Unitary Normal Vectorial Field

© 2004 Robert Ipanaqué Chero
Peruvian Applied& Computational Mathematical Society (Member),Perú
E-mail:robertchero@hotmail.com

Loading the package

Vector 3D

Show[
Graphics3D[
        Vector3D[{0, 0, 0}, {1, 1, -1}]
], 
      Boxed -> False]

Show[
      GraphicsArray[
{Map[
            Graphics3D, 
{Vector3D[{0, 0, 0}, {1, 1, 
                  1}], 
Vector3D[{0, 0, 0}, {1, 1, 1}, 
                VectorHead -> None], 
Vector3D[{0, 0, 
                  0}, {1, 1, 1}, 
                VectorHead -> Polygon], 
Vector3D[{0, 
                  0, 0}, {1, 1, 1}, VectorHead -> Polygon, 
                n -> 20]}
]}]]

Show[Graphics3D[
    Table[
    Vector3D[{0, 0, 0}, x/5 {Sin[x], Cos[x], 1/8},
    VectorHead -> Polygon,n -> 15],
   {x, 1.5, 7, .3}]
], PlotRange -> All]

Unitary Normal Vectorial Field

Unitary normal vectorial field of surfaces defined implicitly

UNVF[x^2 + y^2 - z, {x, -2, 2}, {y, -2, 2}, {z, -1, 2}, 
      Surface -> True, PlotPointsSurface -> {4, 7}, 
      VectorHead -> Polygon]

UNVF[z - x^2 + y^2, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
      Surface -> True, PlotPointsSurface -> {4, 6}, 
      PlotPointsNormalField -> {3, 
          4}, 
VectorHead -> Polygon]

UNVF[
(Sqrt[(Sqrt[x^2 + y^2] - 3)^2 + y^2] - 
              3)^2 + z^2 - 3/2, 
{x, -8, 
        8}, {y, -5, 5}, {z, -3.5, 3.5}, 
      Surface -> 
        True, 
PlotPointsSurface -> {5, 5}, 
      VectorHead -> Polygon, 
HeadLength ->  .35, 
      HeadWidth ->  .15]

UNVF[
(Sqrt[(Sqrt[(Sqrt[x^2 + y^2] - 4)^2 + 
                            x^2] - 3)^2 + x^2] - 3)^2 + z^2 - 
        3/2, 
{x, -4, 4}, {y, -12, 
        12}, {z, -3.5, 3.5}, 
      Surface -> 
        True, 
PlotPointsSurface -> {5, 6}, 
      VectorHead -> Polygon, 
HeadLength ->  .35, 
      HeadWidth ->  .15]

UNVF[
      x^4 + y^4 + z^4 - 16, {x, -2, 2}, {y, -2, 2}, {z, -2, 
        2}, 
Surface -> True, 
      VectorHead -> Polygon, 
      PlotPointsSurface -> {4, 5}, 
Boxed -> 
        False]

Unitary normal vectorial field of surfaces defined in parametric form.

UNVF2[
{u, v, 0.4*(u^2 - v^2)}, {u, -2, 
        2}, {v, -2, 2}, 
Surface -> True, 
      VectorHead -> Polygon, 
      ViewPoint -> {-0.813,  -3.137,  
          0.975}
]

UNVF2[
2*{Cos[u] + v*Cos[u]*Sin[u/2], 
          Sin[u] + v*Sin[u/2]*Sin[u], v*Cos[u/2]}
, {u, 0, 
        4*Pi, Pi/8}, {v, -0.3, 0.3, 0.2}, 
      SurfaceDom -> {{0, 2*Pi}, {-1/2, 1/2}}, Surface -> True, 
      PlotPoints -> {40, 2}, VectorHead -> Polygon, 
      HeadLength -> 0.25, 
HeadWidth -> 
        0.1
]