Surface algorithms using bounds on derivatives
Computer Aided Geometric Design
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Factoring a homogeneous transformation for a more efficient graphics pipeline
Computer Graphics Forum
A marching method for parametric surface/surface intersection
Computer Aided Geometric Design
Vector models for data-parallel computing
Vector models for data-parallel computing
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Surface-to-Surface Intersections
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
The NURBS book
An efficient surface intersection algorithm based on lower-dimensional formulation
ACM Transactions on Graphics (TOG)
On ray tracing parametric surfaces
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Practical ray tracing of trimmed NURBS surfaces
Journal of Graphics Tools
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Ray tracing on programmable graphics hardware
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
IEEE Computer Graphics and Applications
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Photon mapping on programmable graphics hardware
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
UberFlow: a GPU-based particle engine
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Hardware-based simulation and collision detection for large particle systems
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
GPU Gems 2: Programming Techniques for High-Performance Graphics and General-Purpose Computation (Gpu Gems)
Resolution independent curve rendering using programmable graphics hardware
ACM SIGGRAPH 2005 Papers
GPU-based trimming and tessellation of NURBS and T-Spline surfaces
ACM SIGGRAPH 2005 Papers
Fast GPU ray tracing of dynamic meshes using geometry images
GI '06 Proceedings of Graphics Interface 2006
Direct evaluation of NURBS curves and surfaces on the GPU
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Scan primitives for GPU computing
Proceedings of the 22nd ACM SIGGRAPH/EUROGRAPHICS symposium on Graphics hardware
Accelerating geometric queries using the GPU
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
A comparison of sampling strategies for computing general sweeps
Computer-Aided Design
Accurate moment computation using the GPU
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Accurate GPU-accelerated surface integrals for moment computation
Computer-Aided Design
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We present algorithms for evaluating and performing modeling operatyons on NURBS surfaces using the programmable fragment processor on the Graphics Processing Unit (GPU). We extend our GPU-based NURBS evaluator that evaluates NURBS surfaces to compute exact normals for either standard or rational B-spline surfaces for use in rendering and geometric modeling. We build on these calculations in our new GPU algorithms to perform standard modeling operations such as inverse evaluations, ray intersections, and surface-surface intersections on the GPU. Our modeling algorithms run in real time, enabling the user to sketch on the actual surface to create new features. In addition, the designer can edit the surface by interactively trimming it without the need for re-tessellation. We also present a GPU-accelerated algorithm to perform surface-surface intersection operations with NURBS surfaces that can output intersection curves in the model space as well as in the parametric spaces of both the intersecting surfaces at interactive rates.