20,150 research outputs found
Feature based volumes for implicit intersections.
The automatic generation of volumes bounding the intersection of two implicit surfaces (isosurfaces of real functions of 3D point coordinates) or feature based volumes (FBV) is presented. Such FBVs are defined by constructive operations, function normalization and offsetting. By applying various offset operations to the intersection of two surfaces, we can obtain variations in the shape of an FBV. The resulting volume can be used as a boundary for blending operations applied to two corresponding volumes, and also for visualization of feature curves and modeling of surface based structures including microstructures
Conforming restricted Delaunay mesh generation for piecewise smooth complexes
A Frontal-Delaunay refinement algorithm for mesh generation in piecewise
smooth domains is described. Built using a restricted Delaunay framework, this
new algorithm combines a number of novel features, including: (i) an
unweighted, conforming restricted Delaunay representation for domains specified
as a (non-manifold) collection of piecewise smooth surface patches and curve
segments, (ii) a protection strategy for domains containing curve segments that
subtend sharply acute angles, and (iii) a new class of off-centre refinement
rules designed to achieve high-quality point-placement along embedded curve
features. Experimental comparisons show that the new Frontal-Delaunay algorithm
outperforms a classical (statically weighted) restricted Delaunay-refinement
technique for a number of three-dimensional benchmark problems.Comment: To appear at the 25th International Meshing Roundtabl
Multi-scale space-variant FRep cellular structures
Existing mesh and voxel based modeling methods encounter difficulties when dealing with objects containing cellular structures
on several scale levels and varying their parameters in space. We describe an alternative approach based on using real functions evaluated procedurally at any given point. This allows for modeling fully parameterized, nested and multi-scale cellular
structures with dynamic variations in geometric and cellular properties. The geometry of a base unit cell is defined using Function Representation (FRep) based primitives and operations. The unit cell is then replicated in space using periodic
space mappings such as sawtooth and triangle waves. While being replicated, the unit cell can vary its geometry and topology due
to the use of dynamic parameterization. We illustrate this approach by several examples of microstructure generation within a given volume or
along a given surface. We also outline some methods for direct rendering and fabrication not involving auxiliary mesh and voxel
representations
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