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25
Approximate symmetry detection for reverse engineering
 In: Proc. 6th ACM Symp. Solid Modeling and Appl
, 2001
"... The authors are developing an automated reverse engineering system for reconstructing the shape of simple mechanical parts. Brep models are created by fitting surfaces to point clouds obtained by scanning an object using a 3D laser scanner. The resulting models, although valid, are often not suita ..."
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Cited by 28 (16 self)
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The authors are developing an automated reverse engineering system for reconstructing the shape of simple mechanical parts. Brep models are created by fitting surfaces to point clouds obtained by scanning an object using a 3D laser scanner. The resulting models, although valid, are often not suitable for purposes such as redesign because expected regularities and constraints are not present. This information is lost because each face of the model is determined independently. A global approach is required, in particular one that is capable of finding symmetries originally present. This paper describes a practical algorithm for finding global symmetries in suitable Brep models built from planes, spheres, cylinders, cones and tori. It has been implemented and used to determine approximate symmetries of models with up to about 200 vertices in reasonable time. The time performance of the algorithm in the worst case is bounded by O(n3:5 log4 n), and a justification is given that on common engineering objects it takes about O(n2 log4 n), making it a practical tool for use in a reverse engineering package. Details of the algorithm are given, along with some results from a number of illustrative test runs.
Recognizing geometric patterns for beautification of reconstructed solid models
 Proc. Int. Conf. Shape Modelling and Applications
, 2001
"... Boundary representation models reconstructed from 3D range data suffer from various inaccuracies caused by noise in the data and the model building software. The quality of such models can be improved in a beautification step, which finds regular geometric patterns approximately present in the model ..."
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Cited by 17 (10 self)
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Boundary representation models reconstructed from 3D range data suffer from various inaccuracies caused by noise in the data and the model building software. The quality of such models can be improved in a beautification step, which finds regular geometric patterns approximately present in the model and imposes a maximal consistent subset of constraints deduced from these patterns on the model. This paper presents analysis methods seeking geometric patterns defined by similarities. Their specific types are derived from a part survey estimating the frequencies of the patterns in simple mechanical components. The methods seek clusters of similar objects which describe properties of faces, loops, edges and vertices, try to find special values representing the clusters, and seek approximate symmetries of the model. Experiments show that the patterns detected appear to be suitable for the subsequent beautification steps.
Choosing Consistent Constraints for Beautification of Reverse Engineered Geometric Models
 ComputerAided Design
, 2004
"... Boundary representation models reconstructed from 3D range data suffer from various inaccuracies caused by noise in the data and the model building software. Such models can be improved in a beautification step, which finds geometric regularities approximately present in the model and imposes a cons ..."
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Cited by 16 (6 self)
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Boundary representation models reconstructed from 3D range data suffer from various inaccuracies caused by noise in the data and the model building software. Such models can be improved in a beautification step, which finds geometric regularities approximately present in the model and imposes a consistent subset of them on the model. Methods to select regularities consistently such that they are likely to represent the original, ideal design intent are presented. Efficiency during selection is achieved by considering degrees of freedom to analyse the solvability of constraint systems representing the regularities (without actually solving them). Priorities are used to select regularities in case of inconsistencies. The selected set of constraints is solved numerically and an improved model is rebuild from the solution. Experiments show that the presented methods can beautify models by selecting consistent regularities and enforcing major intended regularities.
Approximate congruence detection of model features for reverse engineering. In: Proc. int. conf. shape modelling and applications
, 2003
"... Reverse engineering allows the geometric reconstruction of simple mechanical parts. However, the resulting models suffer from inaccuracies caused by errors in measurement and reconstruction so such models do not have the exact congruences, symmetries and other regularities the original designer inte ..."
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Cited by 15 (9 self)
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Reverse engineering allows the geometric reconstruction of simple mechanical parts. However, the resulting models suffer from inaccuracies caused by errors in measurement and reconstruction so such models do not have the exact congruences, symmetries and other regularities the original designer intended. We wish to impose such regularities in a beautification process. This paper discusses the particular problem of detecting approximate congruences between parts (e.g. a pair of handles) of a reconstructed Brep model, so that a subsequent step can enforce them exactly. A practical detection algorithm is given for models defined using planes, spheres, cylinders, cones and tori. Analysis of the algorithm and experimental results show that expected congruences are detected reasonably quickly.
Detecting approximate symmetries of discrete point subsets
, 2008
"... Detecting approximate symmetries of parts of a model is important when attempting to determine the geometrical design intent of approximate boundaryrepresentation (Brep) solid models produced e.g. by reverse engineering systems. For example, such detected symmetries may be enforced exactly on the ..."
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Cited by 13 (2 self)
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Detecting approximate symmetries of parts of a model is important when attempting to determine the geometrical design intent of approximate boundaryrepresentation (Brep) 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 Brep model: the output comprises the model’s potential local symmetries at various automatically detected tolerance levels. Nontrivial symmetries of subsets of the point set are found as unambiguous permutation cycles, i.e. vertices of an approximately regular polygon or an antiprism, which are sufficiently separate from other points in the point set. The symmetries are detected using a rigorous, tolerancecontrolled, incremental approach, which expands symmetry seed sets by one point at a time. Our symmetry cycle detection approach only depends on interpoint distances. The algorithm takes time O(n 4) where n is the number of input points. Results produced by our algorithm are demonstrated using a variety of examples.
