Computing the extreme distances between two convex polygons
Journal of Algorithms
Surface algorithms using bounds on derivatives
Computer Aided Geometric Design
Vector models for data-parallel computing
Vector models for data-parallel computing
Hidden curve removal for free form surfaces
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Comprehensible rendering of 3-D shapes
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
An efficient surface intersection algorithm based on lower-dimensional formulation
ACM Transactions on Graphics (TOG)
Spatialized normal come hierarchies
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Fast and simple 2D geometric proximity queries using graphics hardware
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Haptic rendering of surface-to-surface sculpted model interaction
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
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
Performing efficient NURBS modeling operations on the GPU
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Patterns for parallel programming
Patterns for parallel programming
Computing the minimum distance between a point and a NURBS curve
Computer-Aided Design
Some techniques for shading machine renderings of solids
AFIPS '68 (Spring) Proceedings of the April 30--May 2, 1968, spring joint computer conference
Performing Efficient NURBS Modeling Operations on the GPU
IEEE Transactions on Visualization and Computer Graphics
Spline surface intersections optimized for GPUs
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Accurate moment computation using the GPU
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Heterogeneous spline surface intersections
Proceedings of the 26th Spring Conference on Computer Graphics
GPU-accelerated Hausdorff distance computation between dynamic deformable NURBS surfaces
Computer-Aided Design
Accurate GPU-accelerated surface integrals for moment computation
Computer-Aided Design
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We present practical algorithms for accelerating geometric queries on models made of NURBS surfaces using programmable Graphics Processing Units (GPUs). We provide a generalized framework for using GPUs as co-processors in accelerating CAD operations. By attaching the data corresponding to surface-normals to a surface bounding-box structure, we can calculate view-dependent geometric features such as silhouette curves in real time. We make use of additional surface data linked to surface bounding-box hierarchies on the GPU to answer queries such as finding the closest point on a curved NURBS surface given any point in space and evaluating the clearance between two solid models constructed using multiple NURBS surfaces. We simultaneously output the parameter values corresponding to the solution of these queries along with the model space values. Though our algorithms make use of the programmable fragment processor, the accuracy is based on the model space precision, unlike earlier graphics algorithms that were based only on image space precision. In addition, we provide theoretical bounds for both the computed minimum distance values as well as the location of the closest point. Our algorithms are at least an order of magnitude faster than the commercial solid modeling kernel ACIS.