The most convenient numerical method for defining surfaces is by bipararnetric vectors. The paper describes the conditions for ensuring second order continuity. A second definition of continuity is given which provides a mathematical generalization to order n between two surface patches.
Nonrectangular surface patches with curvature continuity
β Scribed by A.K. Jones
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 899 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0010-4485
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β¦ Synopsis
Nonrectangular surface patches with curvature
continuity
A K Jones
An n-sided region can be decomposed into n rectangles, all meeting at a common vertex. For odd n, derivative data can be defined for each rectangular patch at the common vertex that allows continuity of tangent planes and, optionally, normal curvatures between all n rectangles. For tangent plane continuity, the resulting patches are biquintic; [or curvature continuity, biseptic.
π SIMILAR VOLUMES
Necessary and sufficient conditions for geometric C 7 continuity (GC 7) that cover all the four combinations between rectangular and triangular B6zier surface patches are presented. Further, some more practical sufficient conditions are developed. The GC ~ conditions in several special cases might b
The method offers a free choice of a tangent direction, two derivatives, and a curvature at each interpolation point. This flexibility can be achieved by constructing two cubic seoments for each adjacent pair of vertices. The method is also compared with other local schemes for curve construction.
Cu rvatu re-co nti n uous extensions for rational B-spline curves and surfaces