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Update surface_generation.nb #2

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Update surface_generation.nb #2

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25 changes: 25 additions & 0 deletions surface_generation.nb
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Original file line number Diff line number Diff line change
@@ -1 +1,26 @@
Visualize how gradients relate to surfaces
The Points (x, y, z) satisfying w = f (x, y, z) = u x^2 + v y^2 + z^2 for a particular value of w form the the surface shown. As the w varies, the surface deforms along the normals defined by the vector field
gradient f = f_x i + f_y j + f_z k
represented by the arrows.

S1[u_, v_, w_] :=
S1[u, v, w] =
ContourPlot3D[
u*x^2 + v*y^2 + z^2 == w, {x, -3, 3}, {y, -3, 3}, {z, -3, 3},
Boxed -> False, Axes -> False]

S2[u_, v_] :=
S2[u, v] =
VectorPlot3D[{u*2 x, v*2 y, 2 z}, {x, -3, 3}, {y, -3, 3}, {z, -3,
3}, Boxed -> False, Axes -> False]

Manipulate[
Show[{S1[u, v, w], S2[u, v]}, ImageSize -> {400, 400}],
{u, -3, 3, Appearance -> "Labeled"},
{v, -3, 3, Appearance -> "Labeled"},
{w, 0, 2, Appearance -> "Labeled"},
(*the evaluation will not time out*)SynchronousUpdating -> False,
SaveDefinitions -> True]