Procedural elements for computer graphics
Procedural elements for computer graphics
A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Ray tracing parametric surface patches utilizing numerical techniques and ray coherence
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Comparison of three curve intersection algorithms
Computer-Aided Design
Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Algorithm for algebraic curve intersection
Computer-Aided Design
Real-time rendering of trimmed surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Ray tracing parametric surfaces by subdivision in viewing plane
Theory and practice of geometric modeling
An introduction to ray tracing
An introduction to ray tracing
Tutorial: computer graphics; image synthesis
Tutorial: computer graphics; image synthesis
Fat arcs: a bounding region with cubic convergence
Computer Aided Geometric Design
On ray tracing parametric surfaces
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
An improved illumination model for shaded display
Communications of the ACM
Rendering trimmed NURBS with adaptive forward differencing
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Ray tracing parametric patches
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
An updated cross-indexed guide to the ray-tracing literature
ACM SIGGRAPH Computer Graphics
Solving polynomial systems for curve, surface and solid modeling
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Low cost illumination computation using an approximation of light wavefronts
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Method of displaying optical effects within water using accumulation buffer
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Image metamorphosis using snakes and free-form deformations
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Comparison of surface and derivative evaluation methods for the rendering of NURB surfaces
ACM Transactions on Graphics (TOG)
Display of clouds taking into account multiple anisotropic scattering and sky light
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Accelerated walkthrough of large spline models
Proceedings of the 1997 symposium on Interactive 3D graphics
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Kizamu: a system for sculpting digital characters
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Multiresolution rendering by sewing trimmed NURBS surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
Step length problem for trimming curve approximation in tessellating trimmed surfaces
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Interactive Display of Large NURBS Models
IEEE Transactions on Visualization and Computer Graphics
Ray-Tracing Triangular Trimmed Free-Form Surfaces
IEEE Transactions on Visualization and Computer Graphics
IEEE Computer Graphics and Applications
Budget sampling of parametric surface patches
I3D '03 Proceedings of the 2003 symposium on Interactive 3D graphics
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
A Scan Line Algorithm for Rendering Curved Tubular Objects
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Visualization of Optical Phenomena Caused by Multilayer Films with Complex Refractive Indices
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Target curvature driven fairing algorithm for planar cubic B-spline curves
Computer Aided Geometric Design
Interactive ray tracing of free-form surfaces
AFRIGRAPH '04 Proceedings of the 3rd international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
Computer graphics for water modeling and rendering: a survey
Future Generation Computer Systems - Special issue: Computer graphics and geometric modeling
GPU-based trimming and tessellation of NURBS and T-Spline surfaces
ACM SIGGRAPH 2005 Papers
Blind Robust Watermarking Schemes for Copyright Protection of 3D Mesh Objects
IEEE Transactions on Visualization and Computer Graphics
Robust and numerically stable Bézier clipping method for ray tracing NURBS surfaces
Proceedings of the 21st spring conference on Computer graphics
Computing roots of polynomials by quadratic clipping
Computer Aided Geometric Design
Direct evaluation of NURBS curves and surfaces on the GPU
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Real-time rendering of textures with feature curves
ACM Transactions on Graphics (TOG)
Performing efficient NURBS modeling operations on the GPU
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Subdivision methods for solving polynomial equations
Journal of Symbolic Computation
Direct trimming of NURBS surfaces on the GPU
ACM SIGGRAPH 2009 papers
Fast approach for computing roots of polynomials using cubic clipping
Computer Aided Geometric Design
A New Approach to Point Membership Classification in B-rep Solids
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
A symbolic-numerical envelope algorithm using quadratic MOS patches
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Computation of singularities and intersections of offsets of planar curves
Computer Aided Geometric Design
Single-set and class-of-sets semantics for geometric models
Computer-Aided Design
A new method for speeding up ray tracing NURBS surfaces
Computers and Graphics
Optimized GPU evaluation of arbitrary degree NURBS curves and surfaces
Computer-Aided Design
Adaptive quasi-interpolating quartic splines
Computing - Geometric Modelling, Dagstuhl 2008
Computer graphics for water modeling and rendering: a survey
Future Generation Computer Systems
Technical Section: Real-time ray casting of algebraic B-spline surfaces
Computers and Graphics
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
Surface parameterization of nonsimply connected planar Bézier regions
Computer-Aided Design
Efficient point projection to freeform curves and surfaces
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Efficient point-projection to freeform curves and surfaces
Computer Aided Geometric Design
Interactive high quality trimmed NURBS visualization using appearance preserving tessellation
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
An architecture for ray - bezier patch intersection
EGGH'93 Proceedings of the Eighth Eurographics conference on Graphics Hardware
Hybrid ray tracing and path tracing of Bezier surfaces using a mixed hierarchy
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
Virtual volume resection using multi-resolution triangular representation of B-spline surfaces
Computer Methods and Programs in Biomedicine
A second order geometric method for ray/parametric surface intersection
Computer Aided Geometric Design
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This paper presents a new algorithm for computing the points at which a ray intersects a rational Bézier surface patch, and also an algorithm for determining if an intersection point lies within a region trimmed by piecewise Bézier curves. Both algorithms are based on a recent innovation known as Bézier clipping, described herein. The intersection algorithm is faster than previous methods for which published performance data allow reliable comparison. It robustly finds all intersections without requiring special preprocessing.