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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.
Detecting Approximate Incomplete Symmetries in Discrete Point Sets
 ACM Symp. Solid and Physical Modeling
, 2007
"... 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 ..."
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Cited by 1 (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.
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.
Choosing Consistent Constraints for Beautification of Reverse Engineered Geometric Models
"... 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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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.
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.