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Rida T. Farouki
I-XVI
Front matter
1-86
I / Algebra
1-8
Introduction
11-28
Preamble
29-43
Polynomials
45-60
Complex Numbers
61-77
Quaternions
79-86
Clifford Algebra
89-246
II / Geometry
89-129
Coordinate Systems
131-196
Differential Geometry
197-230
Algebraic Geometry
231-246
Non—Euclidean Geometry
249-366
III / Computer Aided Geometric Design
249-260
The Bernstein Basis
261-293
Numerical Stability
295-322
Bézier Curves and Surfaces
323-343
C 2 Cubic Spline Curves
345-366
Spline Basis Functions
369-452
IV / Planar Pythagorean-hodograph Curves
369-380
Arc—length Parameterization
381-391
Pythagorean—hodograph Curves
393-406
Tschirnhausen's Cubic
407-425
Complex Representation
427-452
Rational Pythagorean-hodograph Curves
455-519
V / Spatial Pythagorean-hodograph Curves
455-467
Pythagorean Hodographs in ℝ3
469-484
Quaternion Representation
485-506
Helical Polynomial Curves
507-519
Minkowski Pythagorean Hodographs
523-615
VI / Algorithms
523-541
Planar Hermite Interpolants
543-553
Elastic Bending Energy
555-594
Planar C 2 PH Quintic Splines
595-615
Spatial Hermite Interpolants
619-695
VII / Applications
619-660
Real—time CNC Interpolators
661-691
Rotation—minimizing Frames
693-695
Closure
697-729
Back matter
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