18948\\t1.05979\\t0.985499\\\ t1.07697\\t1.18668\\t1.01934\\t0.674628\\t0.422772\\t0.535705\\t0.661295\\t0.\ 484808\\t0.191781\\t-0.0121891\\t-0.190384\\t-0.214274\\t-0.203854\\t-0.\ 348139\\t-0.442006\\t-0.436873\\t-0.596485\\t-0.827422\\t-0.91409\\t-0.90911\\\ t-1.12914\\t-1.59547\\t-2.06422\\t-2.48912\\t-2.87057\\t-3.04939\\t-3.15554\\\ t-3.35285\\t-3.64093\\t-3.9245\\t-4.09598\\t-4.15831\\t-4.04596\\t-3.73171\\t-\ 3.38664\\t-3.13744\\t-2.79001\\t-2.30433\\t-1.78485\\t-1.40509\\t-1.21952\\t-\ 1.13783\\t-1.0613\\t-0.894\\t-0.758083\\t-0.687864\\t-0.721977\\t-0.723088\\t-\ 0.533845\\t-0.14792\\t0.242064\\t0.550474\\t0.752758\\t0.734539\\t0.656939\\\ t0.584151\\t0.620243\\t0.837488\\n-2.56315\\t-2.53132\\t-2.49369\\t-2.51245\\\ t-2.60264\\t-2.71562\\t-2.73522\\t-2.58183\\t-2.27558\\t-2.01581\\t-1.94895\\\ t-1.88691\\t-1.67045\\t-1.31977\\t-0.963719\\t-0.704759\\t-0.474475\\t-0.\ 124597\\t0.218084\\t0.403918\\t0.570798\\t0.765081\\t0.890226\\t1.02281\\t1.\ 18419\\t1.23215\\t1.19815\\t1.17578\\t1.13905\\t1.13062\\t1.24169\\t1.31849\\\ t1.40542\\t1.5944\\t1.76812\\t1.71042\\t1.5287\\t1.37446\\t1.29894\\t1.02586\\\ t0.620873\\t0.479234\\t0.489316\\t0.571515\\t0.854198\\t1.19562\\t1.37413\\t1.\ 50992\\t1.62666\\t1.62922\\t1.56848\\t1.43346\\t1.21329\\t1.02309\\t0.789002\\\ t0.54854\\t0.251041\\t-0.128817\\t-0.302201\\t-0.214031\\t-0.046326\\t-0.\ 00191593\\t0.0689047\\t0.212872\\t0.35474\\t0.50943\\t0.658508\\t0.708061\\t0.\ 681008\\t0.656542\\t0.69687\\t0.797464\\t0.908383\\t0.751564\\t0.329983\\t0.\ 0351991\\t0.130444\\t0.221664\\t0.0697782\\t-0.181282\\t-0.366064\\t-0.507565\ \\t-0.43185\\t-0.368234\\t-0.527628\\t-0.592038\\t-0.563365\\t-0.656654\\t-0.\ 811071\\t-0.944418\\t-1.00118\\t-1.22869\\t-1.63436\\t-2.11406\\t-2.56183\\t-\ 2.97895\\t-3.18999\\t-3.3503\\t-3.63491\\t-3.92422\\t-4.12678\\t-4.25741\\t-4.\ 32482\\t-4.23483\\t-3.94868\\t-3.66054\\t-3.40283\\t-3.04768\\t-2.61927\\t-2.\ 10444\\t-1.62695\\t-1.31999\\t-1.11318\\t-0.940671\\t-0.779082\\t-0.644253\\t-\ 0.592192\\t-0.672741\\t-0.687226\\t-0.541927\\t-0.281263\\t0.0758762\\t0.\ 375384\\t0.537656\\t0.539364\\t0.548993\\t0.544828\\t0.538424\\t0.736057\\n-2.\ 28427\\t-2.3394\\t-2.41428\\t-2.47422\\t-2.55434\\t-2.62068\\t-2.63158\\t-2.\ 56807\\t-2.29655\\t-1.99569\\t-1.88313\\t-1.75445\\t-1.47212\\t-1.16301\\t-0.\ 855381\\t-0.579508\\t-0.328174\\t-0.0323182\\t0.319569\\t0.592406\\t0.798038\\\ t0.833447\\t0.828695\\t1.03318\\t1.326\\t1.38127\\t1.25532\\t1.2096\\t1.31401\ \\t1.44471\\t1.52026\\t1.44146\\t1.43039\\t1.66117\\t1.8237\\t1.73144\\t1.\ 49122\\t1.24678\\t1.0874\\t0.803126\\t0.433568\\t0.359532\\t0.41707\\t0.\ 447419\\t0.736902\\t1.06596\\t1.19855\\t1.31492\\t1.4491\\t1.38738\\t1.22809\\\ t1.10455\\t0.92413\\t0.647179\\t0.337498\\t0.105451\\t-0.241198\\t-0.615559\\\ t-0.764595\\t-0.625824\\t-0.434596\\t-0.313041\\t-0.111161\\t0.00391759\\t-0.\ 0113728\\t0.00797316\\t0.150597\\t0.314042\\t0.371657\\t0.375254\\t0.378688\\\ t0.373583\\t0.396351\\t0.272181\\t-0.0192897\\t-0.196838\\t-0.146878\\t-0.\ 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Currently the ", StyleBox["Mathematica", FontSlant->"Italic"], " lighting command specifies light sources in coordinates that either move \ with a graphic or are fixed relative to the final displayed image. While \ this is nice for setting up default behavior of lighting, it seems inadequate \ to the task of easy manipulation of such a crucial factor as lighting 3D \ graphics. Ideally there would be options to include or exclude lighting for \ interactive or code based transformations such as scale, rotate, or \ translate. (Even finer control could be achieved by permitting the \ specification of associated transformation properties at the time each light \ source is defined.) At the very least it should be made easier to apply such \ transformations collectively to all or individually to any light source or \ sources. To keep things simple this demonstration considers only scale and \ plot range transformations, but the essential distinction is between graphic \ object transformations that by default do not include lighting and coordinate \ frame transformations that by default do include lighting. 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$CellContext`lightsource$$ = { "fixed", "variable"}, $CellContext`s$$ = Rational[ 5, 4], $CellContext`\[CurlyTheta]$$ = Rational[1, 3] Pi, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`s$$], Rational[5, 4], "spheroid"}, Rational[1, 2], 2}, {{ Hold[$CellContext`\[CurlyTheta]$$], Rational[1, 3] Pi, "light angle"}, 0, Pi}, {{ Hold[$CellContext`lightsource$$], {"fixed", "variable"}, "light source"}, {{"fixed"} -> "fixed", {"variable"} -> "variable", {"fixed", "variable"} -> "both", {} -> "neither"}}, {{ Hold[$CellContext`details$$], "advanced"}, { "none", "basic", "advanced"}}, { Hold[ Grid[{{ Manipulate`Place[1], Manipulate`Place[2], SpanFromLeft}, { Manipulate`Place[3], Manipulate`Place[4]}}, Alignment -> Left, Spacings -> {2, Rational[1, 2]}]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = {600., {207., 213.