Conversion from Be´zier rectangles to Be´zier triangles
Computer-Aided Design
Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations
IBM Journal of Research and Development
On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
Algorithms for polynomials in Bernstein form
Computer Aided Geometric Design
Intrinsic parametrization for approximation
Computer Aided Geometric Design
Genus of the intersection curve of two rational surface patches
Computer Aided Geometric Design
Necessary and sufficient conditions for tangent plane continuity of Be´zier surfaces
Computer Aided Geometric Design
Geometric Hermite approximation of surface patch intersection curves
Computer Aided Geometric Design
Conversion of a triangular Be´zier patch into three rectangular Be´zier patches
Computer Aided Geometric Design
On the optimal stability of the Bernstein basis
Mathematics of Computation
Approximate Boolean operations on free-form solids
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
ACM Transactions on Mathematical Software (TOMS)
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
The Mathematical Basis of the UNISURF CAD System
The Mathematical Basis of the UNISURF CAD System
Total least squares fitting of Bézier and B-spline curves to ordered data
Computer Aided Geometric Design
Implicit and parametric curves and surfaces for computer aided geometric design
Implicit and parametric curves and surfaces for computer aided geometric design
Computer Aided Geometric Design
Trimming for subdivision surfaces
Computer Aided Geometric Design
Accuracy and semantics in shape-interrogation applications
Graphical Models - Solid modeling theory and applications
ACM SIGGRAPH 2008 papers
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A scheme to approximate the trimmed surfaces defined by two tensor-product surface patches, intersecting in a smooth curve segment that extends between diametrically opposite patch corners, is formulated. The trimmed surface approximations are specified by triangular Bézier patches, whose tangent planes agree precisely with those of the tensor-product surfaces along the two sides where they coincide. Topological consistency of the two trimmed surfaces is achieved by requiring the "hypotenuse" sides of the triangular patches to be coincident. In the case of bicubic tensor-product patches and quintic triangular trimmed surface approximations, enforcing these conditions entails the solution of a linear system of 30 equations in 32 unknowns. The two remaining scalar freedoms, together with four additional free control points, are employed to enhance the accuracy and/or smoothness properties of the intersection curve and trimmed surface approximations. By means of an appropriate subdivision preprocessing, the trimmed surface scheme may be used on models described by arbitrary bicubic surface patches.