Complex Solid Objects Research Articles

An hp-Adaptive Discretization Algorithm for Signed Distance Field Generation.

In this paper we present an hp-adaptive algorithm to generate discrete higher-order polynomial Signed Distance Fields (SDFs) on axis-aligned hexahedral grids from manifold polygonal input meshes. Using an orthonormal polynomial basis, we efficiently fit the polynomials to the underlying signed distance function on each cell. The proposed error-driven construction algorithm is globally adaptive and iteratively refines the SDFs using either spatial subdivision ( h-refinement) following an octree scheme or by cell-wise adaption of the polynomial approximation's degree ( p-refinement). We further introduce a novel decision criterion based on an error-estimator in order to decide whether to apply p- or h-refinement. We demonstrate that our method is able to construct more accurate SDFs at significantly lower memory consumption compared to previous approaches. While the cell-wise polynomial approximation will result in highly accurate SDFs, it can not be guaranteed that the piecewise approximation is continuous over cell interfaces. Therefore, we propose an optimization-based post-processing step in order to weakly enforce continuity. Finally, we apply our generated SDFs as collision detector to the physically-based simulation of geometrically highly complex solid objects in order to demonstrate the practical relevance and applicability of our method.

The Visual Aesthetics of Snowflakes.

In two experiments, participants evaluated the perceived beauty of snowflakes and solid objects. The snowflake silhouettes used as experimental stimuli were created from photographs of natural snowflakes. Both the snowflake silhouettes and computer-generated solid objects varied in complexity. In Experiment 1, 204 participants selected the single snowflake and single solid object that was the most beautiful. In Experiment 2, 33 participants rated the perceived complexity and beauty of the entire set of 100 snowflakes and solid objects. When considered as a group, the participants' results for the solid objects replicated previous findings: The most and least complex objects were perceived as being the most beautiful. This pattern did not necessarily occur, however, for individual participants. Some participants in Experiment 2, for example, found only complex solid objects to be most beautiful ( N = 10); other participants found only the simple solid objects to be most beautiful ( N = 11). Additional participants perceived both the most and least complex solid objects to be beautiful ( N = 10), while one participant only found moderately complex solid objects to be most beautiful. The results for the snowflakes were more uniform: 91% of participants perceived only the complex snowflakes as being most beautiful.

Adaptive Skinning for Interactive Hair-Solid Simulation.

Reduced hair models have proven successful for interactively simulating a full head of hair strands, building upon a fundamental assumption that only a small set of guide hairs are needed for explicit simulation, and the rest of the hair move coherently and thus can be interpolated using guide hairs. Unfortunately, hair-solid interactions is a pathological case for traditional reduced hair models, as the motion coherence between hair strands can be arbitrarily broken by interacting with solids. In this paper, we propose an adaptive hair skinning method for interactive hair simulation with hair-solid collisions. We precompute many eligible sets of guide hairs and the corresponding interpolation relationships that are represented using a compact strand-based hair skinning model. At runtime, we simulate only guide hairs; for interpolating every other hair, we adaptively choose its guide hairs, taking into account motion coherence and potential hair-solid collisions. Further, we introduce a two-way collision correction algorithm to allow sparsely sampled guide hairs to resolve collisions with solids that can have small geometric features. Our method enables interactive simulation of more than 150 K hair strands interacting with complex solid objects, using 400 guide hairs. We demonstrate the efficiency and robustness of the method with various hairstyles and user-controlled arbitrary hair-solid interactions.

Towards positivity preservation for monolithic two-way solid–fluid coupling

We consider complex scenarios involving two-way coupled interactions between compressible fluids and solid bodies under extreme conditions where monolithic, as opposed to partitioned, schemes are preferred for maintaining stability. When considering such problems, spurious numerical cavitation can be quite common and have deleterious consequences on the flow field stability, accuracy, etc. Thus, it is desirable to devise numerical methods that maintain the positivity of important physical quantities such as density, internal energy and pressure. We begin by showing that for an arbitrary flux function, one can put conditions on the time step in order to preserve positivity by solving a linear equation for density fluxes and a quadratic equation for energy fluxes. Our formulation is independent of the underlying equation of state. After deriving the method for forward Euler time integration, we further extend it to higher order accurate Runge–Kutta methods. Although the scheme works well in general, there are some cases where no lower bound on the size of the allowable time step exists. Thus, to prevent the size of the time step from becoming arbitrarily small, we introduce a conservative flux clamping scheme which is also positivity preserving. Exploiting the generality of our formulation, we then design a positivity preserving scheme for a semi-implicit approach to time integration that solves a symmetric positive definite linear system to determine the pressure associated with an equation of state. Finally, this modified semi-implicit approach is extended to monolithic two-way solid–fluid coupling problems for modeling fluid structure interactions such as those generated by blast waves impacting complex solid objects.

