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14
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.
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.
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.
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.
R.R.: Detecting design intent in approximate CAD models using symmetry, ComputerAided Design
, 2009
"... 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 1 (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.
Fast global and partial reflective symmetry analyses using boundary surfaces of mechanical components
"... Axisymmetry and planar reflective symmetry properties of mechanical components can be used throughout a product development process to restructure the modeling process of a component, simplify the computation of tool path trajectories, assembly trajectories, etc. To this end, the restructured geo ..."
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Axisymmetry and planar reflective symmetry properties of mechanical components can be used throughout a product development process to restructure the modeling process of a component, simplify the computation of tool path trajectories, assembly trajectories, etc. To this end, the restructured geometric model of such components must be at least as accurate as the manufacturing processes used to produce them, likewise their symmetry properties must be extracted with the same level of accuracy to preserve the accuracy of their geometric model. The proposed symmetry analysis is performed on a BRep CAD model through a divideandconquer approach over the boundary of a component with faces as atomic entities. As a result, it is possible to identify rapidly all global symmetry planes and axisymmetry as well as local symmetries. Also, the corresponding algorithm is fast enough to be inserted in CAD/CAM operators as part of interactive modeling processes,
www.elsevier.com/locate/cad Detecting approximate symmetries of discrete point subsets ✩
, 2006
"... 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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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.
*Highlights (for review) Fast global and partial reflective symmetry analyses using boundary surfaces of mechanical components
, 2014
"... Axisymmetry and planar reflective symmetry properties of mechanical components can be used throughout a product development process to restructure the modeling process of a component, simplify the computation of tool pathtrajectories, assembly trajectories, etc. To thisend, the restructured geometri ..."
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Axisymmetry and planar reflective symmetry properties of mechanical components can be used throughout a product development process to restructure the modeling process of a component, simplify the computation of tool pathtrajectories, assembly trajectories, etc. To thisend, the restructured geometric model of such components must be at least as accurate as the manufacturing processes used to produce them, likewise their symmetry properties must be extracted with the same level of accuracy to preserve the accuracy of their geometric model. The proposed symmetry analysis is performed on a BRep CAD model through a divideandconquer approach over the boundary of a component with faces as atomic entities. As a result, it is possible to identify rapidly all global symmetry planes and axisymmetry as well as local symmetries. Also, the corresponding algorithm is fast enough to be inserted in CAD/CAM operators as part of interactive modeling processes,
Computational Geometry
"... s of Talks Army Research Office and MSI Stony Brook Workshop on COMPUTATIONAL GEOMETRY October 1416, 1993 Brownestone Hotel Raleigh, North Carolina Hosted by the Department of Computer Science North Carolina State University Sponsored by the U.S. Army Research Office, and the Mathematical Scienc ..."
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s of Talks Army Research Office and MSI Stony Brook Workshop on COMPUTATIONAL GEOMETRY October 1416, 1993 Brownestone Hotel Raleigh, North Carolina Hosted by the Department of Computer Science North Carolina State University Sponsored by the U.S. Army Research Office, and the Mathematical Sciences Institute, Stony Brook. Organizers: Pankaj Agarwal (pankaj@cs.duke.edu) Esther Arkin (estie@ams.sunysb.edu) Kenneth Clark (clark@adm.csc.ncsu.edu) Rex Dwyer (dwyer@csc.ncsu.edu) Joseph Mitchell (jsbm@ams.sunysb.edu) Steven Skiena (skiena@sbcs.sunysb.edu) Program Thursday, October 14, 1993 8:009:00 Breakfast buffet. 9:009:45 Geometric Complexity in Graphics. Jarek Rossignac, IBM Research, Yorktown Heights 9:4510:05 Maintenance of geometric representations through space decompositions. Vadim Shapiro, GM R&D Center 10:0510:25 Combining spatial data representations for rapid visualization and analysis. Lori L. Scarlatos, Grumman Data Systems / SUNY Stony Brook 10:2510:45 Bre...