Sets of Points, Surfaces and Solids
Implicit surface: set of all points that satisfy F(x,y,z)=0
The points that satisfy F(x,y,z)ɘ define a solid (or solids) bounded by the surface
The solid is directly defined (unlike definitions using parametric surfaces)
Example
- An infinitely long (solid) cylinder with radius r:
-
- To limit cylinder to length L, abs(z) < L/2 and keep the function implicit use max:
-
Implicit functions for a cube? Any convex polyhedron?