On algebraic surfaces meeting with geometric continuity
On algebraic surfaces meeting with geometric continuity
The approximation of non-degenerate offset surfaces
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
Computer Aided Geometric Design
Polygonization of implicit surfaces
Computer Aided Geometric Design
Proceedings on Mathematics of surfaces II
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Computer Aided Geometric Design
Algebraic surface design with Hermite interpolation
ACM Transactions on Graphics (TOG)
Surface fitting using implicit algebraic surface patches
Topics in surface modeling
Smoothing polyhedra using implicit algebraic splines
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
On surface design with implicit algebraic surfaces
On surface design with implicit algebraic surfaces
Collaborative multimedia scientific design in SHASTRA
MULTIMEDIA '93 Proceedings of the first ACM international conference on Multimedia
Surfaces: Techniques for Cubic Algebraic Surfaces
IEEE Computer Graphics and Applications
Techniques for Cubic Algebraic Surfaces
IEEE Computer Graphics and Applications
Geometric Modeling with Algebraic Surfaces
Proceedings of the 3rd IMA Conference on the Mathematics of Surfaces
Geometric continuity: a parametrization independent measure of continuity for computer aided geometric design (curves, surfaces, splines)
Using particles to sample and control implicit surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Fitting Curves and Surfaces With Constrained Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognizing 3D Objects Using Tactile Sensing and Curve Invariants
Journal of Mathematical Imaging and Vision
A survey of methods for recovering quadrics in triangle meshes
ACM Computing Surveys (CSUR)
Approximate implicitization via curve fitting
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
G2 Blending of Corners with Piecewise Algebraic Surfaces
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Topologically Faithful Fitting of Simple Closed Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing all parametric solutions for blending parametric surfaces
Journal of Symbolic Computation
Stable Fitting of 2D Curves and 3D Surfaces by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Aided Geometric Design
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
Using particles to sample and control implicit surfaces
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
Computer Aided Geometric Design
Automated freehand sketch segmentation using radial basis functions
Computer-Aided Design
Parallel algorithm for landform attributes representation on multicore and Multi-GPU systems
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
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In this article, we characterize the solution space of low-degree, implicitly defined, algebraic surfaces which interpolate and/or least-squares approximate a collection of scattered point and curve data in three-dimensional space. The problem of higher-order interpolation and least-squares approximation with algebraic surfaces under a proper normalization reduces to a quadratic minimization problem with elegant and easily expressible solutions. We have implemented our algebraic surface-fitting algorithms, and included them in the distributed and collaborative geometric environment SHASTRA. Several examples are given to illustrate how our algorithms are applied to algebraic surface design.