N-sided patches with B-spline boundaries

Autor:	M. Vigo-Anglada, N. Pla-Garcia, J. Cotrina-Navau
Rok vydání:	2006
Předmět:	Surface (mathematics) B-spline Mathematical analysis General Engineering Regular polygon Boundary (topology) Geometry Computer Graphics and Computer-Aided Design Human-Computer Interaction Computer Science::Graphics Parametric surface Piecewise De Boor's algorithm Knot (mathematics) Mathematics
Zdroj:	Computers & Graphics. 30:959-970
ISSN:	0097-8493
DOI:	10.1016/j.cag.2006.05.001
Popis:	We present a method for constructing an n-sided patch of parametric surface, with n greater than 2. The main property of the resulting patch is that its boundary coincides with a B-spline. Thus, it can easily be connected to given B-spline surfaces with fixed continuity conditions. The patch is built from a star-shaped input mesh that outlines a generic n-hole and a surface in a vicinity of the hole. The main advantages of the method are the following: continuity conditions of arbitrary order k can be imposed; the mesh involved can have an arbitrary number of sides and an arbitrary shape (convex or not); the simplicity of the construction process makes it an easy and flexible method; and finally, the surface near the boundary is a B-spline with piecewise uniform knot sequences and whose control points are vertices of the mesh (both knot sequences and control points are easily computed). We give implementation details for evaluating a surface point and show that the de Boor algorithm can be exploited for efficiency.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b3840a67afaf61efc4e2149f2eafcacb https://doi.org/10.1016/j.cag.2006.05.001 Zobrazit plný text záznamu Full Text from ScienceDirect