Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implicit Curves and Surfaces in CAGD
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Approximate implicitization using monoid curves and surfaces
Graphical Models and Image Processing
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Mathematical Methods for Curves and Surfaces
Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains
Computer Aided Geometric Design
Approximate implicitization via curve fitting
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Approximate algebraic methods for curves and surfaces and their applications
Proceedings of the 21st spring conference on Computer graphics
Weak Approximate Implicitization
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Implicitization of curves and (hyper)surfaces using predicted support
Theoretical Computer Science
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We discuss how Dokken's methods of approximate implicitization can be applied to triangular Bézier surfaces in both the original and weak forms. The matrices D and M that are fundamental to the respective forms of approximate implicitization are shown to be constructed essentially by repeated multiplication of polynomials and by matrix multiplication. A numerical approach to weak approximate implicitization is also considered and we show that symmetries within this algorithm can be exploited to reduce the computation time of M. Explicit examples are presented to compare the methods and to demonstrate properties of the approximations.