SGP04: Eurographics Symposium on Geometry Processing
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Browsing SGP04: Eurographics Symposium on Geometry Processing by Subject "Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling"
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Item Connectivity Transformation for Mesh Metamorphosis(The Eurographics Association, 2004) Ahn, Minsu; Lee, Seungyong; Seidel, Hans-Peter; Roberto Scopigno and Denis ZorinIn previous mesh morphing techniques, the vertex set and connectivity of an in-between mesh are fixed and only the vertex positions are interpolated between input meshes. With this restriction, to accurately represent both source and target shapes, an in-between mesh should contain a much larger number of vertices than input meshes. This paper proposes a novel approach for mesh morphing, which includes connectivity changes in a metamorphosis. With the approach, an in-between mesh contains only the vertices from the input meshes and so the in-between vertex count does not exceed the sum of source and target vertex counts. The connectivity changes are realized by a sequence of edge swap operations, determined by considering the geometric errors from the input meshes. Experimental results demonstrate that the proposed approach generates almost same in-between shapes as the metamesh-based approach with a much smaller number of vertices.Item Lofting Curve Networks using Subdivision Surfaces(The Eurographics Association, 2004) Schaefer, S.; Warren, J.; Zorin, D.; Roberto Scopigno and Denis ZorinLofting is a traditional technique for creating a curved shape by first specifying a network of curves that approximates the desired shape and then interpolating these curves with a smooth surface. This paper addresses the problem of lofting from the viewpoint of subdivision. First, we develop a subdivision scheme for an arbitrary network of cubic B-splines capable of being interpolated by a smooth surface. Second, we provide a quadrangulation algorithm to construct the topology of the surface control mesh. Finally, we extend the Catmull-Clark scheme to produce surfaces that interpolate the given curve network. Near the curve network, these lofted subdivision surfaces are C2 bicubic splines, except for those points where three or more curves meet. We prove that the surface is C1 with bounded curvature at these points in the most common cases; empirical results suggest that the surface is also C1 in the general case.Item Registration of Point Cloud Data from a Geometric Optimization Perspective(The Eurographics Association, 2004) Mitra, Niloy J.; Gelfand, Natasha; Pottmann, Helmut; Guibas, Leonidas; Roberto Scopigno and Denis ZorinWe propose a framework for pairwise registration of shapes represented by point cloud data (PCD). We assume that the points are sampled from a surface and formulate the problem of aligning two PCDs as a minimization of the squared distance between the underlying surfaces. Local quadratic approximants of the squared distance function are used to develop a linear system whose solution gives the best aligning rigid transform for the given pair of point clouds. The rigid transform is applied and the linear system corresponding to the new orientation is build. This process is iterated until it converges. The point-to-point and the point-to-plane Iterated Closest Point (ICP) algorithms can be treated as special cases in this framework. Our algorithm can align PCDs even when they are placed far apart, and is experimentally found to be more stable than point-to-plane ICP. We analyze the convergence behavior of our algorithm and of point-to-point and point-to-plane ICP under our proposed framework, and derive bounds on their rate of convergence. We compare the stability and convergence properties of our algorithm with other registration algorithms on a variety of scanned data.Item Smooth Subdivision of Tetrahedral Meshes(The Eurographics Association, 2004) Schaefer, S.; Hakenberg, J.; Warren, J.; Roberto Scopigno and Denis ZorinWe describe a new subdivision scheme for unstructured tetrahedral meshes. Previous tetrahedral schemes based on generalizations of box splines have encoded arbitrary directional preferences in their associated subdivision rules that were not reflected in tetrahedral base mesh. Our method avoids this choice of preferred directions resulting a scheme that is simple to implement via repeated smoothing. In an extended appendix, we analyze this tetrahedral scheme and prove that the scheme generates C2 deformations everywhere except along edges of the tetrahedral base mesh. Along edges shared by four or more tetrahedra in the base mesh, we present strong evidence that the scheme generates C1 deformations.Item Topology Preserving Surface Extraction Using Adaptive Subdivision(The Eurographics Association, 2004) Varadhan, Gokul; Krishnan, Shankar; Sriram, TVN; Manocha, Dinesh; Roberto Scopigno and Denis ZorinWe address the problem of computing a topology preserving isosurface from a volumetric grid using Marching Cubes for geometry processing applications. We present a novel topology preserving subdivision algorithm to generate an adaptive volumetric grid. Our algorithm ensures that every grid cell satisfies two local geometric criteria: a complex cell criterion and a star-shaped criterion. We show that these two criteria are sufficient to ensure that the surface extracted from the grid using Marching Cubes has the same genus and connectedness as that of the exact isosurface. We use our subdivision algorithm for accurate boundary evaluation of CSG combinations of polyhedra and low degree algebraic primitives, translational motion planning, model simplification and remeshing. The running time of our algorithm varies between a few seconds for simple models composed of a few thousand triangles to tens of seconds for complex polyhedral models represented using hundreds of thousands of triangles.