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
Journal of Mathematical Imaging and Vision - Special issue on mathematical imaging
Controlled perturbation for arrangements of polyhedral surfaces with application to swept volumes
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
The sweep-envelope differrential equation algorithm for general deformed swept volumes
Computer Aided Geometric Design
Semi-regular mesh extraction from volumes
Proceedings of the conference on Visualization '00
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
A three-dimensional holes closing algorithm
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Fast swept volume approximation of complex polyhedral models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Isosurface Reconstruction with Topology Control
PG '02 Proceedings of the 10th 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
Isotopic implicit surface meshing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Dual Marching Cubes: Primal Contouring of Dual Grids
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
VIS '04 Proceedings of the conference on Visualization '04
Dual Contouring with Topology-Preserving Simplification Using Enhanced Cell Representation
VIS '04 Proceedings of the conference on Visualization '04
Topology preserving surface extraction using adaptive subdivision
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
Approximate the swept volume of revolutions along curved trajectories
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Interactive topology-aware surface reconstruction
ACM SIGGRAPH 2007 papers
Boundary of the volume swept by a free-form solid in screw motion
Computer-Aided Design
Classifying points for sweeping solids
Computer-Aided Design
A topological hierarchy for functions on triangulated surfaces
IEEE Transactions on Visualization and Computer Graphics
Conservative swept volume boundary approximation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
High accuracy NC milling simulation using composite adaptively sampled distance fields
Computer-Aided Design
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We present a simple algorithm to generate a topology-preserving, error-bounded approximation of the outer boundary of the volume swept by a polyhedron along a parametric trajectory. Our approach uses a volumetric method that generates an adaptive volumetric grid, computes signed distance on the grid points, and extracts an isosurface from the distance field. In order to guarantee geometric and topological bounds, we present a novel sampling and front propagation algorithm for adaptive grid generation. We highlight the performance of our algorithm on many complex benchmarks that arise in geometric and solid modeling, motion planning and CNC milling applications. To the best of our knowledge, this is the first practical algorithm that can generate swept volume approximations with geometric and topological guarantees on complex polyhedral models swept along any parametric trajectory.