An algorithm for piecewise linear approximation of implicitly defined two-dimensional surfaces
SIAM Journal on Numerical Analysis
Polygonization of implicit surfaces
Computer Aided Geometric Design
Hermite interpolation of rational space curves using real algebraic surfaces
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Bounded aspect ration triangulation of smooth solids
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Implicit representation of rational parametric surfaces
Journal of Symbolic Computation
Modeling arbitrary smooth objects with algebraic surfaces
Modeling arbitrary smooth objects with algebraic surfaces
Cubicoids: Modeling and visualization
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
Surface approximations in geometric modeling
Surface approximations in geometric modeling
A relational model for interactive manipulation of form features based on algebraic geometry
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Function representation for sweeping by a moving solid
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
The 3L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mathematical Methods for Curves and Surfaces
Towards the &mgr;-basis of a rational surface
Mathematical Methods for Curves and Surfaces
A new implicit representation of a planar rational curve with high order singularity
Computer Aided Geometric Design
Function Representation for Sweeping by a Moving Solid
IEEE Transactions on Visualization and Computer Graphics
Elimination and Resultants - Part 1: Elimination and Bivariate Resultants
IEEE Computer Graphics and Applications
Implicitization of Parametric Curves by Matrix Annihilation
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Approximate implicitization via curve fitting
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
The Classical Theory of Invariants and Object Recognition Using Algebraic Curve and Surfaces
Journal of Mathematical Imaging and Vision
Interval implicitization of rational curves
Computer Aided Geometric Design
Efficient Groebner walk conversion for implicitization of geometric objects
Computer Aided Geometric Design
Implicit curve and surface design using smooth unit step functions
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Lines of curvature and umbilical points for implicit surfaces
Computer Aided Geometric Design
Efficient Groebner walk conversion for implicitization of geometric objects
Computer Aided Geometric Design
Approximate implicitization of triangular Bézier surfaces
Proceedings of the 26th Spring Conference on Computer Graphics
Interval implicitization of parametric surfaces
ICICA'10 Proceedings of the First international conference on Information computing and applications
Computing curve intersection by homotopy methods
Journal of Computational and Applied Mathematics
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The role of implicit curves and surfaces in computer-aided geometric design (CAGD) are described. The ways in which the study of implicit algebraic curves and surfaces draws on algebraic geometry are reviewed. The implicitization of parametric curves and surfaces, parameterization of implicits, and techniques used to circumvent conversions between implicit and parametric representations are discussed.