An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
Box splines
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Rational ruled surfaces and their offsets
Graphical Models and Image Processing
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
The Types of Triangular Bézier Surfaces
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Computing the Minkowski sum of ruled surfaces
Graphical Models
Isophote Properties as Features for Object Detection
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Surfaces parametrized by the normals
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Rational hypersurfaces with rational convolutions
Computer Aided Geometric Design
Computing exact rational offsets of quadratic triangular Bézier surface patches
Computer-Aided Design
Mathematics and Computers in Simulation
On rationally supported surfaces
Computer Aided Geometric Design
Silhouette Smoothing for Real-Time Rendering of Mesh Surfaces
IEEE Transactions on Visualization and Computer Graphics
Journal of Symbolic Computation
An Isophote-Oriented Image Interpolation Method
ISCSCT '08 Proceedings of the 2008 International Symposium on Computer Science and Computational Technology - Volume 01
Support function of pythagorean hodograph cubics and G1 hermite interpolation
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
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The support function of a free-form-surface is closely related to the implicit equation of the dual surface, and the process of computing both the dual surface and the support function can be seen as dual implicitization. The support function can be used to parameterize a surface by its inverse Gauss map. This map makes it relatively simple to study isophotes (which are simply images of spherical circles) and offset surfaces (which are obtained by adding the offsetting distance to the support function). We present several classes of surfaces which admit a particularly simple computation of the dual surfaces and of the support function. These include quadratic polynomial surfaces, ruled surfaces with direction vectors of low degree and polynomial translational surfaces of bidegree (3,2). In addition, we use a quasi-interpolation scheme for bivariate quadratic splines over criss-cross triangulations in order to formulate a method for approximating the support function. The inverse Gauss maps of the bivariate quadratic spline surfaces are computed and used for approximate isophote computation. The approximation order of the isophote approximation is shown to be 2.