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`s$151206$$ = 0, $CellContext`\[CurlyTheta]$151207$$ = 0, $CellContext`lightsource$151208$$ = False, $CellContext`details$151209$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 2, StandardForm, "Variables" :> {$CellContext`details$$ = "advanced", $CellContext`lightsource$$ = { "fixed", "variable"}, $CellContext`s$$ = Rational[5, 4], $CellContext`\[CurlyTheta]$$ = Rational[1, 3] Pi}, "ControllerVariables" :> { Hold[$CellContext`s$$, $CellContext`s$151206$$, 0], Hold[$CellContext`\[CurlyTheta]$$, \ $CellContext`\[CurlyTheta]$151207$$, 0], Hold[$CellContext`lightsource$$, $CellContext`lightsource$151208$$, False], Hold[$CellContext`details$$, $CellContext`details$151209$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ( If[$CellContext`details$$ != "none", $CellContext`lightsource$$ = {"fixed", "variable"}]; With[{$CellContext`a$ = Which[0 < $CellContext`s$$ < 1, 1, $CellContext`s$$ == 1, 1, 1 < $CellContext`s$$, 1/$CellContext`s$$, True, 1], $CellContext`c$ = Which[0 < $CellContext`s$$ < 1, $CellContext`s$$, $CellContext`s$$ == 1, 1, 1 < $CellContext`s$$, 1, True, 1]}, Switch[$CellContext`details$$, "none", Graphics3D[{ Opacity[4/5], Lighting -> Function[{$CellContext`a$, $CellContext`c$, $CellContext`f\ \[CurlyTheta]$, $CellContext`f\[CurlyPhi]$, $CellContext`transform$, \ $CellContext`lightsource$}, Cases[ Switch[$CellContext`transform$, "object", { If[ MemberQ[$CellContext`lightsource$, "variable"], { "Directional", Magenta, { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], {0, 0, 0}}}, {}], If[ MemberQ[$CellContext`lightsource$, "fixed"], { "Directional", Cyan, { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][$CellContext`f\[CurlyTheta]$, $CellContext`f\ \[CurlyPhi]$], {0, 0, 0}}}, {}]}, "frame", { If[ MemberQ[$CellContext`lightsource$, "variable"], { "Directional", Magenta, { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][$CellContext`f\[CurlyTheta]$, $CellContext`f\ \[CurlyPhi]$], {0, 0, 0}}}, {}], If[ MemberQ[$CellContext`lightsource$, "fixed"], { "Directional", Cyan, { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{ 1/$CellContext`a$, 1/$CellContext`c$} $CellContext`f\[CurlyTheta]$], \ $CellContext`f\[CurlyPhi]$], {0, 0, 0}}}, {}]}], Except[{}]]][$CellContext`a$, $CellContext`c$, Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][$CellContext`\[CurlyTheta]$$], Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][Rational[-1, 8] Pi], "object", $CellContext`lightsource$$], Scale[ Sphere[], {$CellContext`a$, $CellContext`a$, $CellContext`c$}, { 0, 0, 0}], Lighting -> Function[{$CellContext`a$, $CellContext`c$, $CellContext`f\ \[CurlyTheta]$, $CellContext`f\[CurlyPhi]$, $CellContext`transform$, \ $CellContext`lightsource$}, Cases[ Switch[$CellContext`transform$, "object", { If[ MemberQ[$CellContext`lightsource$, "variable"], { 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{1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Dot[{{0, 1}, {-1, 0}}, $CellContext`f\[CurlyTheta]$], $CellContext`f\ \[CurlyPhi]$], Append[{ 1/$CellContext`a$, (-1)/$CellContext`a$} $CellContext`f\ \[CurlyPhi]$, 0]}]]][$CellContext`a$, $CellContext`c$, Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][$CellContext`\[CurlyTheta]$$]\ , Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][Rational[-1, 8] Pi], Null, "object", "variable", True], Function[{$CellContext`a$, $CellContext`c$, $CellContext`f\ \[CurlyTheta]$, $CellContext`f\[CurlyPhi]$, $CellContext`transform$, \ $CellContext`lightsource$}, With[{$CellContext`normal$ = Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Switch[$CellContext`lightsource$, "fixed", Normalize[{ 1/$CellContext`a$, 1/$CellContext`c$} $CellContext`f\[CurlyTheta]$], "variable", $CellContext`f\[CurlyTheta]$], $CellContext`f\ \[CurlyPhi]$]}, Switch[$CellContext`transform$, "object", Scale[ $CellContext`circle3D[{0, 0, 0}, $CellContext`normal$, 1, $CellContext`style -> "line"], {$CellContext`a$, $CellContext`a$, \ $CellContext`c$}, {0, 0, 0}], "frame", $CellContext`circle3D[{0, 0, 0}, $CellContext`normal$, 1, $CellContext`style -> "line"]]]][$CellContext`a$, $CellContext`c$, Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][$CellContext`\[CurlyTheta]$$]\ , Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][Rational[-1, 8] Pi], "object", "variable"], Blend[{Cyan, Blue}, 1/5], Function[{$CellContext`a$, $CellContext`c$, $CellContext`f\ \[CurlyTheta]$, $CellContext`f\[CurlyPhi]$, $CellContext`vp$, \ $CellContext`transform$, $CellContext`lightsource$, $CellContext`simple$}, Apply[If[ Not[$CellContext`simple$], { $CellContext`arrow3D[# - 0.1 #4, # + 0.1 #4, {{{-0.041666666666666664`, 0.041666666666666664`}, {-0.041666666666666664`, \ -0.041666666666666664`}}, {{0.01658249769834222, -0.041666666666666664`}, { 0., -0.10355339059327379`}, {0.25, 0.