research-article

Approximating Catmull-Clark subdivision surfaces with bicubic patches

Authors:

Scott SchaeferAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 27, Issue 1

Article No.: 8, Pages 1 - 11

https://doi.org/10.1145/1330511.1330519

Published: 20 March 2008 Publication History

Abstract

We present a simple and computationally efficient algorithm for approximating Catmull-Clark subdivision surfaces using a minimal set of bicubic patches. For each quadrilateral face of the control mesh, we construct a geometry patch and a pair of tangent patches. The geometry patches approximate the shape and silhouette of the Catmull-Clark surface and are smooth everywhere except along patch edges containing an extraordinary vertex where the patches are C⁰. To make the patch surface appear smooth, we provide a pair of tangent patches that approximate the tangent fields of the Catmull-Clark surface. These tangent patches are used to construct a continuous normal field (through their cross-product) for shading and displacement mapping. Using this bifurcated representation, we are able to define an accurate proxy for Catmull-Clark surfaces that is efficient to evaluate on next-generation GPU architectures that expose a programmable tessellation unit.

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Index Terms

Approximating Catmull-Clark subdivision surfaces with bicubic patches
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 27, Issue 1

March 2008

135 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1330511

Issue’s Table of Contents

Copyright © 2008 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 20 March 2008

Accepted: 01 November 2007

Received: 01 June 2007

Published in TOG Volume 27, Issue 1

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Peng BThannasi PCelik K(2025)3D shape reconstruction and generation of natural pozzolan particlesPowder Technology10.1016/j.powtec.2024.120443451(120443)Online publication date: Feb-2025
https://doi.org/10.1016/j.powtec.2024.120443
Marsala MMantzaflaris AMourrain B(2024)G1 spline functions for point cloud fittingApplied Mathematics and Computation10.1016/j.amc.2023.128279460(128279)Online publication date: Jan-2024
https://doi.org/10.1016/j.amc.2023.128279
Marsala MMantzaflaris AMourrain BWhyman SGammon M(2024)From CAD to representations suitable for isogeometric analysis: a complete pipelineEngineering with Computers10.1007/s00366-024-02065-040:6(3429-3447)Online publication date: 23-Sep-2024
https://doi.org/10.1007/s00366-024-02065-0
Wang MJing JGao SBian PMa YZhou N(2023)Improved adaptive tessellation rendering algorithmTechnology and Health Care10.3233/THC-23600931:S1(81-95)Online publication date: 28-Apr-2023
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Xie WHuang TWang MElkind E(2023)3D surface super-resolution from enhanced 2D normal imagesProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/175(1578-1586)Online publication date: 19-Aug-2023
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Kuth BOberberger MChajdas MMeyer Q(2023)Edge‐Friend: Fast and Deterministic Catmull‐Clark Subdivision SurfacesComputer Graphics Forum10.1111/cgf.1486342:8Online publication date: 3-Aug-2023
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Farahat AJüttler BKapl MTakacs T(2023) Isogeometric analysis with -smooth functions over multi-patch surfaces Computer Methods in Applied Mechanics and Engineering10.1016/j.cma.2022.115706403(115706)Online publication date: Jan-2023
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Khan DGui SCheng Z(2023)Molecular Surface Mesh Smoothing with SubdivisionAdvances in Computer Graphics10.1007/978-3-031-50072-5_19(236-248)Online publication date: 28-Aug-2023
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Zhou JHettinga GHouwink SKosinka J(2022)Feature‐Adaptive and Hierarchical Subdivision Gradient MeshesComputer Graphics Forum10.1111/cgf.1444241:1(389-401)Online publication date: 22-Jan-2022
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Xie WHuang TWang M(2022)MNSRNet: Multimodal Transformer Network for 3D Surface Super-Resolution2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR52688.2022.01237(12693-12702)Online publication date: Jun-2022
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