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27
Turning shape decision problems into measures
 Int. J. Shape Modelling
"... This paper considers the problem of constructing shape measures; we start by giving a short overview of areas of practical application of such measures. Shapes can be characterised in terms of a set of properties, some of which are Boolean in nature. E.g. is this shape convex? We show how it is poss ..."
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This paper considers the problem of constructing shape measures; we start by giving a short overview of areas of practical application of such measures. Shapes can be characterised in terms of a set of properties, some of which are Boolean in nature. E.g. is this shape convex? We show how it is possible in many cases to turn such Boolean properties into continuous measures of that property e.g. convexity, in the range [0–1]. We give two general principles for constructing measures in this way, and show how they can be applied to construct various shape measures, including ones for convexity, circularity, ellipticity, triangularity, rectilinearity, rectangularity and symmetry in two dimensions, and 2.5Dness, stability, and imperforateness in three dimensions. Some of these measures are new; others are well known and we show how they fit into this general framework. We also show how such measures for a single shape can be generalised to multiple shapes, and briefly consider as particular examples measures for containment, resemblance, congruence, and similarity.
CAD/CAM Methods for Reverse Engineering: A Case Study of Reengineering Jewelry
 ComputerAided Design & Applications
, 2006
"... ..."
Local topological beautification of reverse engineered models
 ComputerAided Design
, 2004
"... Boundary representation models reconstructed from 3D range data suffer from various inaccuracies caused by noise in the data and by numerical errors in the model building software. The quality of such models can be improved in a beautification step, where geometric regularities need to be detected a ..."
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Boundary representation models reconstructed from 3D range data suffer from various inaccuracies caused by noise in the data and by numerical errors in the model building software. The quality of such models can be improved in a beautification step, where geometric regularities need to be detected and imposed on the model, and defects requiring topological change need to be corrected. This paper considers changes to the topology such as the removal of short edges, small faces and sliver faces, filling of holes in the surface of the model (arising due to missing data), adjusting pinched faces, etc. A practical algorithm for detecting and correcting such problems is presented. Analysis of the algorithm and experimental results show that the algorithm is able to quickly provide the desired changes. Most of the time required for topological beautification is spent on adjusting the geometry to agree with the new topology.
Skewed mirror symmetry in the 3D reconstruction of polyhedral models
, 2003
"... We aim to reconstruct threedimensional polyhedra from axonometric line drawings. Existence of mirror symmetry in polyhedra can assist the reconstruction process. We present a new approach for determining planes of mirror symmetry of such polyhedral objects based on prior detection of their planar f ..."
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We aim to reconstruct threedimensional polyhedra from axonometric line drawings. Existence of mirror symmetry in polyhedra can assist the reconstruction process. We present a new approach for determining planes of mirror symmetry of such polyhedral objects based on prior detection of their planar faces and any axes of symmetry of these faces. The axes are obtained from skewed facial symmetries, for which we also give a new method of determination.
Local Topological Beautication of Reverse Engineered Models
, 2003
"... Boundary representation models reconstructed from 3D range data suffer from various inaccuracies caused by noise in the data and by numerical errors in the model building software. The quality of such models can be improved in a beautication step, where geometric regularities need to be detected a ..."
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Boundary representation models reconstructed from 3D range data suffer from various inaccuracies caused by noise in the data and by numerical errors in the model building software. The quality of such models can be improved in a beautication step, where geometric regularities need to be detected and imposed on the model, and defects requiring topological change need to be corrected. This paper considers changes to the topology such as the removal of short edges, small faces and sliver faces, lling of holes in the surface of the model (arising due to missing data), adjusting pinched faces, etc. A practical algorithm for detecting and correcting such problems is presented. Analysis of the algorithm and experimental results show that the algorithm is able to quickly provide the desired changes. Most of the time required for topological beautication is spent on adjusting the geometry to agree with the new topology.
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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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,
Analysis of Global Properties of Shapes
, 2010
"... With increasing amounts of data describing 3D geometry at scales small and large, shape analysis is becoming increasingly important in fields ranging from computer graphics to robotics to computational biology. While a great deal of research exists on local shape analysis, less work has been done on ..."
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With increasing amounts of data describing 3D geometry at scales small and large, shape analysis is becoming increasingly important in fields ranging from computer graphics to robotics to computational biology. While a great deal of research exists on local shape analysis, less work has been done on global shape analysis. This thesis aims to advance global shape analysis in three directions: symmetryaware mesh processing, part decomposition of 3D models, and analysis of 3D scenes. First, we propose a pipeline for making mesh processing algorithms “symmetryaware”, using largescale symmetries to aid the processing of 3D meshes. Our pipeline can be used to emphasize the symmetries of a mesh, establish correspondences between symmetric features of a mesh, and decompose a mesh into symmetric parts and asymmetric residuals. We make technical contributions towards two of the main steps in this pipeline: a method for symmetrizing the geometry of an object, and a method for remeshing an object to have a symmetric triangulation. We offer several applications of this pipeline: modeling, beautification, attribute transfer, and simplification of approximately symmetric surfaces. Second, we conduct several investigations into part decomposition of 3D meshes. We propose a hierarchical mesh segmentation method as a basis for consistently segmenting a set of meshes.
Choosing Consistent Constraints for Beauti cation of Reverse Engineered Geometric Models
"... Boundary representation models reconstructed from 3D range data suer from various inaccuracies caused by noise in the data and the model building software. Such models can be improved in a beautication step, which nds geometric regularities approximately present in the model and imposes a consisten ..."
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Boundary representation models reconstructed from 3D range data suer from various inaccuracies caused by noise in the data and the model building software. Such models can be improved in a beautication step, which nds 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. Eciency 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.
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.