2015
DOI: 10.1109/tvcg.2014.2388205
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On Linear Spaces of Polyhedral Meshes

Abstract: Abstract-Polyhedral meshes (PM) -meshes having planar faces -have enjoyed a rise in popularity in recent years due to their importance in architectural and industrial design. However, they are also notoriously difficult to generate and manipulate. Previous methods start with a smooth surface and then apply elaborate meshing schemes to create polyhedral meshes approximating the surface. In this paper, we describe a reverse approach: given the topology of a mesh, we explore the space of possible planar meshes wi… Show more

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Cited by 8 publications
(13 citation statements)
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“…Linear space exploration is common in computer graphics, and can be applied to the modelling of surface discretizations that meet construction constraints. Poranne et al proposed different methods to model meshes with planar facets with linear transformations of the nodal coordinates [22]. Applications to the modelling of gridshell structures have been proposed in [23,24,25].…”
Section: Previous Workmentioning
confidence: 99%
See 1 more Smart Citation
“…Linear space exploration is common in computer graphics, and can be applied to the modelling of surface discretizations that meet construction constraints. Poranne et al proposed different methods to model meshes with planar facets with linear transformations of the nodal coordinates [22]. Applications to the modelling of gridshell structures have been proposed in [23,24,25].…”
Section: Previous Workmentioning
confidence: 99%
“…Such transformations have already been studied in previous literature and are known as discrete Combescure transformations [34]. Poranne et al showed how to construct the linear space of discrete Combescure transformations by assembling linear constraints computed on each mesh faces [22]. These trasnformations are found in various contexts, for example in the study of equilibrium of thin shell structures [35].…”
Section: Null-space and Geometrical Interpretationmentioning
confidence: 99%
“…Various numerical approaches have been used: constrained minimization, nonlinear least squares, penalty methods, augmented Lagrange methods, and others. For computing polyhedral surfaces, we mention [64], the work by Poranne et al [76,75], the projection method of Bouaziz et al [20], the augmented Lagrangian method of Deng et al [25], and the guided projection method of Tang et al [100]. This list is not exhaustive.…”
Section: Computational Methodologymentioning
confidence: 99%
“…The method of Yang et al works by approximation and does not allow for a change in combinatorics. For the special case of polyhedral meshes, Poranne et al [75] devised a method for exploring the linear subspaces in the constraint variety.…”
Section: Interactive Design Systems and Design Explorationmentioning
confidence: 99%
“…In this method, a new mesh is computed by applying affine transformations to the faces of the old mesh. Poranne et al [27] provided a characterization of maximal linear subspaces within the manifold of polyhedral surfaces, allowing shape exploration in a larger space than [26]. For meshes with general shape constraints, Bouaziz et al [28] proposed a framework for imposing constraints to mesh elements.…”
Section: Related Workmentioning
confidence: 99%