}, {0., 0.10355339059327379`}, {0.01658249769834222, 0.041666666666666664`}}}, 0.25, (2 1.3916666666666668`) $CellContext`vp$, \ $CellContext`arrowheadplacement -> "outsidedimension", $CellContext`secondaryviewpoint -> \ #2], $CellContext`arrow3D[# - 0.1 #3, # + 0.1 #3, {{{-0.041666666666666664`, 0.041666666666666664`}, {-0.041666666666666664`, \ -0.041666666666666664`}}, {{0.01658249769834222, -0.041666666666666664`}, { 0., -0.10355339059327379`}, {0.25, 0.}, {0., 0.10355339059327379`}, {0.01658249769834222, 0.041666666666666664`}}}, 0.25, (2 1.3916666666666668`) $CellContext`vp$, \ $CellContext`arrowheadplacement -> "outsidedimension", $CellContext`secondaryviewpoint -> \ #2], $CellContext`arrow3D[# - 0.1 #2, # + 0.1 #2, {{{-0.041666666666666664`, 0.041666666666666664`}, {-0.041666666666666664`, \ -0.041666666666666664`}}, {{0.01658249769834222, -0.041666666666666664`}, { 0., -0.10355339059327379`}, {0.25, 0.}, {0., 0.10355339059327379`}, {0.01658249769834222, 0.041666666666666664`}}}, 0.25, (2 1.3916666666666668`) $CellContext`vp$, \ $CellContext`arrowheadplacement -> "outsidedimension", $CellContext`secondaryviewpoint -> \ #4]}, { CapForm["Round"], Thickness[Large], Arrowheads[Medium, Appearance -> "Projected"], Arrow[{#, # + 0.5 #2 + {10^(-4), 0, 0}}], Arrowheads[{-Medium, Medium}, Appearance -> "Projected"], Arrow[{# - 0.5 #3, # + 0.5 #3}], Arrow[{# - 0.5 #4, # + 0.5 #4}]}]& , Switch[ StringJoin[$CellContext`transform$, \ $CellContext`lightsource$], "objectfixed", {{$CellContext`a$, $CellContext`a$, \ $CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][$CellContext`f\[CurlyTheta]$, $CellContext`f\ \[CurlyPhi]$], Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Dot[{{0, 1}, {-1, 0}}, $CellContext`f\[CurlyTheta]$], $CellContext`f\ \[CurlyPhi]$], Append[{1, -1} $CellContext`f\[CurlyPhi]$, 0]}, "objectvariable", {{$CellContext`a$, $CellContext`a$, \ $CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$^2, $CellContext`c$^2} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[ Dot[{{0, 1}, {-1, 0}}, {$CellContext`a$, $CellContext`c$} $CellContext`f\ \[CurlyTheta]$]], $CellContext`f\[CurlyPhi]$], Append[{1, -1} $CellContext`f\[CurlyPhi]$, 0]}, "framevariable", { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$^2, $CellContext`c$^2} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], { 1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], { 1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[ Dot[{{0, 1}, {-1, 0}}, {$CellContext`a$, $CellContext`c$} $CellContext`f\ \[CurlyTheta]$]], $CellContext`f\[CurlyPhi]$], Append[{ 1/$CellContext`a$, (-1)/$CellContext`a$} $CellContext`f\ \[CurlyPhi]$, 0]}, "framefixed", { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], { 1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][$CellContext`f\[CurlyTheta]$, $CellContext`f\ \[CurlyPhi]$], {1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Dot[{{0, 1}, {-1, 0}}, $CellContext`f\[CurlyTheta]$], $CellContext`f\ \[CurlyPhi]$], Append[{ 1/$CellContext`a$, (-1)/$CellContext`a$} $CellContext`f\ \[CurlyPhi]$, 0]}]]][$CellContext`a$, $CellContext`c$, Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][$CellContext`\[CurlyTheta]$$]\ , Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][Rational[-1, 8] Pi], Null, "object", "fixed", True], Function[{$CellContext`a$, $CellContext`c$, $CellContext`f\ \[CurlyTheta]$, $CellContext`f\[CurlyPhi]$, $CellContext`transform$, \ $CellContext`lightsource$}, With[{$CellContext`normal$ = Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Switch[$CellContext`lightsource$, "fixed", Normalize[{ 1/$CellContext`a$, 1/$CellContext`c$} $CellContext`f\[CurlyTheta]$], "variable", $CellContext`f\[CurlyTheta]$], $CellContext`f\ \[CurlyPhi]$]}, Switch[$CellContext`transform$, "object", Scale[ $CellContext`circle3D[{0, 0, 0}, $CellContext`normal$, 1, $CellContext`style -> "line"], {$CellContext`a$, $CellContext`a$, \ $CellContext`c$}, {0, 0, 0}], "frame", $CellContext`circle3D[{0, 0, 0}, $CellContext`normal$, 1, $CellContext`style -> "line"]]]][$CellContext`a$, $CellContext`c$, Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][$CellContext`\[CurlyTheta]$$]\ , Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][Rational[-1, 8] Pi], "object", "fixed"]}, Boxed -> False, PlotRange -> 1.5 {{-1, 1}, {-1, 1}, {-1, 1}}, BoxRatios -> {1, 1, 1}, ViewPoint -> $CellContext`vp$$, ViewVertical -> $CellContext`vv$$, ViewAngle -> (6/5) $CellContext`va$$, ImageSize -> 160, ImageMargins -> {{140, 0}, {10, 0}}, Background -> LightGray], Graphics3D[{ Lighting -> Function[{$CellContext`a$, $CellContext`c$, $CellContext`f\ \[CurlyTheta]$, $CellContext`f\[CurlyPhi]$, $CellContext`transform$, \ $CellContext`lightsource$}, Cases[ Switch[$CellContext`transform$, "object", { If[ MemberQ[$CellContext`lightsource$, "variable"], { "Directional", Magenta, { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], {0, 0, 0}}}, {}], If[ MemberQ[$CellContext`lightsource$, "fixed"], { "Directional", Cyan, { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][$CellContext`f\[CurlyTheta]$, $CellContext`f\ \[CurlyPhi]$], {0, 0, 0}}}, {}]}, "frame", { If[ MemberQ[$CellContext`lightsource$, "variable"], { "Directional", Magenta, { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][$CellContext`f\[CurlyTheta]$, $CellContext`f\ \[CurlyPhi]$], {0, 0, 0}}}, {}], If[ MemberQ[$CellContext`lightsource$, "fixed"], { "Directional", Cyan, { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{ 1/$CellContext`a$, 1/$CellContext`c$} $CellContext`f\[CurlyTheta]$], \ $CellContext`f\[CurlyPhi]$], {0, 0, 0}}}, {}]}], Except[{}]]][$CellContext`a$, $CellContext`c$, Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][$CellContext`\[CurlyTheta]$$]\ , Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][Rational[-1, 8] Pi], "frame", {"fixed", "variable"}], FaceForm[ Opacity[2/3], None], Sphere[], Opacity[1], Blend[{Cyan, Blue}, 1/5], Function[{$CellContext`a$, $CellContext`c$, $CellContext`f\ \[CurlyTheta]$, $CellContext`f\[CurlyPhi]$, $CellContext`vp$, \ $CellContext`transform$, $CellContext`lightsource$, $CellContext`simple$}, Apply[If[ Not[$CellContext`simple$], { $CellContext`arrow3D[# - 0.1 #4, # + 0.1 #4, {{{-0.041666666666666664`, 0.041666666666666664`}, {-0.041666666666666664`, \ -0.041666666666666664`}}, {{0.01658249769834222, -0.041666666666666664`}, { 0., -0.10355339059327379`}, {0.25, 0.}, {0., 0.10355339059327379`}, {0.01658249769834222, 0.041666666666666664`}}}, 0.25, (2 1.3916666666666668`) $CellContext`vp$, \ $CellContext`arrowheadplacement -> "outsidedimension", $CellContext`secondaryviewpoint -> \ #2], $CellContext`arrow3D[# - 0.1 #3, # + 0.1 #3, {{{-0.041666666666666664`, 0.041666666666666664`}, {-0.041666666666666664`, \ -0.041666666666666664`}}, {{0.01658249769834222, -0.041666666666666664`}, { 0., -0.10355339059327379`}, {0.25, 0.}, {0., 0.10355339059327379`}, {0.01658249769834222, 0.041666666666666664`}}}, 0.25, (2 1.3916666666666668`) $CellContext`vp$, \ $CellContext`arrowheadplacement -> "outsidedimension", $CellContext`secondaryviewpoint -> \ #2], $CellContext`arrow3D[# - 0.1 #2, # + 0.1 #2, {{{-0.041666666666666664`, 0.041666666666666664`}, {-0.041666666666666664`, \ -0.041666666666666664`}}, {{0.01658249769834222, -0.041666666666666664`}, { 0., -0.10355339059327379`}, {0.25, 0.}, {0., 0.10355339059327379`}, {0.01658249769834222, 0.041666666666666664`}}}, 0.25, (2 1.3916666666666668`) $CellContext`vp$, \ $CellContext`arrowheadplacement -> "outsidedimension", $CellContext`secondaryviewpoint -> \ #4]}, { CapForm["Round"], Thickness[Large], Arrowheads[Medium, Appearance -> "Projected"], Arrow[{#, # + 0.5 #2 + {10^(-4), 0, 0}}], Arrowheads[{-Medium, Medium}, Appearance -> "Projected"], Arrow[{# - 0.5 #3, # + 0.5 #3}], Arrow[{# - 0.5 #4, # + 0.5 #4}]}]& , Switch[ StringJoin[$CellContext`transform$, \ $CellContext`lightsource$], "objectfixed", {{$CellContext`a$, $CellContext`a$, \ $CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][$CellContext`f\[CurlyTheta]$, $CellContext`f\ \[CurlyPhi]$], Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Dot[{{0, 1}, {-1, 0}}, $CellContext`f\[CurlyTheta]$], $CellContext`f\ \[CurlyPhi]$], Append[{1, -1} $CellContext`f\[CurlyPhi]$, 0]}, "objectvariable", {{$CellContext`a$, $CellContext`a$, \ $CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$^2, $CellContext`c$^2} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[ Dot[{{0, 1}, {-1, 0}}, {$CellContext`a$, $CellContext`c$} $CellContext`f\ \[CurlyTheta]$]], $CellContext`f\[CurlyPhi]$], Append[{1, -1} $CellContext`f\[CurlyPhi]$, 0]}, "framevariable", { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$^2, $CellContext`c$^2} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], { 1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], { 1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[ Dot[{{0, 1}, {-1, 0}}, {$CellContext`a$, $CellContext`c$} $CellContext`f\ \[CurlyTheta]$]], $CellContext`f\[CurlyPhi]$], Append[{ 1/$CellContext`a$, (-1)/$CellContext`a$} $CellContext`f\ \[CurlyPhi]$, 0]}, "framefixed", { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], { 1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][$CellContext`f\[CurlyTheta]$, $CellContext`f\ \[CurlyPhi]$], {1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Dot[{{0, 1}, {-1, 0}}, $CellContext`f\[CurlyTheta]$], $CellContext`f\ \[CurlyPhi]$], Append[{ 1/$CellContext`a$, (-1)/$CellContext`a$} $CellContext`f\ \[CurlyPhi]$, 0]}]]][$CellContext`a$, $CellContext`c$, Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][$CellContext`\[CurlyTheta]$$]\ , Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][Rational[-1, 8] Pi], Null, "frame", "fixed", True], Function[{$CellContext`a$, $CellContext`c$, $CellContext`f\ \[CurlyTheta]$, $CellContext`f\[CurlyPhi]$, $CellContext`transform$, \ $CellContext`lightsource$}, With[{$CellContext`normal$ = Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Switch[$CellContext`lightsource$, "fixed", Normalize[{ 1/$CellContext`a$, 1/$CellContext`c$} $CellContext`f\[CurlyTheta]$], "variable", $CellContext`f\[CurlyTheta]$], $CellContext`f\ \[CurlyPhi]$]}, Switch[$CellContext`transform$, "object", Scale[ $CellContext`circle3D[{0, 0, 0}, $CellContext`normal$, 1, $CellContext`style -> "line"], {$CellContext`a$, $CellContext`a$, \ $CellContext`c$}, {0, 0, 