Chapter 2: Operations on Polynomial Curves and Surfaces
نویسندگان
چکیده
1 Plane Curves 2 1.1 Computation of Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Expansion at Simple Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2 Expansion at Singular Points . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.3 Newton Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.4 Local Parametrization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.5 C1 Continuous Padé Approximation . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.6 The Computation of the Singularity . . . . . . . . . . . . . . . . . . . . . . . 11 1.1.7 Implementation Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.2 Newton Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Rational Curve Hermite Interpolation between Simple Points . . . . . . . . . . . . . 15 1.4 Rational B-spline Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.5 Isolating the Singular Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.6 The Local Approximation at Singular Points . . . . . . . . . . . . . . . . . . . . . . 21
منابع مشابه
Chapter 3: Piecewise Polynomial Curves and Surfaces (Finite Elements)
1 Piecewise Polynomials 2 1.1 Barycentric and Bernstein-Bézier Bases . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 B-Spline Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Trimmed Freeform Patches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Implicit Algebraic Surface Patches . . . . . . . . . . . . . . . . . . . . . ....
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