Finding Approximate Shape Regularities In Reverse Engineered Solid Models Bounded By Simple Surfaces
 Proc. ACM Symp. Solid Modelling and Applications
, 2001
"... Current reverse engineering systems are able to generate simple valid boundary representation (Brep) models from 3D range data. Such models suffer from various inaccuracies caused by noise in the input data and algorithms. The quality of reverse engineered geometric models can potentially be improv ..."
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Cited by 12 (9 self)
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Current reverse engineering systems are able to generate simple valid boundary representation (Brep) models from 3D range data. Such models suffer from various inaccuracies caused by noise in the input data and algorithms. The quality of reverse engineered geometric models can potentially be improved by finding candidate shape regularities in such an initial model, and imposing a suitable subset of them on the model by using constraints, in a postprocessing step called beautification. Finding such candidate regularities is a necessary first step, and is discussed in this paper. Algorithms for analysis are presented which use feature objects to describe properties of faces, edges and vertices, and small groups of these elements in a Brep model with only planar, spherical, cylindrical, conical and toroidal faces. The methods seek similarities between feature objects, e.g. axes which are parallel, for each property type. For each group of similar feature objects they also try to find a special feature object which might represent the group, e.g. an integer value which approximates the radius of similar cylinders. The feature objects used represent shape parameters, directions, axes and positions present in the model. Experiments show that the regularities found by these algorithms include the desired regularities. Although other spurious regularities which must be discarded in subsequent beautification steps are also produced, their number can be reduced by appropriate choice of tolerance values.
Constructing regularity feature trees for solid models, in
 Lecture Notes in Computer Science LNCS 4077, GMP 2006
, 2013
"... Abstract. Approximate geometric models, e.g. as created by reverse engineering, describe the approximate shape of an object, but do not record the underlying design intent. Automatically inferring geometric aspects of the design intent, represented by feature trees and geometric constraints, enhance ..."
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Cited by 11 (4 self)
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Abstract. Approximate geometric models, e.g. as created by reverse engineering, describe the approximate shape of an object, but do not record the underlying design intent. Automatically inferring geometric aspects of the design intent, represented by feature trees and geometric constraints, enhances the utility of such models for downstream tasks. One approach to design intent detection in such models is to decompose them into regularity features. Geometric regularities such as symmetries may then be sought in each regularity feature, and subsequently be combined into a global, consistent description of the model’s geometric design intent. This paper describes a systematic approach for finding such regularity features based on recovering broken symmetries in the model. The output is a tree of regularity features for subsequent use in regularity detection and selection. Experimental results are given to demonstrate the operation and efficiency of the algorithm. 1
Detecting Design Intent in Approximate CAD Models Using Symmetry
"... Finding design intent embodied as highlevel geometric relations between a CAD model’s subparts facilitates various tasks such as model editing and analysis. This is especially important for boundaryrepresentation models arising from, e.g., reverse engineering or CAD data transfer. These lack expl ..."
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Cited by 11 (0 self)
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Finding design intent embodied as highlevel geometric relations between a CAD model’s subparts facilitates various tasks such as model editing and analysis. This is especially important for boundaryrepresentation 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. The novel solution to this problem presented is based on detecting approximate local incomplete symmetries, in a hierarchical decomposition of the model into simpler, more symmetric subparts. Design intent is detected as congruencies, symmetries and symmetric arrangements of the leafparts in this decomposition. All elementary 3D symmetry types and common symmetric arrangements are considered. They may be present only locally in subsets of the leafparts, and may also be incomplete, i.e. not all elements required for a symmetry need be present. Adaptive tolerance intervals are detected automatically for matching interpoint distances, enabling efficient, robust and consistent detection of approximate 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.
Making the Most of Using Depth Reasoning to Label Line Drawings of Engineering Objects
 Patrikalakis and P. Brunet, 9th ACM Symposium on Solid Modeling and Applications SM’04
, 2004
"... Automatic creation of Brep models of engineering objects from freehand sketches would benefit designers. A subgoal is to take a single line drawing (with hidden lines removed), and from it deduce an initial 3D geometric realisation of the visible part of the object. Junction and line labels, and pr ..."
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Cited by 10 (5 self)
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Automatic creation of Brep models of engineering objects from freehand sketches would benefit designers. A subgoal is to take a single line drawing (with hidden lines removed), and from it deduce an initial 3D geometric realisation of the visible part of the object. Junction and line labels, and provisional depth coordinates, are important components of this frontal geometry.
Detecting approximate incomplete symmetries in discrete point sets
 in: ACM Symp. Solid and physical modeling
"... Motivated by the need to detect design intent in approximate boundary representation models, we give an algorithm to detect incomplete symmetries of discrete points, giving the models ’ potential local symmetries at various automatically detected tolerances. Here, incomplete symmetry is defined a ..."
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Cited by 7 (1 self)
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Motivated by the need to detect design intent in approximate boundary representation models, we give an algorithm to detect incomplete symmetries of discrete points, giving the models ’ potential local symmetries at various automatically detected tolerances. Here, incomplete symmetry is defined as a set of incomplete cycles which are constructed by, e.g., a set of consecutive vertices of an approximately regular polygon, induced by a single isometry. All seven 3D elementary isometries are considered for symmetry detection. Incomplete cycles are first found using a tolerancecontrolled point expansion approach. Subsequently, these cycles are clustered for incomplete symmetry detection. The resulting clusters have welldefined, unambiguous approximate symmetries suitable for design intent detection, as demonstrated experimentally.