Detecting Design Intent in Approximate CAD Models using Symmetry M. Li, F. Langbein, R. Martin Submitted to Computer-Aided Design.  Figure: Flowchat for detecting design intent on an approximate model. Abstract: Finding design intent embodied as high-level geometric relations between a CAD model's sub-parts facilitates various tasks such as model editing and analysis. This is especially important for boundary-representation models arising from e.g. reverse engineering or CAD data transfer. These lack explicit information about design intent, and often, the intended geometric relations are only approximately present. We give a novel solution to this problem based on detecting approximate local incomplete symmetries, in a hierarchical decomposition of the model into simpler, more symmetric sub-parts. Design intent is detected as congruencies, symmetries and symmetric arrangements of the leaf-parts in this decomposition. All elementary 3D symmetry types are considered. They may be present only locally in subsets of the leaf-parts, and may also be incomplete, i.e. not all elements required for a symmetry need be present. Adaptive tolerance intervals are used for matching inter-point distances, enabling efficient, robust and consistent detection of approxi- mate symmetries. Doing so avoids finding many spurious relations, reliably resolves ambiguities between relations, and reduces inconsistencies. Experiments show that detected relations reveal significant design intent. Detecting approximate symmetries of discrete point subsets M. Li, F. Langbein, R. Martin Computer-Aided Design, 40(1),76-93,2008
Figure: symmetries detected by our algorithm Left: approximate local symmetries detected on a 4X4 grid disturbed by other 20 random points Middle: a mechanical object MISUFA Right: incomplete symmetries detected from the characteristic points extracted from from the MISUFA model Abstract: Detecting approximate symmetries of parts of a model is important when attempting to determine the geometrical design intent of approximate boundary-representation (B-rep) solid models produced e.g. by reverse engineering systems. For example, such detected symmetries may be enforced exactly on the model to improve its shape, to simplify its analysis, or to constrain it during editing. We give an algorithm to detect local approximate symmetries in a discrete point set derived from a B-rep model: the output comprises the model’s potential local symmetries at various automatically detected tolerance levels. Non-trivial symmetries of subsets of the point set are found as unambiguous permutation cycles, i.e. vertices of an approximately regular polygon or an anti-prism, which are sufficiently separate from other points in the point set. The symmetries are detected using a rigorous, tolerance-controlled, incremental approach, which expands symmetry seed sets by one point at a time. Our symmetry cycle detection approach only depends on inter-point distances. The algorithm takes time O(n4) where n is the number of input points. Results produced by our algorithm are demonstrated using a variety of examples. Rational Quadratic Approximation to Real Algebraic Curves Xiao-Shan Gao, Ming Li Computer Aided Geometric Design, 21,805-828,2004    Figure: results of rational quadratic approximation for a quatic algebraic curve (topologies of original curves are preserved). Left: our approximation result (tolerance bound 0.003; segment number: 8). Middle: (Xu and Bajaj, 1997)'s approximation result (tolerance bound: 0.1; segment number: 34). Right: approximation result of a spacial algebraic curve (intersection of two algebraic surfaces) of degree 8 under tolerance bound 0.1.
  
  
 Figure: roles of dynamic simulation and model simplification in a product design process. Abstract: Dynamic simulation allows us to investigate, design, visualize, and test a mechanical object even before its real construction, and avoids unnecessary changes occurred in design and unnecessary injuries and damages. However, it is limited by the slow simulation speed due to the complex geometry of mechanical objects. Model simplification is expected to resolve the issue, but previous simplification method cannot be directly applied here --- they are usually geometry-based rather than directly physics-based, and hence are hard to well preserve the original model's dynamic behavior. Furthermore, no explicit fidelity measure is introduced to measure the dynamics difference between the original model and its simplification. This paper aims to construct a physics-based simplified model for improving dynamics simulation. It is achieved by analyzing the essential factors in determining the dynamic performance of a simulated object: inertia matrix, collision detection, joints and mechanical constraints. The model is simplified based on this by trying to keep these key factors in the simplified model while ignoring other un-essential factors. Method to analyze the dynamic fidelity of the simplified model is also introduced. To our best knowledge, the proposed method is the first in constructing a physics-based simplified model to accelerate dynamic simulation and analyze its fidelity. Experimental results of an illustrative example, snake robot, is also shown to demonstrate our algorithm's performance. List of Publications Impact Factors are referred to here. M. Li, F. Langbein, R. Martin, Detecting approximate symmetries of discrete point subsets, Computer-Aided Design, 40(1):76-93, 2008. M. Li, F. Langbein, R. Martin, A Comment on 'Constructing Regularity Feature Trees for Solid Models', Proc. IEEE Geometric Modeling and Processing, LNCS 4975, 2008. |
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