Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Binary partitions with applications to hidden surface removal and solid modelling
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Approximation hierarchies and S-bounds
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Delaunay based shape reconstruction from large data
PVG '01 Proceedings of the IEEE 2001 symposium on parallel and large-data visualization and graphics
Sphere-tree construction using dynamic medial axis approximation
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Dual contouring of hermite data
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Direct reconstruction of a displaced subdivision surface from unorganized points
Graphical Models - Pacific graphics 2001
Fast swept volume approximation of complex polyhedral models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Approximating and intersecting surfaces from points
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A concept for parametric surface fitting which avoids the parametrization problem
Computer Aided Geometric Design
Crest Lines for Surface Segmentation and Flattening
IEEE Transactions on Visualization and Computer Graphics
Bounding Volumes for Linearly Interpolated Shapes
CGI '04 Proceedings of the Computer Graphics International
ACM SIGGRAPH 2004 Papers
BD-tree: output-sensitive collision detection for reduced deformable models
ACM SIGGRAPH 2004 Papers
VIS '04 Proceedings of the conference on Visualization '04
An integrating approach to meshing scattered point data
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Feature-Sensitive Subdivision and Isosurface Reconstruction
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Boundary of the volume swept by a free-form solid in screw motion
Computer-Aided Design
ACM SIGGRAPH 2007 courses
Set Membership Classification: A Unified Approach to Geometric Intersection Problems
IEEE Transactions on Computers
Performing efficient NURBS modeling operations on the GPU
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Classifying points for sweeping solids
Computer-Aided Design
Approximating 3D general sweep boundary using depth-buffer
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Design and Analysis of Optimization Methods for Subdivision Surface Fitting
IEEE Transactions on Visualization and Computer Graphics
Hi-index | 0.00 |
Sweeping moving objects has become one of the basic geometric operations used in engineering design, analysis and physical simulation. Despite its relevance, computing the boundary of the set swept by a non-polyhedral moving object is largely an open problem due to well-known theoretical and computational difficulties of the envelopes. We have recently introduced a generic point membership classification (PMC) test for general solid sweeping. Importantly, this PMC test provides complete geometric information about the set swept by the moving object, including the ability to compute the self-intersections of the sweep itself. In this paper, we compare two recursive strategies for sampling points of the space in which the object moves, and show that the sampling based on a fast marching cubes algorithm possesses the best combination of features in terms of performance and accuracy for the boundary evaluation of general sweeps. Furthermore, we show that the PMC test can be used as the foundation of a generic sweep boundary evaluator in conjunction with efficient space sampling strategies for solids of arbitrary complexity undergoing affine motions.