Recently I had the chance to look at Viewpoint in Graphics3D more closely. Instead of Cartesian coordinates X, Y, Z , it seems more natural for a photographer to use the cylindrical coordinate system of radius, angle and height. Below is the geometry for Cylindrical Coordinate r=2, theta= 45 Degree, z = 1 1/2:
p = {2 Cos[45 Degree], 2 Sin[45 Degree], 1 + 1/2};
Graphics3D[ {
Opacity[.05], Green, Cuboid[{-2, -2, -2}, {2, 2, 2}],
(*object*)
Opacity[1], Yellow,
PolyhedronData["Dodecahedron", "GraphicsComplex"],
Opacity[.15], Blue, Cuboid[{-1, -1, -1}, {1, 1, 1}],
(*cylinder*)
Opacity[.35], Green, EdgeForm[{Thick, Black}],
Cylinder[{{0, 0, -2}, {0, 0, 2}}, 2], Opacity[0], White,
Cylinder[{{0, 0, -2}, {0, 0, 0}}, 2],
(*ViewPoint*)
Opacity[1], Black, Arrow[{p, {0, 0, 0}}],
(*Guides0: Plane, Points,Arrow,Circle*)
Opacity[.90], Gray, Polygon[{{0, 0, 0}, {p[[1]], p[[2]], 0}, p}],
Polygon[{{2, 2, 0}, {2, -2, 0}, {-2, -2, 0}, {-2, 2, 0}}],
Opacity[.0], White, EdgeForm[{Thick, Red}],
Cylinder[{{0, 0, p[[3]] - .01}, {0, 0, p[[3]]}}, 2],
Opacity[1], Red, PointSize[Large], Point[p],
Point[{p[[1]], p[[2]], 0}],
Inset[Style[
"ViewPoint-> Cylindrical Coordinate r=2,\[Theta] = 45°,z=1 1/2",
12], p + {0, 0, .1}], Inset["{2,2,2}", {2, 2, 2}],
Inset["{-2,-2,-2}", {-2, -2, -2}]}, ImageSize -> 1080*4/8,
Boxed -> False]
The conversion is fairly straight forward with r and z both limited to -2 and 2 and angle 0 to 2Pi.
ViewPoint->{ r Cos[theta], r Sin[theta], z}
To fix the view in an lazy susan rotation animation to eliminate view resizing, ViewAngle can be added:
pt[\[Theta]_] := {2 Cos[\[Theta]], 2 Sin[\[Theta]], 2}
Manipulate[Graphics3D[ {
Opacity[.05], Green, Cuboid[{-2, -2, -2}, {2, 2, 2}],
(*object*)
Opacity[1], Yellow,
PolyhedronData["Dodecahedron", "GraphicsComplex"],
Opacity[.15], Blue, Cuboid[{-1, -1, -1}, {1, 1, 1}],
(*cylinder*)
Opacity[.35], Green, EdgeForm[{Thick, Black}],
Cylinder[{{0, 0, -2}, {0, 0, 2}}, 2], Opacity[0], White,
Cylinder[{{0, 0, -2}, {0, 0, 0}}, 2]
(*ViewPoint*),
Opacity[1], Black, Arrow[{p, {0, 0, 0}}],
(*Guides0: Plane, Points,Arrow,Circle*)
Opacity[.90], Gray, Polygon[{{0, 0, 0}, {p[[1]], p[[2]], 0}, p}],
Polygon[{{2, 2, 0}, {2, -2, 0}, {-2, -2, 0}, {-2, 2, 0}}],
Opacity[.0], White, EdgeForm[{Thick, Red}],
Cylinder[{{0, 0, p[[3]] - .01}, {0, 0, p[[3]]}}, 2],
Opacity[1], Red, PointSize[Large], Point[p],
Point[{p[[1]], p[[2]], 0}],
Inset[
Style["ViewPoint-> Cylindrical Coordinate r=2,\[Theta] = 45°,z=1 \
1/2", 12], p + {0, 0, .1}], Inset["{2,2,2}", {2, 2, 2}],
Inset["{-2,-2,-2}", {-2, -2, -2}]}, ImageSize -> 1080*4/8,
Boxed -> False, ViewAngle -> 35 Degree, ViewPoint -> pt[t]], {t, 0,
2 Pi, .005}]
