Real-time shaded NC milling display
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Sweeping of three-dimensional objects
Computer-Aided Design
Geometric representation of swept volumes with application to polyhedral objects
International Journal of Robotics Research
Approximate general sweep boundary of a 2D curved object
CVGIP: Graphical Models and Image Processing
NC milling error assessment and tool path correction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Analytical boundary of the workspace for general 3-DOF mechanisms
International Journal of Robotics Research
Three-dimensional distance field metamorphosis
ACM Transactions on Graphics (TOG)
Handbook of discrete and computational geometry
Using distance maps for accurate surface representation in sampled volumes
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Controlled perturbation for arrangements of polyhedral surfaces with application to swept volumes
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
A unified approach for hierarchical adaptive tesselation of surfaces
ACM Transactions on Graphics (TOG)
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Fast and simple 2D geometric proximity queries using graphics hardware
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Semi-regular mesh extraction from volumes
Proceedings of the conference on Visualization '00
A simple recursive tessellator for adaptive surface triangulation
Journal of Graphics Tools
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Dual contouring of hermite data
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Computational Line Geometry
The CGAL Kernel: A Basis for Geometric Computation
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Boundary Determination for Trivariate Solids
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Using Isosurface Methods for Visualizing the Envelope of a Swept Trivariate Solid
PG '00 Proceedings of the 8th Pacific Conference on Computer Graphics and Applications
Swept volumes and their use in viewpoint computation in robot work-cells
ISATP '95 Proceedings of the 1995 IEEE International Symposium on Assembly and Task Planning
Implicit modeling of swept surfaces and volumes
VIS '94 Proceedings of the conference on Visualization '94
Feature-Sensitive Subdivision and Isosurface Reconstruction
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Fast continuous collision detection for articulated models
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Interactive Continuous Collision Detection Using Swept Volume for Avatars
Presence: Teleoperators and Virtual Environments
An accurate sampling-based method for approximating geometry
Computer-Aided Design
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Classifying points for sweeping solids
Computer-Aided Design
Curve skeleton extraction from incomplete point cloud
ACM SIGGRAPH 2009 papers
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
A comparison of sampling strategies for computing general sweeps
Computer-Aided Design
Conservative swept volume boundary approximation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Uniform offsetting of polygonal model based on Layered Depth-Normal Images
Computer-Aided Design
Fast and accurate machined surface rendering using an octree model
ICCVG'10 Proceedings of the 2010 international conference on Computer vision and graphics: Part II
Voxelized Minkowski sum computation on the GPU with robust culling
Computer-Aided Design
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We present an efficient algorithm to approximate the swept volume (SV) of a complex polyhedron along a given trajectory. Given the boundary description of the polyhedron and a path specified as a parametric curve, our algorithm enumerates a superset of the boundary surfaces of SV. It consists of ruled and developable surface primitives, and the SV corresponds to the outer boundary of their arrangement. We approximate this boundary by using a five-stage pipeline. This includes computing a bounded-error approximation of each surface primitive, computing unsigned distance fields on a uniform grid, classifying all grid points using fast marching front propagation, iso-surface reconstruction, and topological refinement. We also present a novel and fast algorithm for computing the signed distance of surface primitives as well as a number of techniques based on surface culling, fast marching level-set methods and rasterization hardware to improve the performance of the overall algorithm. We analyze different sources of error in our approximation algorithm and highlight its performance on complex models composed of thousands of polygons. In practice, it is able to compute a bounded error approximation in tens of seconds for models composed of thousands of polygons sweeping along a complex trajectory.