Swept Volumes
نویسندگان
چکیده
Given a solid S ⊂ R with a piecewise smooth boundary, we compute an approximation of the boundary surface of the volume which is swept by S under a smooth one-parameter motion. Using knowledge from kinematical and elementary differential geometry, the algorithm computes a set of points plus surface normals from the envelope surface. A study of the evolution speed of the so called characteristic set along the envelope is used to achieve a prescribed sampling density. With a marching algorithm in a grid, the part of the envelope which lies on the boundary of the swept volume is extracted. The final boundary representation of the swept volume is either a triangle mesh, a B-spline surface or a point-set surface.
منابع مشابه
Image-Swept Volumes
Many graphical objects can be represented by swept volumes (including its subset – generalised cylinders) by sweeping 2D or 3D templates along 3D trajectories. In this paper, we present a new approach for constructing swept volumes using image templates. We utilise scalar fields as our underlying data type, and employ volume ray casting techniques for rendering swept volumes in their original s...
متن کاملAutomatic Hexahedral Mesh Generation by Recursive Convex and Swept Volume Decomposition
In this paper we present a recursive volume decomposition method for automatically decomposing complex shaped objects with both protrusions and depressions into simpler sub-objects for automatic hexahedral mesh generation. The sub-volumes after decomposition are classified into either convex or swept volumes. For a convex volume, it is mapped to a collection of hexahedral objects. On the other ...
متن کاملSwept Volumes and Their Use in Viewpoint Computation in Robot Work-Cells
This paper discusses the automaticcomputation of viewpoints for monitoringobjects and features in an active robot work-cell. An important step in our algorithm for finding viewpoints is the computation of the volumes swept by polyhedral objects moving through space. A method for approximating these volumes for arbitrarily moving polyhedra is presented. Some swept volume results are presented, a...
متن کاملComputing Swept Volumes for Sensor Planning Tasks
This paper discusses the computation of the volumes swept by polyhedral objects moving through space and how these volumes can be used for sensor planning in active environments. It presents some new results in the computation of the approximate volumes swept by polyhedral objects as they undergo arbitrary motions. An algorithm is presented which approximates these volumes under a restricted cl...
متن کاملAutomated Hexahedral Mesh Generation by Swept Volume Decomposition and Recomposition
In this paper a method is presented to generate uniform hexahedral meshes automatically. In this method, a solid model with complex geometry is decomposed into swept volumes with simpler geometry. A sweepable face on the solid model is selected as the generator face to generate a swept volume. Each generator face is specified with node density and a quadrilateral mesh is generated from it. Then...
متن کاملComputing swept volumes
The swept volume problem is practical, dif®cult and interesting enough to have received a great deal of attention over the years, and the literature contains much discussion of methods for computing swept volumes in many situations. The method presented here permits an arbitrary polyhedral object (given in a typical boundary representation) to be swept through an arbitrary trajectory. A polyhed...
متن کامل