GraphicsOperations Package Documentation
This package provides functions for general transformations of two and three-dimensional graphics primitives as well as functions for extracting or removing graphics primitives from within existing graphics objects.
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TranslateGraphics[g, {d_x, d_y}] translate all graphics primitives in the two-dimensional graphics object g by the specified vector
TranslateGraphics[g, {d_x, d_y, d_z}] translate all graphics primitives in the three-dimensional graphics object g by the specified vector
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Translating graphics objects.
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ScaleGraphics[g, scale] scale all graphics primitives in the graphics object g by the factor scale
ScaleGraphics[g, {scale_x, scale_y}] scale all graphics primitives in the two-dimensional graphics object g by the respective scale factors
ScaleGraphics[g, {scale_x, scale_y, scale_z}] scale all graphics primitives in the three-dimensional graphics object g by the respective scale factors
ScaleGraphics[g, scale, origin] scale all graphics primitives in the graphics object g with respect to the point origin
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Scaling graphics objects.
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RotateGraphics[g, phi] rotate all graphics primitives in the two-dimensional graphics object g clockwise by the specified angle phi
RotateGraphics[g, {phi, theta, psi}] rotate all graphics primitives in the three-dimensional graphics object g by the specified Euler angles phi, theta and psi
RotateGraphics[g, angles, origin] rotate all graphics primitives in the graphics object g about the point origin
RotateGraphics[g, mat, origin] rotate all graphics primitives in the graphics object g using the rotation matrix mat
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Rotating graphics objects.
option name default value
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TextRotated False determines whether to rotate text orientation
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Options for RotateGraphics
TextRotated determines whether the orientation of any Text graphics primitives is also rotated along with the coordinates of the Text primitives. This option only affects the rotation of two-dimensional Text primitives since three-dimensional Text primitives are always shown in the display plane.
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TransformGraphics[g, f] applies the function f to all lists of coordinates in the graphics object g
SkewGraphics[g, mat] applies the matrix mat to all coordinates in the graphics object g
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Other transformation functions.
The transformation functions can be used with Graphics, Graphics3D, SurfaceGraphics, DensityGraphics, ContourGraphics and GraphicsArray graphics objects. In most cases, a graphics primitive will retain its original identity after applying any of the transformation functions, however there are a few exceptions. Namely, Rectangle, Cuboid, Raster and RasterArray graphics primitives are converted to equivalent lists of Polygon primitives when used with RotateGraphics, TransformGraphics and SkewGraphics.
<Automatic, Axes->True]
This creates a two-dimensional graphics object of some common graphics primitives.
Show[ TranslateGraphics[graph, {10,20}]]
Translate the graphics by the vector {10,20}.
Show[ RotateGraphics[graph, -Pi/3], Axes->False]
Rotate the graphics counterclockwise about the origin.
Show[ ScaleGraphics[graph, {2,1}], Axes->False]
Scale the graphics in the horizontal direction by a factor of 2.
graph = Plot3D[ Sin[x y], {x,0,2},{y,0,2}]
This creates a three-dimensional plot.
Show[ ScaleGraphics[graph, {1,2,3}]]
Scale the plot in the y and z directions by factors of 2 and 3 respectively.
The transformation functions will work with any expression and will affect only graphics objects and graphics primitives which are the expression itself, elements of a List, or elements of a nested List. This is useful when transforming graphics primitives that are not already within Graphics or Graphics3D graphics objects.
TranslateGraphics[{Line[{{0,0},{1,2}}],
PointSize[0.01], Point[{1,1,1}]}, {1,0,7}]
Only the graphics primitives Line and Point are affected by the translation. Note that you can even apply the translation to an expression that contains both two and three-dimensional graphics primitives.
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TakeGraphics[g, {{xmin, ymin},{xmax, ymax}}] extract all graphics primitives in the two-dimensional graphics object g within the rectangular region {{xmin,ymin},{xmax,ymax}}
TakeGraphics[g, {{xmin,ymin,zmin},{xmax,ymax,zmax}}] extract all graphics primitives in the three-dimensional graphics object g within the cube {{xmin,ymin,zmin},{xmax,ymax,zmax}}
DropGraphics[g, {{xmin,ymin},{xmax,ymax}}] remove all graphics primitives in the two-dimensional graphics object g within the rectangular region {{xmin,ymin},{xmax,ymax}}
DropGraphics[g, {{xmin,ymin,zmin},{xmax,ymax,zmax}}] remove all graphics primitives in the three-dimensional graphics object g within the cube {{xmin,ymin,zmin},{xmax,ymax,zmax}}
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Extracting and removing graphics.
graph = Plot3D[ Sin[x y], {x,-3,3},{y,-3,3}]
This creates a three-dimensional plot.
Show[ TakeGraphics[graph, {{0,0},{2,2}}]]
This extracts the graphics within the x-y region {{0,0},{2,2}} where
the default limits on z are {-Infinity,Infinity}.
Show[ DropGraphics[graph, {{0,0},{2,2}}]]
This removes the graphics from that same region. Note that SurfaceGraphics is converted to Graphics3D in order to be able to remove parts of the mesh.
option name default value
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ModifyGraphics False determines whether primitives will be broken
up or modified
RegionTest Inset method for determining when primitives are
within a region
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Options for TakeGraphics and DropGraphics.
Using the default setting of ModifyGraphics -> False insures that the original graphics primitives are not broken up in any way. The exception to this is the Line graphics primitive because one Line primitive is typically generated from a call to two-dimensional plotting functions and we would like to break this single Line primitive up even with a setting of ModifyGraphics -> False.
