Projection operation

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 F-rep 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)

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