Making the Oslo algorithm more efficient
SIAM Journal on Numerical Analysis
Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Curved surfaces and coherence for non-penetrating rigid body simulation
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The NURBS book
An efficient surface intersection algorithm based on lower-dimensional formulation
ACM Transactions on Graphics (TOG)
Direct haptic rendering of sculptured models
Proceedings of the 1997 symposium on Interactive 3D graphics
3D scan conversion of CSG models into distance volumes
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Geometric modeling with splines: an introduction
Geometric modeling with splines: an introduction
Robot Motion Planning
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
Mold Accessibility via Gauss Map Analysis
SMI '04 Proceedings of the Shape Modeling International 2004
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Contouring 1- and 2-Manifolds in Arbitrary Dimensions
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Perspective silhouette of a general swept volume
The Visual Computer: International Journal of Computer Graphics
A higher dimensional formulation for robust and interactive distance queries
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Haptic rendering of surface-to-surface sculpted model interaction
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Computing exact rational offsets of quadratic triangular Bézier surface patches
Computer-Aided Design
Intersecting a freeform surface with a general swept surface
Computer-Aided Design
Global curve analysis via a dimensionality lifting scheme
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Simultaneous precise solutions to the visibility problem of sculptured models
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Presence: Teleoperators and Virtual Environments
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In this paper, a general scheme for solving coherent geometric queries on freeform geometry is presented and demonstrated on a variety of problems common in geometric modeling. The underlying strategy of the approach is to lift the domain of the problem into a higher-dimensional space to enable analysis on the continuum of all possible configurations of the geometry. This higher-dimensional space supports analysis of changes to solution topology by solving for critical points using a B-spline-based constraint solver. The critical points are then used to guide fast, local methods to robustly update repeated queries. This approach effectively combines the speed of local updates with the robustness of global search solutions. The effectiveness of the domain lifting scheme (DLS) is demonstrated on several geometric computations, including accurately generating offset curves and finding minimum distances. Our approach requires a preprocessing step that computes the critical points, but once the topology is analyzed, an arbitrary number of geometry queries can be solved using fast local methods. Experimental results show that the approach solves for several hundred minimum distance computations between planar curves in one second and results in a hundredfold speedup for trimming self-intersections in offset curves.