There are two methods for determining whether a graphics primitive is within the specified region or not. With the default setting of RegionTest -> Inset, a graphics primitive is considered within a specified region if all coordinates describing the primitive are within the region. With the setting RegionTest -> Intersect, a graphics primitive is considered within a region if at least one of the coordinates describing the primitive is within the region.
When you want more exact cuts through the graphics primitives, use ModifyGraphics -> True. In this case, most graphics primitives will be broken up exactly along the border of the region being extracted or removed,
except, for instance, in cases such as Circle, Disk and Text primitives which are never broken up. With a setting of ModifyGraphics -> True the option RegionTest is usually ignored since we are finding an exact intersection with the region boundary and do not need to test whether the entire primitive is within the region or not.
graph = Show[ Graphics[ Raster[{{0.3,0.6,0.8,0.9},{0.2,0.3,0.6,0.8},
{0.1,0.2,0.3,0.6},{0.05,0.1,0.2,0.3}}]], Axes->True]
This creates a graphics object of one Raster primitive.
Show[ DropGraphics[graph, {{1.5,1.5},{3.5,3.5}}, RegionTest->Inset]]
This shows the result of removing the graphics within the region {{1.5,1.5},{3.5,3.5}} with the default setting of RegionTest.
Show[ DropGraphics[graph, {{1.5,1.5},{3.5,3.5}}, RegionTest->Intersect]]
Notice the difference of what is removed with the same region by using the Intersect method for RegionTest.
Show[ DropGraphics[graph, {{1.5,1.5},{3.5,3.5}}, ModifyGraphics->True]]
Here is an exact removal of the specified region. In this case, the Raster primitive is converted to an equivalent list of Polygon primitives in order to get an exact removal of the region.
The graphics object DensityGraphics and the graphics primitive Raster are both represented by two-dimensional graphics. However, they both also contain information about a third dimension. For this reason, a range from the third dimension can also be extracted or removed from DensityGraphics and Raster using TakeGraphics or DropGraphics. The resulting graphics will be Polygon primitives contained in a Graphics graphics object. There is currently no option for extracting or removing a z range from ContourGraphics.
graph = Show[ Graphics[ Raster[{{0.3,0.6,0.8,0.9},{0.2,0.3,0.6,0.8},
{0.1,0.2,0.3,0.6},{0.05,0.1,0.2,0.3}}]], Axes->True]
This creates a graphics object of one Raster primitive.
Show[ TakeGraphics[graph, {{-Infinity,-Infinity,-Infinity},
{Infinity, Infinity, 0.5}}]]
This shows the result of taking the graphics within the z range {-Infinity,0.5}.
graph = DensityPlot[ Sin[x y], {x,-3,3}, {y,-3,3}]
This creates a DensityGraphics graphics object.
Show[ TakeGraphics[graph, {{-Infinity,-Infinity,-Infinity},
{Infinity,Infinity,-0.01}}]]
This shows the result of taking the cells within the z range {-Infinity,-0.01}.
Just as with the transformation functions, TakeGraphics and DropGraphics will work with any expression and will affect only graphics objects and graphics primitives which are the expression itself, elements of a List, or elements of a nested List. This is useful when working with graphics primitives that are not already within Graphics or Graphics3D graphics objects.
DropGraphics[{Line[{{0,0},{7,7}}], PointSize[0.01], Point[{1,3,1}]},
{{1,1},{4,4}}, ModifyGraphics->True]
Only the graphics primitives Line and Point are affected by DropGraphics. Note that DropGraphics cen even be applied to expressions that contain both two and three-dimensional graphics primitives.
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SliceGraphics[g, n] slice the graphics object g into n slices along the x axis
SliceGraphics[g, n, Axis->{x,y,z}] slice the graphics object g into n slices along the axis specified by the vector from the origin to the point {x,y,z}
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Slicing graphics objects.
SliceGraphics actually calls TakeGraphics and TranslateGraphics and, if necessary, RotateGraphics to create the slicing of graphics objects. Thus, SliceGraphics inherits the options of TakeGraphics.
graph = Plot[ BesselJ[2,x], {x,0,10}]
This creates a plot of a Bessel function.
Show[ SliceGraphics[graph, 4, ModifyGraphics->True]]
This breaks the plot up into 4 slices and spreads them apart. ModifyGraphics is used to make sure no line segments are lost.
option name default value
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Axis {1,0,0} axis along which the slices are taken
SliceSpacing Automatic the spacing between slices
SliceRatios Automatic the size of each individual slice
ModifyGraphics False determines whether primitives will be broken
up or modified
RegionTest Inset method for determining when primitives are
within a region
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Options for SliceGraphics.
Only the direction of the option Axis is used, and thus, only the relative magnitudes of the vector components are significant. The default values of the options SliceSpacing and SliceRatios are determined from the number of slices and the total spacial extent of all graphics primitives.
SliceSpacing -> d will evenly space the slices by a distance d. SliceSpacing -> {d_1, d_2, ...}, where {d_1, d_2, ...} is a list of length n-1 where n is the number of slices, will separate the corresponding slices by a distance d_i. SliceSpacing is measured along the direction specified by Axis. SliceRatios -> {r_1, r_2, ...}, where {r_1, r_2, ...} is a list of ratios of length n where n is the number of slices, can be used to make a set of slices with varying sizes. SliceGraphics returns a list of graphics objects representing each slice which can be displayed together using Show or acted on separately if desired. Note that SliceSpacing -> 0 can be used to get a list of slices without the side effect of translating any of the slices.
<True]]
Here we get an exact slice through the sphere using ModifyGraphics -> True, but at the expense of the time required to break up Polygon primitives.