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Variational normal meshes

Friedel, Ilja and Schröder, Peter and Khodakovsky, Andrei (2004) Variational normal meshes. ACM Transactions on Graphics, 23 (4). pp. 1061-1073. ISSN 0730-0301. doi:10.1145/1027411.1027418.

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Hierarchical representations of surfaces have many advantages for digital geometry processing applications. Normal meshes are particularly attractive since their level-to-level displacements are in the local normal direction only. Consequently, they only require scalar coefficients to specify. In this article, we propose a novel method to approximate a given mesh with a normal mesh. Instead of building an associated parameterization on the fly, we assume a globally smooth parameterization at the beginning and cast the problem as one of perturbing this parameterization. Controlling the magnitude of this perturbation gives us explicit control over the range between fully constrained (only scalar coefficients) and unconstrained (3-vector coefficients) approximations. With the unconstrained problem giving the lowest approximation error, we can thus characterize the error cost of normal meshes as a function of the number of nonnormal offsets---we find a significant gain for little (error) cost. Because the normal mesh construction creates a geometry driven approximation, we can replace the difficult geometric distance minimization problem with a much simpler least squares problem. This variational approach reduces magnitude and structure (aliasing) of the error further. Our method separates the parameterization construction into an initial setup followed only by subsequent perturbations, giving us an algorithm which is far simpler to implement, more robust, and significantly faster.

Item Type:Article
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URLURL TypeDescription
Schröder, Peter0000-0002-0323-7674
Additional Information:© 2004 ACM. Received May 2004; revised August 2004; accepted August 2004. This work was supported in part by NSF (DMS-0220905, DMS-0138458, ACI-0219979), the DOE (W-7405-ENG-48/B341492), NVIDIA, the Center for Integrated Multiscale Modeling and Simulation, Alias|Wavefront, and Pixar.
Funding AgencyGrant Number
Department of Energy (DOE)W-7405-ENG-48/B341492
Center for Integrated Multiscale Modeling and SimulationUNSPECIFIED
Subject Keywords:Algorithms, Hierarchy, normal meshes, resampling, (semi-)regular meshes, subdivision, surface approximation
Issue or Number:4
Classification Code:G.1.2 [ Numerical Analysis ]: Approximation— Approximation of surfaces and contours ; G .1.2 [ Numerical Analysis ]: Approximation— W avelets and fractals ; I.3.5 [ Computer Graphics ]: Computational Geometry and Object Modeling— Curve, surface, solid, an
Record Number:CaltechAUTHORS:20161024-174513528
Persistent URL:
Official Citation:Ilja Friedel, Peter Schröder, and Andrei Khodakovsky. 2004. Variational normal meshes. ACM Trans. Graph. 23, 4 (October 2004), 1061-1073. DOI=
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71428
Deposited On:25 Oct 2016 16:54
Last Modified:11 Nov 2021 04:45

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