0}], "frame", $CellContext`circle3D[{0, 0, 0}, $CellContext`normal$, 1, $CellContext`style -> "line"]]]][$CellContext`a$, $CellContext`c$, Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][$CellContext`\[CurlyTheta]$$]\ , Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][Rational[-1, 8] Pi], "frame", "fixed"], Blend[{Magenta, Blue}, 1/5], Function[{$CellContext`a$, $CellContext`c$, $CellContext`f\ \[CurlyTheta]$, $CellContext`f\[CurlyPhi]$, $CellContext`vp$, \ $CellContext`transform$, $CellContext`lightsource$, $CellContext`simple$}, Apply[If[ Not[$CellContext`simple$], { $CellContext`arrow3D[# - 0.1 #4, # + 0.1 #4, {{{-0.041666666666666664`, 0.041666666666666664`}, {-0.041666666666666664`, \ -0.041666666666666664`}}, {{0.01658249769834222, -0.041666666666666664`}, { 0., -0.10355339059327379`}, {0.25, 0.}, {0., 0.10355339059327379`}, {0.01658249769834222, 0.041666666666666664`}}}, 0.25, (2 1.3916666666666668`) $CellContext`vp$, \ $CellContext`arrowheadplacement -> "outsidedimension", $CellContext`secondaryviewpoint -> \ #2], $CellContext`arrow3D[# - 0.1 #3, # + 0.1 #3, {{{-0.041666666666666664`, 0.041666666666666664`}, {-0.041666666666666664`, \ -0.041666666666666664`}}, {{0.01658249769834222, -0.041666666666666664`}, { 0., -0.10355339059327379`}, {0.25, 0.}, {0., 0.10355339059327379`}, {0.01658249769834222, 0.041666666666666664`}}}, 0.25, (2 1.3916666666666668`) $CellContext`vp$, \ $CellContext`arrowheadplacement -> "outsidedimension", $CellContext`secondaryviewpoint -> \ #2], $CellContext`arrow3D[# - 0.1 #2, # + 0.1 #2, {{{-0.041666666666666664`, 0.041666666666666664`}, {-0.041666666666666664`, \ -0.041666666666666664`}}, {{0.01658249769834222, -0.041666666666666664`}, { 0., -0.10355339059327379`}, {0.25, 0.}, {0., 0.10355339059327379`}, {0.01658249769834222, 0.041666666666666664`}}}, 0.25, (2 1.3916666666666668`) $CellContext`vp$, \ $CellContext`arrowheadplacement -> "outsidedimension", $CellContext`secondaryviewpoint -> \ #4]}, { CapForm["Round"], Thickness[Large], Arrowheads[Medium, Appearance -> "Projected"], Arrow[{#, # + 0.5 #2 + {10^(-4), 0, 0}}], Arrowheads[{-Medium, Medium}, Appearance -> "Projected"], Arrow[{# - 0.5 #3, # + 0.5 #3}], Arrow[{# - 0.5 #4, # + 0.5 #4}]}]& , Switch[ StringJoin[$CellContext`transform$, \ $CellContext`lightsource$], "objectfixed", {{$CellContext`a$, $CellContext`a$, \ $CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][$CellContext`f\[CurlyTheta]$, $CellContext`f\ \[CurlyPhi]$], Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Dot[{{0, 1}, {-1, 0}}, $CellContext`f\[CurlyTheta]$], $CellContext`f\ \[CurlyPhi]$], Append[{1, -1} $CellContext`f\[CurlyPhi]$, 0]}, "objectvariable", {{$CellContext`a$, $CellContext`a$, \ $CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$^2, $CellContext`c$^2} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[ Dot[{{0, 1}, {-1, 0}}, {$CellContext`a$, $CellContext`c$} $CellContext`f\ \[CurlyTheta]$]], $CellContext`f\[CurlyPhi]$], Append[{1, -1} $CellContext`f\[CurlyPhi]$, 0]}, "framevariable", { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$^2, $CellContext`c$^2} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], { 1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], { 1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[ Dot[{{0, 1}, {-1, 0}}, {$CellContext`a$, $CellContext`c$} $CellContext`f\ \[CurlyTheta]$]], $CellContext`f\[CurlyPhi]$], Append[{ 1/$CellContext`a$, (-1)/$CellContext`a$} $CellContext`f\ \[CurlyPhi]$, 0]}, "framefixed", { Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Normalize[{$CellContext`a$, $CellContext`c$} \ $CellContext`f\[CurlyTheta]$], $CellContext`f\[CurlyPhi]$], { 1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][$CellContext`f\[CurlyTheta]$, $CellContext`f\ \[CurlyPhi]$], {1/$CellContext`a$, 1/$CellContext`a$, 1/$CellContext`c$} Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Dot[{{0, 1}, {-1, 0}}, $CellContext`f\[CurlyTheta]$], $CellContext`f\ \[CurlyPhi]$], Append[{ 1/$CellContext`a$, (-1)/$CellContext`a$} $CellContext`f\ \[CurlyPhi]$, 0]}]]][$CellContext`a$, $CellContext`c$, Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][$CellContext`\[CurlyTheta]$$]\ , Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][Rational[-1, 8] Pi], Null, "frame", "variable", True], Function[{$CellContext`a$, $CellContext`c$, $CellContext`f\ \[CurlyTheta]$, $CellContext`f\[CurlyPhi]$, $CellContext`transform$, \ $CellContext`lightsource$}, With[{$CellContext`normal$ = Function[{$CellContext`f\[Theta], $CellContext`f\[Phi]}, { Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 2], Part[$CellContext`f\[Theta], 1] Part[$CellContext`f\[Phi], 1], Part[$CellContext`f\[Theta], 2]}][ Switch[$CellContext`lightsource$, "fixed", Normalize[{ 1/$CellContext`a$, 1/$CellContext`c$} $CellContext`f\[CurlyTheta]$], "variable", $CellContext`f\[CurlyTheta]$], $CellContext`f\ \[CurlyPhi]$]}, Switch[$CellContext`transform$, "object", Scale[ $CellContext`circle3D[{0, 0, 0}, $CellContext`normal$, 1, $CellContext`style -> "line"], {$CellContext`a$, $CellContext`a$, \ $CellContext`c$}, {0, 0, 0}], "frame", $CellContext`circle3D[{0, 0, 0}, $CellContext`normal$, 1, $CellContext`style -> "line"]]]][$CellContext`a$, $CellContext`c$, Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][$CellContext`\[CurlyTheta]$$]\ , Function[$CellContext`\[Theta], { Sin[$CellContext`\[Theta]], Cos[$CellContext`\[Theta]]}][Rational[-1, 8] Pi], "frame", "variable"]}, Boxed -> False, PlotRange -> 2. {{-1, 1}, {-1, 1}, {-1, 1}}, BoxRatios -> {1, 1, 1}, ViewPoint -> $CellContext`vp$$, ViewVertical -> $CellContext`vv$$, ViewAngle -> (6/5) $CellContext`va$$, ImageSize -> 160, ImageMargins -> {{0, 140}, {10, 0}}, Background -> LightGray]}}, Spacings -> {0, 0}, Alignment -> {{Right, Left}, Center}]], {600, 420}, Alignment -> Center]]]), "Specifications" :> {{{$CellContext`s$$, Rational[5, 4], "spheroid"}, Rational[1, 2], 2, ControlPlacement -> 1}, {{$CellContext`\[CurlyTheta]$$, Rational[1, 3] Pi, "light angle"}, 0, Pi, ControlPlacement -> 2}, {{$CellContext`lightsource$$, {"fixed", "variable"}, "light source"}, {{"fixed"} -> "fixed", {"variable"} -> "variable", {"fixed", "variable"} -> "both", {} -> "neither"}, Enabled -> Dynamic[$CellContext`details$$ == "none"], ControlPlacement -> 3}, {{$CellContext`details$$, "advanced"}, { "none", "basic", "advanced"}, ControlPlacement -> 4}, Grid[{{ Manipulate`Place[1], Manipulate`Place[2], SpanFromLeft}, { Manipulate`Place[3], Manipulate`Place[4]}}, Alignment -> Left, Spacings -> {2, Rational[1, 2]}]}, "Options" :> {ControlPlacement -> Top, FrameMargins -> 0}, "DefaultOptions" :> {}], ImageSizeCache->{623., {254., 261.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({ Attributes[$CellContext`a$] = {Temporary}, Attributes[$CellContext`c$] = {Temporary}, Attributes[$CellContext`f\[CurlyTheta]$] = {Temporary}, Attributes[$CellContext`f\[CurlyPhi]$] = {Temporary}, Attributes[$CellContext`transform$] = {Temporary}, Attributes[$CellContext`lightsource$] = {Temporary}, Attributes[$CellContext`vp$] = {Temporary}, Attributes[$CellContext`simple$] = {Temporary}, $CellContext`arrow3D[ Pattern[$CellContext`pt1, Blank[]], Pattern[$CellContext`pt2, Blank[]], Pattern[$CellContext`arrowhead, Blank[]], Pattern[$CellContext`headlength, Blank[]], Pattern[$CellContext`viewpointunscaledcoordinates, Blank[]], OptionsPattern[{$CellContext`arrowheadplacement -> Automatic, $CellContext`splitsingularity -> True, $CellContext`secondaryviewpoint -> Automatic, $CellContext`referencefraction -> 1/2, $CellContext`diagnosticdisplay -> False}]] := With[{$CellContext`arrowlength = Norm[$CellContext`pt2 - $CellContext`pt1], $CellContext`\[Alpha] = 1/4, $CellContext`\[Gamma] = 10^(-2), $CellContext`arrowreferencepoint = (1 - OptionValue[$CellContext`referencefraction]) $CellContext`pt1 + OptionValue[$CellContext`referencefraction] $CellContext`pt2, \ $CellContext`fractionalarrow = Function[{$CellContext`orig, $CellContext`delta, \ $CellContext`frac}, With[{$CellContext`\[Epsilon] = 1}, { Opacity[1], Point[$CellContext`orig], Arrow[{$CellContext`orig, $CellContext`orig + ($CellContext`\ \[Epsilon] $CellContext`frac) $CellContext`delta}], Opacity[1/4], Point[$CellContext`orig + ($CellContext`\[Epsilon] \ $CellContext`frac) $CellContext`delta], Arrow[{$CellContext`orig + ($CellContext`\[Epsilon] \ $CellContext`frac) $CellContext`delta, $CellContext`orig + $CellContext`\ \[Epsilon] $CellContext`delta}]}]]}, If[$CellContext`arrowlength/$CellContext`headlength > 10^(-3), With[{$CellContext`primaryviewpoint = \ $CellContext`viewpointunscaledcoordinates - $CellContext`arrowreferencepoint, \ $CellContext`criticalelevation = If[ OptionValue[$CellContext`splitsingularity], $CellContext`\ \[Alpha] ($CellContext`headlength/ Max[$CellContext`arrowlength, $CellContext`headlength]), 0]}, Block[{$CellContext`transverse, $CellContext`blendfraction, \ $CellContext`viewpointtransverse, $CellContext`blendtransverse, \ $CellContext`azimuthdisknormal, $CellContext`xaxis, $CellContext`yaxis, \ $CellContext`zaxis}, {$CellContext`transverse, $CellContext`blendfraction, \ $CellContext`viewpointtransverse, $CellContext`blendtransverse, \ $CellContext`azimuthdisknormal, $CellContext`xaxis, $CellContext`yaxis, \ $CellContext`zaxis} = $CellContext`arrow3Dtransverse[$CellContext`pt1, \ $CellContext`pt2, $CellContext`primaryviewpoint, OptionValue[$CellContext`secondaryviewpoint], \ $CellContext`criticalelevation]; With[{$CellContext`u1 = ($CellContext`pt2 - \ $CellContext`pt1)/$CellContext`arrowlength, $CellContext`u2 = \ $CellContext`transverse, $CellContext`arrow2d = Switch[ OptionValue[$CellContext`arrowheadplacement], Condition[ Alternatives[ Automatic, "singleheaded"], $CellContext`arrowlength > \ $CellContext`headlength], Join[ Part[$CellContext`arrowhead, 1], Apply[{# + $CellContext`arrowlength - \ $CellContext`headlength, #2}& , Part[$CellContext`arrowhead, 2], {1}]], Condition[ Alternatives[ "doubleheaded", "insidedimension"], $CellContext`arrowlength > 2 $CellContext`headlength], Join[ Apply[{-# + $CellContext`headlength, #2}& , Reverse[ Part[$CellContext`arrowhead, 