Bézier Representation

Curves



Bernstein Polynomials
cf. Section 2.1 (PBP'99)
Basis functions for polynomial curves in
Bézier Representation
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Degree elevation
cf. Section ? (PBP'99)
Degree elevation and approximative reduction
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Polynomial Curves
cf. Section 2.2/2.3 (PBP'99)
Bézier representation of polynomial curves and
evaluation with the de Casteljau algorithm.
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Rational Curves
cf. Section 22.7 (BP'94)
Bézier representation of polynomial curves and
evaluation with the de Casteljau algorithm.
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Conics
cf. Sections 14.5 and 22.7 (BP'94)
Conics as special rational curves.
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BSpline Representation

Curves



BSplines
cf. Sections 5.2/5.3 (PBP'99)
Piecewise polynomial functions  basis functions for
polynomial spline curves.
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Spline Curves
cf. Section 5.1 (PBP'99)
Piecewise polynomial curves in Bspline
representation.
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De Boor Scheme
cf. Section 5.4(PBP'99)
Evaluation of a polynomial spline curve by de Boor's algorithm.
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Spline Division
cf. Section 6.1 (PBP'99)
Subdivision of a spline curve into two independent parts.
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BSpline Rendering
cf. Sections 6.1/8.2 (PBP'99)
Visualization of the curve by its subdivided control polygon.
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BSpline Knot Refinement
cf. Section 6.3 (PBP'99)
Knot insertion for Bspline curves.
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Subdivision algorithm of Lane and Riesenfeld
cf. Section 8.2 (PBP'99)
An uniform subdivision algorithm corresponding to
uniform Bsplines.
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Differential geometry

Curves



Polynomial Curves
cf. Sections 30.130.3 (BP'94)
Polynomial curves with Frenet Frame, circle of
curvature, parallels, tangents and evolutes.
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Spline Curves
cf. Sections 30.130.3 (BP'94)
Polynomial spline curves with Frenet Frame, circle of
curvature, parallels, tangents and evolutes  higher order
discontinuities can be observed.
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Space curves
Space curves with Frenet Frame, circle of
curvature and other geometric properties.
cf. Section 30.130.3 (BP'94)
Space curves
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