Mathematical methods for CAD
As computers become the mainstay of most engineering design practices, there has been a growing interest in the theory of computational geometry and computer aided design.
196 pages : illustrations (some color) ; 24 cm
9780521431002, 9780521436915, 052143100X, 0521436915
26766106
Ch. 1. B-splines. 1.1. Piecewise polynomial functions. 1.2. An example: Cubic splines. 1.3. B-splines: Fundamental properties. 1.4. The B-spline basis of P[subscript k, [tau], r]. 1.5. Basic Algorithms for B-splines. 1.6. Approximation by a spline curve. 1.7. Divided differences
Ch. 2. Spline curves and Bezier curves. 2.1. Bernstein polynomials. 2.2. B-spline curves. 2.3. Algorithms for spline curves
Ch. 3. Interpolation and complements. 3.1. Interpolation. 3.2. Other properties of the matrix N. 3.3. Matrix representation. 3.4. Junction between two curves. 3.5. Rational curves
Ch. 4. Spline Surfaces. 4.1. Tensor products. 4.2. Particular case of Bezier surfaces. 4.3. Interpolation and approximation. 4.4. Bernstein polynomials. 4.5. Triangular Bezier patches. 4.6. Junction between Bezier patches. 4.7. Base points of rational Bezier patches. 4.8. Polyhedral splines. 4.9. Box splines
Ch. 5. Triangulations. 5.1. Voroni diagram. 5.2. Generalities about triangulations. 5.3. Delaunay triangulations. 5.4. Construction Algorithm. 5.5. Remarks about complexity
Ch. 6. Notions of real algebraic geometry. 6.1. Roots of one variable polynomials. 6.2. Resultants and discriminants. 6.3. Notions of semi-algebraic sets