I recently discovered a very beautiful Steiner surface which is owned by the Whitney Museum of American Art in New York City. It was created in 1970 by Ruth Landshoff Vollmer (1903 - 1982), a German-born conceptual artist who was forced to emigrate to the United States in 1935.
Ruth Vollmer, Steiner Surface, 1970, (26.7 × 30.2 × 29.5 cm)
Reproduction attempt
steiner = {Cos[u] Sin[u] Sin[v]^2, Cos[u] Cos[v] Sin[v], Sin[u] Cos[v] Sin[v]};
hull =
ParametricPlot3D[steiner, {u, 0, 2 Pi}, {v, 0, Pi/2},
Lighting -> "Accent",
Mesh -> 0,
PlotPoints -> 32,
PlotStyle -> MaterialShading[{"Glazed", RGBColor[0.75, 0.75, 0.75, 0.25]}]];
mesh =
ParametricPlot3D[steiner, {u, 0, 2 Pi}, {v, 0, Pi/2},
ColorFunction -> (Gray &),
Mesh -> {3, 2},
MeshStyle -> Tube[0.0075],
PlotPoints -> 64,
PlotStyle -> None];
Framed @ Show[
hull,
mesh,
Axes -> False,
Boxed -> False,
ViewAngle -> 40 Degree,
ViewPoint -> {1, 1, 0}]
The above hull is transparent and shows some reflections, but it is also flat and not very glass-like. My next step was to add a floor and two walls as well as directional lights to create a certain depth:
walls =
Table[
Graphics3D[{GrayLevel[0.9],
GeometricTransformation[
Polygon[{{-1, -1, -0.5}, {-1, 1, -0.5}, {1, 1, -0.5}, {1, -1, -0.5}}],
{RotationMatrix[Pi/2, w], {0, 0, 0}}]}],
{w, {{-1, 0, 0}, {0, 1, 0}, {0, 0, 1}}}];
Framed @ Show[
hull,
mesh,
walls,
Axes -> False,
Boxed -> False,
Lighting -> {
{"Directional", Orange, ImageScaled[{1, -0.5, 1}]},
{"Directional", Gray, ImageScaled[{-1, -0.5, 1}]},
{"Directional", Gray, ImageScaled[{0, 1, 1}]},
{"Ambient", GrayLevel[0.2]}},
ViewAngle -> 40 Degree,
ViewPoint -> {1, 1, 0}]
A certain improvement, but still far from showing a "glassy volume".
Question
I am aware of the fact that Mathematica
has very limited ray-tracing capabilities. On the other hand I think that my above reproduction attempt could be significantly improved. What are your ideas to produce a volumetric acrylic surface?