Geometric modeling using focal surfaces

Jingyi Yu; Xiaotian Yin; Xianfeng Gu; Leonard McMillan; Steve Gortler

doi:10.1145/1278780.1278865

Geometric modeling using focal surfaces

Jingyi Yu
, Xiaotian Yin
, Xianfeng Gu
, Leonard McMillan
, Steve Gortler

Computer Science

University of Delaware
Stony Brook University
University of North Carolina at Chapel Hill

Research output: Contribution to conference › Paper › peer-review

Abstract

The differential geometry of smooth three-dimensional surfaces can be interpreted from one of two perspectives: in terms of oriented frames located on the surface, or in terms of a pair of associated focal surfaces. These focal surfaces are swept by the loci of the principal curvatures' radii. The normal of each focal surface indicates a principal direction at the corresponding point on the original surface [Pottmann and Wallner 2001]. In this article, we utilize piecewise linear focal surfaces, which we call focal meshes, to model smooth surfaces.

Original language	English
DOIs	https://doi.org/10.1145/1278780.1278865
State	Published - 2007
Event	ACM SIGGRAPH 2007 Sketches, SIGGRAPH'07 - San Diego, CA, United States Duration: Aug 5 2007 → Aug 9 2007

Conference

Conference	ACM SIGGRAPH 2007 Sketches, SIGGRAPH'07
Country/Territory	United States
City	San Diego, CA
Period	08/5/07 → 08/9/07

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10.1145/1278780.1278865

Cite this

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title = "Geometric modeling using focal surfaces",

abstract = "The differential geometry of smooth three-dimensional surfaces can be interpreted from one of two perspectives: in terms of oriented frames located on the surface, or in terms of a pair of associated focal surfaces. These focal surfaces are swept by the loci of the principal curvatures' radii. The normal of each focal surface indicates a principal direction at the corresponding point on the original surface [Pottmann and Wallner 2001]. In this article, we utilize piecewise linear focal surfaces, which we call focal meshes, to model smooth surfaces.",

author = "Jingyi Yu and Xiaotian Yin and Xianfeng Gu and Leonard McMillan and Steve Gortler",

year = "2007",

doi = "10.1145/1278780.1278865",

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note = "ACM SIGGRAPH 2007 Sketches, SIGGRAPH'07 ; Conference date: 05-08-2007 Through 09-08-2007",

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T1 - Geometric modeling using focal surfaces

AU - Yu, Jingyi

AU - Yin, Xiaotian

AU - Gu, Xianfeng

AU - McMillan, Leonard

AU - Gortler, Steve

PY - 2007

Y1 - 2007

N2 - The differential geometry of smooth three-dimensional surfaces can be interpreted from one of two perspectives: in terms of oriented frames located on the surface, or in terms of a pair of associated focal surfaces. These focal surfaces are swept by the loci of the principal curvatures' radii. The normal of each focal surface indicates a principal direction at the corresponding point on the original surface [Pottmann and Wallner 2001]. In this article, we utilize piecewise linear focal surfaces, which we call focal meshes, to model smooth surfaces.

AB - The differential geometry of smooth three-dimensional surfaces can be interpreted from one of two perspectives: in terms of oriented frames located on the surface, or in terms of a pair of associated focal surfaces. These focal surfaces are swept by the loci of the principal curvatures' radii. The normal of each focal surface indicates a principal direction at the corresponding point on the original surface [Pottmann and Wallner 2001]. In this article, we utilize piecewise linear focal surfaces, which we call focal meshes, to model smooth surfaces.

UR - https://www.scopus.com/pages/publications/64249132856

U2 - 10.1145/1278780.1278865

DO - 10.1145/1278780.1278865

M3 - Paper

AN - SCOPUS:64249132856

T2 - ACM SIGGRAPH 2007 Sketches, SIGGRAPH'07

Y2 - 5 August 2007 through 9 August 2007

ER -

Geometric modeling using focal surfaces

Abstract

Conference

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