A smooth model of Boy's surface using simple pieces
Most meshes are built with ad hoc C++ programs and/or using Blender. The scene is usually set up with Blender. Rendering is done with Luxrender for low resolution, and with Blender/Cycles for high resolution versions.
Hi-res pictures are attached as “source” files for the images, and a few supplementary high resolution pictures can be found in the Files section.
More on Boy’s surface: http://www. math.univ-toulouse.fr/~cheritat/boy-surface/index.html
Pieces for Boy's surface
All pieces here are parts of either:
- a sphere
that have been cut by intersecting with planes or cylinders.
They can be assembled to make a model of Boy’s surface.
A CSG model of Boy's surface
It is possible to make a smooth* model of Boy’s surface with simple primitives using Constructive Solid Geometry (CSG)
*: there is a tangent everywhere, and it varies continuously** with the point.
**: the modulus of continuity of the normal with respect to its base is Lipschitz: we have a C1+Lip surface.
The blue piece is part of a sphere, cut by cylinders and rectangles. It is quite a miracle that it smoothly fits to close the surface.
For this, I had to build a seamless mesh. I had to desing a specific C++ program, which was time consuming. Perhaps there is a faster way using CAD software.