To project a surface or a solid in geometric modeling is a much more difficult problem than to project points and line segments in computer graphics. The result of this operation in FRep is an object of the lower dimension with its own defining function. We have compared the following approaches: analytical methods, approximate projections and global maximum searches. There are several applications:

• 3D solid projection onto a 2D plane (pictures below);
• 4D to 3D projection for sweeping by a moving solid ;
• 3D reconstruction from the medial axis (picture above).

3D to 2D

The projection operation with F-rep is described in the paper:

Pasko A.A., Savchenko V.V. “Projection operation for multidimensional geometric modeling with real functions”, Theory and Practice of Geometric Modeling, Blaubeuren II conference, W. Strasser (Ed.), October 14-18, 1996, Tuebingen, Germany.
Electronic version: PostScript + gzip (170K)