3,543 research outputs found
QuickCSG: Fast Arbitrary Boolean Combinations of N Solids
QuickCSG computes the result for general N-polyhedron boolean expressions
without an intermediate tree of solids. We propose a vertex-centric view of the
problem, which simplifies the identification of final geometric contributions,
and facilitates its spatial decomposition. The problem is then cast in a single
KD-tree exploration, geared toward the result by early pruning of any region of
space not contributing to the final surface. We assume strong regularity
properties on the input meshes and that they are in general position. This
simplifying assumption, in combination with our vertex-centric approach,
improves the speed of the approach. Complemented with a task-stealing
parallelization, the algorithm achieves breakthrough performance, one to two
orders of magnitude speedups with respect to state-of-the-art CPU algorithms,
on boolean operations over two to dozens of polyhedra. The algorithm also
outperforms GPU implementations with approximate discretizations, while
producing an output without redundant facets. Despite the restrictive
assumptions on the input, we show the usefulness of QuickCSG for applications
with large CSG problems and strong temporal constraints, e.g. modeling for 3D
printers, reconstruction from visual hulls and collision detection
QuickCSG: Fast Arbitrary Boolean Combinations of N Solids
QuickCSG computes the result for general N-polyhedron boolean expressions
without an intermediate tree of solids. We propose a vertex-centric view of the
problem, which simplifies the identification of final geometric contributions,
and facilitates its spatial decomposition. The problem is then cast in a single
KD-tree exploration, geared toward the result by early pruning of any region of
space not contributing to the final surface. We assume strong regularity
properties on the input meshes and that they are in general position. This
simplifying assumption, in combination with our vertex-centric approach,
improves the speed of the approach. Complemented with a task-stealing
parallelization, the algorithm achieves breakthrough performance, one to two
orders of magnitude speedups with respect to state-of-the-art CPU algorithms,
on boolean operations over two to dozens of polyhedra. The algorithm also
outperforms GPU implementations with approximate discretizations, while
producing an output without redundant facets. Despite the restrictive
assumptions on the input, we show the usefulness of QuickCSG for applications
with large CSG problems and strong temporal constraints, e.g. modeling for 3D
printers, reconstruction from visual hulls and collision detection
Medial Axis Transform using Ridge Following
The intent of this investigation has been to find a robust algorithm for generation of the medial axis transform (MAT). The MAT is an invertible, object centered, shape representation defined as the collection of the centers of disks contained in the shape but not in any other such disk. Its uses include feature extraction, shape smoothing, and data compression. MAT generating algorithms include brushfire, Voronoi diagrams, and ridge following. An improved implementation of the ridge following algorithm is given. Orders of the MAT generating algorithms are compared. The effects of the number of edges in the polygonal approximation, shape area, number of holes, and number/distribution of concave vertices are shown from test results. Finally, a set of useful extensions to the ridge following algorithm are discussed
Reshaping Convex Polyhedra
Given a convex polyhedral surface P, we define a tailoring as excising from P
a simple polygonal domain that contains one vertex v, and whose boundary can be
sutured closed to a new convex polyhedron via Alexandrov's Gluing Theorem. In
particular, a digon-tailoring cuts off from P a digon containing v, a subset of
P bounded by two equal-length geodesic segments that share endpoints, and can
then zip closed.
In the first part of this monograph, we primarily study properties of the
tailoring operation on convex polyhedra. We show that P can be reshaped to any
polyhedral convex surface Q a subset of conv(P) by a sequence of tailorings.
This investigation uncovered previously unexplored topics, including a notion
of unfolding of Q onto P--cutting up Q into pieces pasted non-overlapping onto
P.
In the second part of this monograph, we study vertex-merging processes on
convex polyhedra (each vertex-merge being in a sense the reverse of a
digon-tailoring), creating embeddings of P into enlarged surfaces. We aim to
produce non-overlapping polyhedral and planar unfoldings, which led us to
develop an apparently new theory of convex sets, and of minimal length
enclosing polygons, on convex polyhedra.
All our theorem proofs are constructive, implying polynomial-time algorithms.Comment: Research monograph. 234 pages, 105 figures, 55 references. arXiv
admin note: text overlap with arXiv:2008.0175
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