Finite element mesh generation and adaptive meshing

AbstractThis review paper gives a detailed account of the development of mesh generation techniques on planar regions, over curved surfaces and within volumes for the past years. Emphasis will be on the generation of the unstructured meshes for purpose of complex industrial applications and adaptive refinement finite element analysis. Over planar domains and on curved surfaces, triangular and quadrilateral elements will be used, whereas for three‐dimensional structures, tetrahedral and hexahedral elements have to be generated. Recent advances indicate that mesh generation on curved surfaces is quite mature now that elements following closely to surface curvatures could be generated more or less in an automatic manner. As the boundary recovery procedure are getting more and more robust and efficient, discretization of complex solid objects into tetrahedra by means of Delaunay triangulation and other techniques becomes routine work in industrial applications. However, the decomposition of a general object into hexahedral elements in a robust and efficient manner remains as a challenge for researchers in the mesh generation community. Algorithms for the generation of anisotropic meshes on 2D and 3D domains have also been proposed for problems where elongated elements along certain directions are required. A web‐site for the latest development in meshing techniques is included for the interested readers.

Distributed boundary representation and Boolean operations on a massively parallel computer

Boolean operation is usually the most expensive task in solid modelling. Considerable amount of time is required in a union, difference, or intersection operation especially when an object grows in complexity after a series of operations. Parallel processing seems to be a promising technique for improving the speed in the manipulation of complex solid objects. This paper presents a technique for performing Boolean operations in a distributed environment. In this method, a distributed boundary representation scheme is adopted for representing objects in an array of processors of a SIMD computer. Solid objects with non-manifold boundary is assumed and is modelled with a cell-complex based boundary representation. The concept of half-wedge is employed to allow easy retrieval of neighbourhood or topological information in a distributed processing environment. Parallel algorithms for obtaining the complement of solids are presented. Algorithms for evaluating the intersecting regions and hence the result of Boolean operations between objects are also discussed. The proposed method is implemented on a DECmpp 1200/Sx machine with 8K processors. Test results on the experimental system shows that the method is efficient for a test piece with 1300 or more entities. The actual performance of the system may also depends on the relative sizes of the entities involved.

Fast collision detection between complex solids using rasterizing graphics hardware

We present an efficient method for detecting collisions between complex solid objects. The method features a stable processing time and low sensitivity to the complexity of contact between objects. The algorithm handles both concave and convex objects; however, the best performance is achieved when at least one object is convex in the proximity of the collision zone (our techniques check the required convexity property as a byproduct of the calculations). The method achieves real-time performance when calculations are supported by the standard functionality of graphics hardware available on high-end workstations.

Efficient display of quadric CSG models

CSG (Constructive Solid Geometry) is a method for defining complex solid objects as a combination of simple primitives. This paper gives a short overview of modeling with CSG and of methods for generating shaded images of CSG models. An efficient scanline algorithm for CSG models with quadric primitives is presented, which gives reasonable display times on a general-purpose workstation. Some remarks on the performance on future workstations are made.

CAD/CAM/CAE for ring design and manufacture

The integration of computer numerical control (CNC), metrology and three-dimensional CAD/CAM systems provides a powerful means of capturing geometrical data of complex solid objects for which no drawings exist. The captured geometry can then be modified, analysed and submitted for machining as desired. In this article, the effectiveness of such an integrated system is illustrated in the particular application of the design and manufacture of rings.

Technical summaries of GEMS

GEMS is a solid modelling system running on CAD workstation or 32 bits microcomputer with graphics terminal. Complex solid objects are built from transformation and set operations upon box, cylinder, cone, sphere, torus, sweeping object and other primitives. CEMS has explicit features, e. g. hierarchical modular structure, interactive user interface, intuitional input, screen menu driven by data table, defining and instancing object in network construction, storage bases on CSG (Constructive Solid Geometry) and BReps (Boundary Representations), regularized set operations, transformation pipeline consistent with PHIGS graphics standard, various transformations, cutting object with two sections in arbitrary angle, patrolling to view the inside of an object, mapping patterns onto surfaces of an object etc.. Not only can it be used for the fields of spatial planning, architectural plan, CAD/CAM for machining, structure analysis, but it is also fundamental for developing the practical system of simulation, computer vision, robotics and so on.