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11. Offset Curves and Surfaces

11.1 Introduction
- 11.1.1 Background and motivation
- 11.1.2 NC machining
- 11.1.3 Medial axis
  - 11.1.3.1 Algorithms for determining the MAT or related sets
  - 11.1.3.2 Theoretical analysis of the MAT properties
- 11.1.4 Tolerance region
11.2 Planar offset curves
- 11.2.1 Differential geometry
- 11.2.2 Classification of singularities
- 11.2.3 Computation of singularities
- 11.2.4 Approximations
11.3 Offset surfaces
- 11.3.1 Differential geometry
- 11.3.2 Singularities of offset surfaces
- 11.3.3 Self-intersection of offsets of implicit quadratic surfaces
- 11.3.4 Self-intersection of offsets of explicit quadratic surfaces
- 11.3.5 Self-intersection of offsets of polynomial parametric surface patches
- 11.3.6 Tracing of self-intersection curves
- 11.3.7 Approximations
11.4 Pythagorean hodograph
- 11.4.1 Curves
- 11.4.2 Surfaces
11.5 General offsets
11.6 Pipe surfaces
- 11.6.1 Introduction
- 11.6.2 Local self-intersection of pipe surfaces
- 11.6.3 Global self-intersection of pipe surfaces
  - 11.6.3.1 End circle to end circle global self-intersection
  - 11.6.3.2 Body to body global self-intersection
  - 11.6.3.3 End circle to body global self-intersection
  - 11.6.3.4 A necessary and sufficient condition for nonsingularity

December 2009