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1、Detecting Design Intent in Approximate CAD Models Using SymmetryMing Lia,b, Frank C. Langbeina, Ralph R. MartinaaSchool of Computer Science, CardiffUniversity, Cardiff, UK bState Key Lab of CAD design intent is often not explicitly transferred. Detecting design intent in such approximate models can
2、reveal high-level information that is necessary for the models function or purpose. Such information may be used to constrain and guide editing operations. It may also allow us to improve an approximate model by enforcing intended regularities. It may enable faster analysis and more compact represen
3、tation, if the model has symmetric sub-parts. It may also allow models to be more meaningfully indexed for shape search, etc. Thus, this paper considers algorithmic detection of geometric design intent in ap- proximate boundary-representation (B-rep) models of engineering objects, such as the one in
4、 Fig. 1. Symmetry is a key concept in design.Engineering objects often ex- hibit symmetries for functional, aesthetic, and manufacturing reasons 2, 40. Many regularities can be represented via symmetries 19. A symmetry is an isometry that maps a set exactly onto itself. However, symmetry may be pres
5、ent approximatelythe set is almost invariant under an isometry, lo- callyonly part of the set is invariant, incompletelynot all elements build- ing a symmetry are present, and compatiblymultiple subsets share the samesymmetry. We thus later define a precise concept of approximate incomplete symmetry
6、 which includes exact and global symmetries as special cases, gen- eralising the ideas in 29. For brevity, henceforth, we refer to approximate symmetry or congruency as symmetry or congruency, unless stated otherwise. An alternative approach 21 considers asymmetries in a model to describe design int
7、ent as a sequence of symmetry breaking operations.2Figure 1: An example of an approximate CAD model: MonsterComplex models often exhibit far too many alternative plausible approx- imate regularities for exhaustive methods to be able to determine which reg- ularities represent the original design int
8、ent of the whole model 20.As a simple example, consider a rectangular block with many prisms attachedto its faces. Analysing the whole model without finding the prisms creates many candidate angles and distances forming plausible regularities betweenthe models planes. By first identifying the indivi
9、dual prisms as sub-parts, we can detect their approximate prismatic symmetries, and separately determine symmetric arrangements of the prisms on the block. Analysing sub-parts of the model separately increases the speed of regularity detection and provides more reliable results. Hence, our design in
10、tent detection algorithm performs model decomposition before detecting regularities in the resulting sub-parts. The decomposition phase builds a regularity feature tree (RFT) forming a hierarchy of regularity features: simple, closed volumes which in combi- nation describe the original shape. The re
11、gularity features at the leaves of the RFT describe the complete shape of the object; the tree indicates how to build the complete model from the leaf-parts. Unlike a CSG tree, the RFT does not contain standard primitives, nor does it give a Boolean de- composition 22. Instead, the emphasis is on th
12、e fact that the leaf-parts are simpler and more symmetric than other parts in the tree, and not on3Figure 2: Overview of algorithmic steps for detecting design intent of the Monster model in Fig. 1how the object was or might have been constructed. The second phase of the algorithm seeks regularities
13、 within the model in terms of congruencies, incomplete symmetries and symmetric arrangements of these leaf-parts. Itfirst detects congruencies to partition the leaf-parts into congruence sets, each containing one or more congruent leaf-parts. Next, for each congruence set, it seeks subsets forming i
14、ncomplete symmetries and incomplete symmetric arrangements. Compatible symmetries shared by leaf-parts, and symmetric arrangements, are further combined before we output all detected regular- ities as transformations matching sub-parts of the model. The process is illustrated in Fig. 2 for the model
15、 in Fig. 1. Fig. 2(a) shows the computed RFT, Fig. 2(b) shows the congruent leaf-parts found, and the detected sym- metries are given in Figs. 2(c)(e). The output may, e.g., be used to describe a model by geometric constraints 36, or be processed by regularity selection techniques 20, 45. As the mod
16、els are approximate, the method has to consider tolerances carefully. We compute suitable (tolerance) validity intervals directly from distances present in the model to ensure that model entities match unam- biguously (i.e.in a one-to-one manner) at any tolerance in the interval.During decomposition, each different validity interval yields a different, well-4defined RFT. We let the user select a suitable RFT, which is often straight- forward as appropriate tolerances are
