Dynamic Remeshing and Applications

[+] Author and Article Information
J. Vorsatz, Ch. Rössl, H.-P. Seidel

Max-Planck-Institut für Informatik, Saarbrücken, Germany

J. Comput. Inf. Sci. Eng 3(4), 338-344 (Dec 24, 2003) (7 pages) doi:10.1115/1.1631021 History: Received August 01, 2003; Revised October 01, 2003; Online December 24, 2003
Copyright © 2003 by ASME
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Grahic Jump Location
Simple projections into a fitting plane leads to degeneracies in areas with high curvature (left), whereas a local mapping with Floater’s shape preserving parametrizations performs well (right).
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Example for calculating the shift vector for the vertex inside triangle (left), on edge (middle), and on vertex (right) case. The remesh M is drawn in wireframe, the domain mesh D is shaded. The arrow shows the vector calculated by the relaxation operator U , the shift is restricted to the shaded area, the dot marks the final position of the center vertex.
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The remesh M (straight lines) might miss some feature part of the domain mesh D (curved) if we set ωij=1. We have to incorporate the area of the triangles of D that are covered by a 1-ring of a vertex in M into the relaxation operator to solve this problem and get a uniform sampling of D .
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The original fandisk dataset with its skeleton and corner-vertices (left) gets remeshed (middle). Due to the restrictions imposed on the relaxation and topological operators, the skeleton is preserved even though we generated a really coarse approximation (right) of the original mesh.
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After a split of a bone-edge of M the newly inserted bone-vertex (light) gets attached to a bone-edge of D (thick lines). If the new vertex has a corner-vertex as its parent (central vertex), we attach it to that bone-edge that has the smallest enclosing angle with the bone-edge that was split. Additionally we require, that the opposite vertex of M can be reached via D ’s skeleton (dotted arc). After that, the new vertex is allowed to move on bone-edges of D exclusively.
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An interactive remeshing session on a mechanical part. The original triangulation on the left gets refined in order to have more degrees of freedom for further processing. Note that the partially remeshed area automatically connects to the fixed vertices of the original mesh.
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Remeshing of a geometrically and topological more complex model (original data-set on the left, remeshed version on the right). Generating a global parameterization an an explicit patch-layout would be a challenging and time consuming task.
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(√3)-remeshing of a tooth-model (original upper left). We first generate the coarse base domain (upper right) and start the refinement steps by applying the topological (√3) split operator twice per step (middle row). The newly inserted vertices are get evenly distributed on the input mesh by the particle system. The lower row shows the final remesh.




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