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

Simple and Robust Boolean Operations for Triangulated Surfaces

Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two stages: (1) We firstly find out candidate intersected-triangles pairs based on Octree and then compute the inter-section lines for all pairs of triangles with parallel algorithm; (2) We form closed or open intersection-loops, sub-surfaces and sub-blocks quite robustly only according to the cleared and updated topology of meshes while without coordinate computations for geometric enti-ties. A novel technique instead of inside/outside classification is also proposed to distinguish the resulting union, subtraction and intersection. Several examples have been given to illus-trate the effectiveness of our approach.Comment: Novel method for determining Union, Subtraction and Intersectio

QuickCSG: Arbitrary and Faster Boolean Combinations of N Solids

While studied over several decades, the computation of boolean operations on polyhedra is almost always addressed by focusing on the case of two polyhedra. For multiple input polyhedra and an arbitrary boolean operation to be applied, the operation is decomposed over a binary CSG tree, each node being processed separately in quasilinear time. For large trees, this is both error prone due to intermediate geometry and error accumulation, and inefficient because each node yields a specific overhead. We introduce a fundamentally new approach to polyhedral CSG evaluation, addressing the general N-polyhedron case. We propose a new vertex-centric view of the problem, which both simplifies the algorithm computing resulting geometric contributions, and vastly facilitates its spatial decomposition. We then embed the entire problem in a single KD-tree, specifically geared toward the final result by early pruning of any region of space not contributing to the final surface. This not only improves the robustness of the approach, it also gives it a fundamental speed advantage, with an output complexity depending on the output mesh size instead of the input size as with usual approaches. 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 several dozen polyhedra. The algorithm is also shown to outperform recent GPU implementations and approximate discretizations, while producing an exact output without redundant facets.Quoique étudié depuis des décennies, le calcul d'opérations booléennes sur des polyèdres est quasiment toujours fait sur deux opérandes. Pour un plus grand nombre de polyèdres et une opération booléenne arbitraire à effectuer, l'opération est décomposée sur un arbre binaire CSG (géométrie constructive), dans lequel chaque nœud est traité séparément en temps quasi-linéaire. Pour de grands arbres, ceci est à la fois source d'erreurs, à cause des calculs géométriques intermédiaires, et inefficace à cause des traitements superflus au niveau des nœuds. Nous introduisons une approche fondamentalement nouvelle qui traite le cas général de N polyèdres. Nous proposons une vue du problème centrée sur les sommets, ce qui simplifie l'algorithme et facilite sa décomposition spatiale. Nous traitons le problème dans un seul KD-tree, qui est dirigé vers le résultat final, en élaguant les régions de l'espace qui ne contribuent pas à la surface finale. Non seulement ceci améliore la robustesse de l'approche mais ça lui donne un avantage en vitesse, car la complexité dépend plus de la taille de la sortie que celle d'entrée. En la combinant avec une parallélisation basée sur du vol de tâche, l'algorithme a des performances inouïes, d'un ou deux ordres de grandeur plus rapide que les algorithmes de l'état de l'art sur CPU et GPU. De plus il produit un résultat exact, sans aucune primitive géométrique superflue

QuickCSG: Arbitrary and Faster Boolean Combinations of N Solids

While studied over several decades, the computation of boolean operations on polyhedra is almost always addressed by focusing on the case of two polyhedra. For multiple input polyhedra and an arbitrary boolean operation to be applied, the operation is decomposed over a binary CSG tree, each node being processed separately in quasilinear time. For large trees, this is both error prone due to intermediate geometry and error accumulation, and inefficient because each node yields a specific overhead. We introduce a fundamentally new approach to polyhedral CSG evaluation, addressing the general N-polyhedron case. We propose a new vertex-centric view of the problem, which both simplifies the algorithm computing resulting geometric contributions, and vastly facilitates its spatial decomposition. We then embed the entire problem in a single KD-tree, specifically geared toward the final result by early pruning of any region of space not contributing to the final surface. This not only improves the robustness of the approach, it also gives it a fundamental speed advantage, with an output complexity depending on the output mesh size instead of the input size as with usual approaches. 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 several dozen polyhedra. The algorithm is also shown to outperform recent GPU implementations and approximate discretizations, while producing an exact output without redundant facets.Quoique étudié depuis des décennies, le calcul d'opérations booléennes sur des polyèdres est quasiment toujours fait sur deux opérandes. Pour un plus grand nombre de polyèdres et une opération booléenne arbitraire à effectuer, l'opération est décomposée sur un arbre binaire CSG (géométrie constructive), dans lequel chaque nœud est traité séparément en temps quasi-linéaire. Pour de grands arbres, ceci est à la fois source d'erreurs, à cause des calculs géométriques intermédiaires, et inefficace à cause des traitements superflus au niveau des nœuds. Nous introduisons une approche fondamentalement nouvelle qui traite le cas général de N polyèdres. Nous proposons une vue du problème centrée sur les sommets, ce qui simplifie l'algorithme et facilite sa décomposition spatiale. Nous traitons le problème dans un seul KD-tree, qui est dirigé vers le résultat final, en élaguant les régions de l'espace qui ne contribuent pas à la surface finale. Non seulement ceci améliore la robustesse de l'approche mais ça lui donne un avantage en vitesse, car la complexité dépend plus de la taille de la sortie que celle d'entrée. En la combinant avec une parallélisation basée sur du vol de tâche, l'algorithme a des performances inouïes, d'un ou deux ordres de grandeur plus rapide que les algorithmes de l'état de l'art sur CPU et GPU. De plus il produit un résultat exact, sans aucune primitive géométrique superflue

Proto-Plasm: parallel language for adaptive and scalable modelling of biosystems

This paper discusses the design goals and the first developments of Proto-Plasm, a novel computational environment to produce libraries of executable, combinable and customizable computer models of natural and synthetic biosystems, aiming to provide a supporting framework for predictive understanding of structure and behaviour through multiscale geometric modelling and multiphysics simulations. Admittedly, the Proto-Plasm platform is still in its infancy. Its computational framework—language, model library, integrated development environment and parallel engine—intends to provide patient-specific computational modelling and simulation of organs and biosystem, exploiting novel functionalities resulting from the symbolic combination of parametrized models of parts at various scales. Proto-Plasm may define the model equations, but it is currently focused on the symbolic description of model geometry and on the parallel support of simulations. Conversely, CellML and SBML could be viewed as defining the behavioural functions (the model equations) to be used within a Proto-Plasm program. Here we exemplify the basic functionalities of Proto-Plasm, by constructing a schematic heart model. We also discuss multiscale issues with reference to the geometric and physical modelling of neuromuscular junctions

A semi-automatic computer-aided method for surgical template design

This paper presents a generalized integrated framework of semi-automatic surgical template design. Several algorithms were implemented including the mesh segmentation, offset surface generation, collision detection, ruled surface generation, etc., and a special software named TemDesigner was developed. With a simple user interface, a customized template can be semi- automatically designed according to the preoperative plan. Firstly, mesh segmentation with signed scalar of vertex is utilized to partition the inner surface from the input surface mesh based on the indicated point loop. Then, the offset surface of the inner surface is obtained through contouring the distance field of the inner surface, and segmented to generate the outer surface. Ruled surface is employed to connect inner and outer surfaces. Finally, drilling tubes are generated according to the preoperative plan through collision detection and merging. It has been applied to the template design for various kinds of surgeries, including oral implantology, cervical pedicle screw insertion, iliosacral screw insertion and osteotomy, demonstrating the efficiency, functionality and generality of our method.Comment: 18 pages, 16 figures, 2 tables, 36 reference