2]], {1}], Apply[{# + $CellContext`arrowlength - \ $CellContext`headlength, #2}& , Part[$CellContext`arrowhead, 2], {1}]], Alternatives["outsidedimension", Blank[]], With[{$CellContext`minimalarrowhead = Apply[Join, $CellContext`arrowhead]}, { Apply[{# - $CellContext`headlength, #2}& , \ $CellContext`minimalarrowhead, {1}], Apply[{-# + $CellContext`arrowlength + \ $CellContext`headlength, #2}& , Reverse[$CellContext`minimalarrowhead], {1}]}]]}, { Polygon[ Apply[$CellContext`pt1 + $CellContext`u1 # + $CellContext`u2 \ #2& , $CellContext`arrow2d, {-2}]], If[ And[ OptionValue[$CellContext`diagnosticdisplay], OptionValue[$CellContext`splitsingularity]], { Blend[{Blue, Cyan}, 1/3], Thickness[Large], PointSize[Medium], Arrowheads[Medium, Appearance -> "Projected"], $CellContext`fractionalarrow[$CellContext`\ arrowreferencepoint, $CellContext`viewpointtransverse, 1 - $CellContext`blendfraction], Red, $CellContext`fractionalarrow[$CellContext`\ arrowreferencepoint, $CellContext`blendtransverse, \ $CellContext`blendfraction], Opacity[1/4], Glow[Black], FaceForm[White], EdgeForm[{ Thickness[Medium], Black}], $CellContext`circle3D[$CellContext`arrowreferencepoint, \ $CellContext`zaxis, 1], $CellContext`circle3D[$CellContext`arrowreferencepoint, \ $CellContext`yaxis, 1], $CellContext`circle3D[$CellContext`arrowreferencepoint, \ $CellContext`azimuthdisknormal, 1, $CellContext`axis -> -$CellContext`zaxis, \ $CellContext`arc -> {0, Pi}], With[{$CellContext`c = Cos[$CellContext`criticalelevation], $CellContext`s = Sin[$CellContext`criticalelevation]}, {Black, Opacity[2/3], PointSize[Medium], Point[$CellContext`arrowreferencepoint + $CellContext`c \ $CellContext`xaxis + $CellContext`s $CellContext`zaxis], Point[$CellContext`arrowreferencepoint + $CellContext`c \ $CellContext`xaxis - $CellContext`s $CellContext`zaxis], Point[$CellContext`arrowreferencepoint - $CellContext`c \ $CellContext`xaxis + $CellContext`s $CellContext`zaxis], Point[$CellContext`arrowreferencepoint - $CellContext`c \ $CellContext`xaxis - $CellContext`s $CellContext`zaxis]}], Black, Opacity[1/2], Arrow[{$CellContext`arrowreferencepoint, \ $CellContext`arrowreferencepoint + Normalize[$CellContext`primaryviewpoint]}]}, {}]}]]], \ {}]], $CellContext`arrow3Dtransverse[ Pattern[$CellContext`pt1, Blank[]], Pattern[$CellContext`pt2, Blank[]], Pattern[$CellContext`primaryviewpoint, Blank[]], Pattern[$CellContext`secondaryviewpoint, Blank[]], Pattern[$CellContext`criticalelevation, Blank[]]] := With[{$CellContext`viewpointtransverse = (If[# == {0, 0, 0}, #, Normalize[#]]& )[ Cross[$CellContext`primaryviewpoint, $CellContext`pt2 - \ $CellContext`pt1]], $CellContext`\[Beta] = 2/10, $CellContext`s2v = { "x" -> {1, 0, 0}, "y" -> {0, 1, 0}, "z" -> {0, 0, 1}}}, If[$CellContext`criticalelevation == 0, {$CellContext`viewpointtransverse, 0, $CellContext`viewpointtransverse, Null, Null, Null, Null, Null}, With[{$CellContext`checksecondaryviewpoint = If[ Not[$CellContext`secondaryviewpoint === Automatic], Abs[ Sin[ VectorAngle[$CellContext`secondaryviewpoint, \ $CellContext`pt2 - $CellContext`pt1]]] >= $CellContext`\[Beta], False]}, If[ And[ Not[$CellContext`checksecondaryviewpoint], Abs[ Sin[ VectorAngle[ ReplaceAll[$CellContext`arrow3Dsecondaryviewpoint, \ $CellContext`s2v], $CellContext`pt2 - $CellContext`pt1]]] < $CellContext`\ \[Beta]], $CellContext`arrow3Dsecondaryviewpoint = ReplaceAll[$CellContext`arrow3Dsecondaryviewpoint, { "x" -> "y", "y" -> "z", "z" -> "x"}]]; With[{$CellContext`xaxis = Normalize[$CellContext`pt2 - $CellContext`pt1], \ $CellContext`zaxis = Normalize[ Cross[ If[$CellContext`checksecondaryviewpoint, \ $CellContext`secondaryviewpoint, ReplaceAll[$CellContext`arrow3Dsecondaryviewpoint, \ $CellContext`s2v]], $CellContext`pt2 - $CellContext`pt1]], \ $CellContext`unitviewpoint = Normalize[$CellContext`primaryviewpoint]}, With[{$CellContext`yaxis = Cross[$CellContext`zaxis, $CellContext`xaxis], \ $CellContext`blendtransverse = If[Dot[$CellContext`viewpointtransverse, $CellContext`zaxis] >= 0, $CellContext`zaxis, -$CellContext`zaxis]}, With[{$CellContext`viewpointelevation = Mod[ ArcSin[ Dot[$CellContext`unitviewpoint, $CellContext`zaxis]], Pi, (-Pi)/2], $CellContext`viewpointazimuth = ArcTan[ Dot[$CellContext`unitviewpoint, $CellContext`xaxis], Dot[$CellContext`unitviewpoint, $CellContext`yaxis]]}, With[{$CellContext`blendfraction = \ $CellContext`arrow3Dblendfraction[$CellContext`viewpointelevation/$\ CellContext`criticalelevation, Mod[$CellContext`viewpointazimuth, Pi, (-Pi)/ 2]/$CellContext`criticalelevation], \ $CellContext`viewpointradius = Sqrt[$CellContext`viewpointelevation^2 + Mod[$CellContext`viewpointazimuth, Pi, (-Pi)/ 2]^2], $CellContext`azimuthdisknormal = \ $CellContext`xaxis Sin[$CellContext`viewpointazimuth] - $CellContext`yaxis Cos[$CellContext`viewpointazimuth]}, With[{$CellContext`transverse = If[$CellContext`viewpointradius < 10^(-3), $CellContext`blendtransverse, If[ Or[$CellContext`blendfraction == 0, Abs[$CellContext`viewpointelevation/$CellContext`\ viewpointradius] < 