Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
Loop detection in surface patch intersections
Computer Aided Geometric Design
Sweeping of three-dimensional objects
Computer-Aided Design
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
The bisector surface of rational space curves
ACM Transactions on Graphics (TOG)
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
IEEE Computer Graphics and Applications
Problem Reduction to Parameter Space
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Boundary Determination for Trivariate Solids
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Minimizing the distortion of affine spline motions
Graphical Models - Pacific graphics 2001
Modeling and Deformation of Arms and Legs Based on Ellipsoidal Sweeping
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Precise Voronoi cell extraction of free-form rational planar closed curves
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Selfintersections of a bézier bicubic surface
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Geometric computations in parameter space
Proceedings of the 21st spring conference on Computer graphics
The convex hull of freeform surfaces
Computing - Geometric modelling dagstuhl 2002
Complete subdivision algorithms, I: intersection of Bezier curves
Proceedings of the twenty-second annual symposium on Computational geometry
Computing roots of polynomials by quadratic clipping
Computer Aided Geometric Design
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Sliding windows algorithm for B-spline multiplication
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Minimum distance between two sphere-swept surfaces
Computer-Aided Design
Self-intersection detection and elimination in freeform curves and surfaces
Computer-Aided Design
Computing the Voronoi cells of planes, spheres and cylinders in R3
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Voronoi diagram computations for planar NURBS curves
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Performing efficient NURBS modeling operations on the GPU
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Topology and arrangement computation of semi-algebraic planar curves
Computer Aided Geometric Design
Computing the minimum distance between a point and a NURBS curve
Computer-Aided Design
Subdivision methods for solving polynomial equations
Journal of Symbolic Computation
Computing the minimum distance between two Bézier curves
Journal of Computational and Applied Mathematics
Fast approach for computing roots of polynomials using cubic clipping
Computer Aided Geometric Design
Computing the Voronoi cells of planes, spheres and cylinders in R3
Computer Aided Geometric Design
Computing surface offsets and bisectors using a sampled constraint solver
Proceedings of Graphics Interface 2009
Continued fraction expansion of real roots of polynomial systems
Proceedings of the 2009 conference on Symbolic numeric computation
On NURBS algorithms using tangent cones
Computer Aided Geometric Design
Tracing ridges on B-Spline surfaces
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Nonlinear systems solver in floating-point arithmetic using LP reduction
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Intersecting a freeform surface with a general swept surface
Computer-Aided Design
Precise global collision detection in multi-axis NC-machining
Computer-Aided Design
Surface self-intersection computation via algebraic decomposition
Computer-Aided Design
Extracting Principal Curvature Ridges from B-Spline Surfaces with Deficient Smoothness
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Visualizing Arcs of Implicit Algebraic Curves, Exactly and Fast
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Regularity criteria for the topology of algebraic curves and surfaces
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Hausdorff and minimal distances between parametric freeforms in R2and R3
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Critical point analysis using domain lifting for fast geometry queries
Computer-Aided Design
Theoretical Computer Science
Linear programming for Bernstein based solvers
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
GPU-based parallel solver via the Kantorovich theorem for the nonlinear Bernstein polynomial systems
Computers & Mathematics with Applications
A hybrid parallel solver for systems of multivariate polynomials using CPUs and GPUs
Computer-Aided Design
Computing medial axes of generic 3D regions bounded by B-spline surfaces
Computer-Aided Design
Tracking point-curve critical distances
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Subdivision termination criteria in subdivision multivariate solvers
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Piecewise developable surface approximation of general NURBS surfaces, with global error bounds
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Simultaneous precise solutions to the visibility problem of sculptured models
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Efficient point projection to freeform curves and surfaces
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Approximating algebraic space curves by circular arcs
Proceedings of the 7th international conference on Curves and Surfaces
Efficient point-projection to freeform curves and surfaces
Computer Aided Geometric Design
Generalized Swept Mid-structure for Polygonal Models
Computer Graphics Forum
Shortest path in a multiply-connected domain having curved boundaries
Computer-Aided Design
Minimum area enclosure and alpha hull of a set of freeform planar closed curves
Computer-Aided Design
Technical note: Modeling by composition
Computer-Aided Design
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We present a new approach to building a solver for a set of geometric constraints represented by multivariate rational functions. The constraints are formulated using inequalities as well as equalities. When the solution set has dimension larger than zero, we approximate it by fitting a hypersurface to discrete solution points. We also consider a variety of constraint solving problems common in geometric modeling. These include computing ray-traps, bisectors, sweep envelopes, and regions accessible during 5-axis machining.