InhaltsangabePreface Chapter 1: Introduction PART I: ALGEBRA Chapter 2: Preamble Chapter 3: Polynomials Chapter 4: Complex numbers Chapter 5: Quaternions Chapter 6: Clifford algebra PART II: GEOMETRY Chapter 7: Coordinate systems Chapter 8: Differential geometry Chapter 9: Algebraic geometry Chapter 10: Non-Euclidean geometry PART III: COMPUTER-AIDED GEOMETRIC DESIGN Chapter 11: The Bernstein basis Chapter 12: Numerical stability Chapter 13: Bezier curves and surfaces Chapter 14: C^2 cubic spline curves Chapter 15: Spline basis functions PART IV: PLANAR PYTHAGOREAN-HODOGRAPH CURVES Chapter 16: Arc-length parameterization Chapter 17: Pythagorean-hodograph curves Chapter 18: Tschirnhausen's cubic Chapter 19: Complex representation Chapter 20: Rational Pythagorean-hodograph curves PART V: SPATIAL PYTHAGOREAN-HODOGRAPH CURVES Chapter 21: Pythagorean hodographs in R^3 Chapter 22: Quaternion representation Chapter 23: Helical polynomial curves Chapter 24: Minkowski Pythagorean hodographs PART VI: ALGORITHMS Chapter 25: Planar Hermite interpolants Chapter 26: Elastic bending energy Chapter 27: Planar C^2 PH quintic splines Chapter 28: Spatial Hermite interpolants PART VII: APPLICATIONS Chapter 29: Real-time CNC interpolators Chapter 30: Rotation-minimizing frames Chapter 31: Closure References Index

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Preface Chapter 1: Introduction PART I: ALGEBRA Chapter 2: Preamble Chapter 3: Polynomials Chapter 4: Complex numbers Chapter 5: Quaternions Chapter 6: Clifford algebra PART II: GEOMETRY Chapter 7: Coordinate systems Chapter 8: Differential geometry Chapter 9: Algebraic geometry Chapter 10: Non-Euclidean geometry PART III: COMPUTER-AIDED GEOMETRIC DESIGN Chapter 11: The Bernstein basis Chapter 12: Numerical stability Chapter 13: Bezier curves and surfaces Chapter 14: C^2 cubic spline curves Chapter 15: Spline basis functions PART IV: PLANAR PYTHAGOREAN-HODOGRAPH CURVES Chapter 16: Arc-length parameterization Chapter 17: Pythagorean-hodograph curves Chapter 18: Tschirnhausen''s cubic Chapter 19: Complex representation Chapter 20: Rational Pythagorean-hodograph curves PART V: SPATIAL PYTHAGOREAN-HODOGRAPH CURVES Chapter 21: Pythagorean hodographs in R^3 Chapter 22: Quaternion representation Chapter 23: Helical polynomial curves Chapter 24: Minkowski Pythagorean hodographs PART VI: ALGORITHMS Chapter 25: Planar Hermite interpolants Chapter 26: Elastic bending energy Chapter 27: Planar C^2 PH quintic splines Chapter 28: Spatial Hermite interpolants PART VII: APPLICATIONS Chapter 29: Real-time CNC interpolators Chapter 30: Rotation-minimizing frames Chapter 31: Closure References Index