10^(-3)], $CellContext`viewpointtransverse, With[{$CellContext`blendangle = \ $CellContext`blendfraction VectorAngle[$CellContext`viewpointtransverse, \ $CellContext`blendtransverse], $CellContext`orthogonalblendtransverse = Normalize[$CellContext`blendtransverse - Projection[$CellContext`blendtransverse, \ $CellContext`viewpointtransverse]]}, Cos[$CellContext`blendangle] \ $CellContext`viewpointtransverse + Sin[$CellContext`blendangle] \ $CellContext`orthogonalblendtransverse]]]}, {$CellContext`transverse, \ $CellContext`blendfraction, $CellContext`viewpointtransverse, \ $CellContext`blendtransverse, $CellContext`azimuthdisknormal, \ $CellContext`xaxis, $CellContext`yaxis, $CellContext`zaxis}]]]]]]]], \ $CellContext`arrow3Dsecondaryviewpoint = "x", $CellContext`arrow3Dblendfraction[ Pattern[$CellContext`\[Theta], Blank[]], Pattern[$CellContext`\[Phi], Blank[]]] := With[{$CellContext`\[Delta] = 1, $CellContext`\[Epsilon] = 1, $CellContext`e1 = Function[$CellContext`x, (-2) $CellContext`x^3 + 3 $CellContext`x^2]}, With[{$CellContext`r1 = Sqrt[$CellContext`\[Theta]^2 + $CellContext`\[Phi]^2], \ $CellContext`r2 = Sqrt[($CellContext`\[Delta] - Abs[$CellContext`\[Theta]])^2 + $CellContext`\[Phi]^2], \ $CellContext`a2 = If[ And[$CellContext`\[Delta] == Abs[$CellContext`\[Theta]], $CellContext`\[Phi] == 0], 1, Abs[ ArcTan[Abs[$CellContext`\[Theta]] - $CellContext`\[Delta], \ $CellContext`\[Phi]]/Pi]], $CellContext`w = $CellContext`e1[ Piecewise[{{ 1 - Abs[$CellContext`\[Phi]]/ Sqrt[$CellContext`\[Epsilon]^2 - ( Abs[$CellContext`\[Theta]] - $CellContext`\[Delta])^2], \ $CellContext`\[Phi]^2 + ( Abs[$CellContext`\[Theta]] - $CellContext`\[Delta])^2 < \ $CellContext`\[Epsilon]^2}}]], $CellContext`e2 = Function[$CellContext`x, Piecewise[{{ 1, $CellContext`x <= $CellContext`\[Delta] - $CellContext`\ \[Epsilon]}, {1/2 + (3/( 4 $CellContext`\[Epsilon])) (($CellContext`x - \ $CellContext`\[Delta])^3/( 3 $CellContext`\[Epsilon]^2) - ($CellContext`x - \ $CellContext`\[Delta])), $CellContext`\[Delta] - $CellContext`\[Epsilon] < \ $CellContext`x < $CellContext`\[Delta] + $CellContext`\[Epsilon]}, { 0, $CellContext`x >= $CellContext`\[Delta] + $CellContext`\ \[Epsilon]}}]]}, ( 1 - $CellContext`w) $CellContext`e2[$CellContext`r1] + \ $CellContext`w $CellContext`e1[$CellContext`a2]]], $CellContext`circle3D[ Pattern[$CellContext`origin, Blank[]], Pattern[$CellContext`normal, Blank[]], Pattern[$CellContext`radius, Blank[]], OptionsPattern[{$CellContext`segments -> Automatic, $CellContext`axis -> Automatic, $CellContext`arc -> Automatic, $CellContext`style -> Automatic}]] := With[{$CellContext`u2 = Normalize[ Cross[$CellContext`normal, If[OptionValue[$CellContext`axis] === Automatic, ReplacePart[{0, 0, 0}, Ordering[ Abs[$CellContext`normal], 1] -> 1], OptionValue[$CellContext`axis]]]], $CellContext`arclength = If[OptionValue[$CellContext`arc] === Automatic, 2 Pi, With[{$CellContext`\[Theta] = Mod[-Apply[Subtract, OptionValue[$CellContext`arc]], 2 Pi]}, Which[ And[$CellContext`\[Theta] == 0, OrderedQ[-OptionValue[$CellContext`arc]]], 0, $CellContext`\[Theta] == 0, 2 Pi, True, $CellContext`\[Theta]]]]}, With[{$CellContext`u1 = Normalize[ Cross[$CellContext`u2, $CellContext`normal]], $CellContext`n = If[OptionValue[$CellContext`segments] === Automatic, Ceiling[(64 ($CellContext`arclength/2)) Pi], True, OptionValue[$CellContext`segments]], $CellContext`\[Theta]1 = If[$CellContext`arclength == 2 Pi, 0, First[ OptionValue[$CellContext`arc]]]}, With[{$CellContext`pts = Table[ With[{$CellContext`\[Theta] = N[$CellContext`\[Theta]1 + $CellContext`arclength \ ($CellContext`i/$CellContext`n)]}, $CellContext`origin + ($CellContext`u1 \ $CellContext`radius) Cos[$CellContext`\[Theta]] + ($CellContext`u2 \ $CellContext`radius) Sin[$CellContext`\[Theta]]], {$CellContext`i, 1, $CellContext`n}]}, Switch[ OptionValue[$CellContext`style], Alternatives[Automatic, "polygon"], Switch[$CellContext`arclength, 0, Line[{$CellContext`origin, $CellContext`origin + \ $CellContext`u1 $CellContext`radius}], 2 Pi, Polygon[$CellContext`pts], Blank[], Polygon[ Join[{$CellContext`origin, $CellContext`origin + \ $CellContext`u1 $CellContext`radius}, $CellContext`pts]]], Alternatives["line", Blank[]], Switch[$CellContext`arclength, 0, Line[{$CellContext`origin, $CellContext`origin + \ $CellContext`u1 $CellContext`radius}], 2 Pi, Line[ Join[{$CellContext`origin + $CellContext`u1 \ $CellContext`radius}, $CellContext`pts]], Blank[], Line[ Join[{$CellContext`origin, $CellContext`origin + \ $CellContext`u1 $CellContext`radius}, $CellContext`pts, \ {$CellContext`origin}]]]]]]], $CellContext`i = {{1, 2, 5}, {2, 3, 5}, {3, 4, 5}, {4, 1, 5}}, Attributes[$CellContext`normal$] = {Temporary}}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]], DynamicModuleValues:>{}]], "Output", CellChangeTimes->{ 3.56439405337495*^9, 3.564394133527581*^9, {3.564394312196559*^9, 3.564394358396727*^9}, {3.5643945780213423`*^9, 3.564394618127079*^9}, 3.564395113914803*^9, 3.5643951914979*^9, {3.5643953417311907`*^9, 3.564395369978253*^9}, 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