Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Smooth piecewise quadric surfaces
Mathematical methods in computer aided geometric design
Be´zier representation for quadric surface patches
Computer-Aided Design - Special Issue: Be´zier Techniques
Constructing easily invertible Be´zier surfaces that parameterize general quadrics
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
NURB curves and surfaces: from projective geometry to practical use
NURB curves and surfaces: from projective geometry to practical use
Weighted radial displacement: a geometric look at Bézier conics and quadrics
Computer Aided Geometric Design
Piecewise Quadratic Approximations on Triangles
ACM Transactions on Mathematical Software (TOMS)
Rational Quadratic Bézier Triangles on Quadrics
CGI '98 Proceedings of the Computer Graphics International 1998
Computer Aided Geometric Design
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An algorithm for constructing arbitrary parametric quadratic quadric triangles in rational Bézier form is presented. The algorithm does not require the knowledge of the underlying quadric, an important property in view of applying this method for the interpolation of triangulated 3D data points. The algorithm consists of four steps starting with the arbitrary choice of the three corner points and corner weights of the patch, by then constructing a certain triangle and a tetrahedron by means of which the: remaining inner control points and weights are obtained guaranteeing the resulting patch to lie on a quadric surface.