Smoothing of free-form surfaces with Bézier patches

Lizhuang Ma; Qunsheng Peng

doi:10.1016/0167-8396(94)00003-B

Smoothing of free-form surfaces with Bézier patches

Lizhuang Ma, Qunsheng Peng

Zhejiang University

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

In this paper, a unified method for smoothing free-form surfaces with Bézier patches is presented. A non-smooth surface consisting of bicubic patches is turned into a G¹ surface by the following process. Trim each patch along user-defined parameter lines using subdivision. Attach eight patches (one to each edge and one to each vertex) to each trimmed patch to blend between it and its neighbor patches. Using this method, solid objects bounded with bicubic Bézier patches can be G¹ smoothed with bicubic patches. The operation is local. It provides designers with the facility to adjust the shape of a smoothed object interactively. The method can also be used for constructing smooth closed surfaces whose modeling is important for CAD/CG (cf. (Barnhill, 1985)).

Original language	English
Pages (from-to)	231-249
Number of pages	19
Journal	Computer Aided Geometric Design
Volume	12
Issue number	3
DOIs	https://doi.org/10.1016/0167-8396(94)00003-B
State	Published - May 1995
Externally published	Yes

Keywords

Bézier surfaces
CAD/CG
CAGD
Computational geometry and object modeling-curve, surface, solid, and object representation
Geometric continuity
Smoothing
Transition surfaces

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10.1016/0167-8396(94)00003-B

Cite this

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title = "Smoothing of free-form surfaces with B{\'e}zier patches",

abstract = "In this paper, a unified method for smoothing free-form surfaces with B{\'e}zier patches is presented. A non-smooth surface consisting of bicubic patches is turned into a G1 surface by the following process. Trim each patch along user-defined parameter lines using subdivision. Attach eight patches (one to each edge and one to each vertex) to each trimmed patch to blend between it and its neighbor patches. Using this method, solid objects bounded with bicubic B{\'e}zier patches can be G1 smoothed with bicubic patches. The operation is local. It provides designers with the facility to adjust the shape of a smoothed object interactively. The method can also be used for constructing smooth closed surfaces whose modeling is important for CAD/CG (cf. (Barnhill, 1985)).",

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author = "Lizhuang Ma and Qunsheng Peng",

year = "1995",

month = may,

doi = "10.1016/0167-8396(94)00003-B",

language = "英语",

volume = "12",

pages = "231--249",

journal = "Computer Aided Geometric Design",

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publisher = "Elsevier B.V.",

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}

TY - JOUR

T1 - Smoothing of free-form surfaces with Bézier patches

AU - Ma, Lizhuang

AU - Peng, Qunsheng

PY - 1995/5

Y1 - 1995/5

N2 - In this paper, a unified method for smoothing free-form surfaces with Bézier patches is presented. A non-smooth surface consisting of bicubic patches is turned into a G1 surface by the following process. Trim each patch along user-defined parameter lines using subdivision. Attach eight patches (one to each edge and one to each vertex) to each trimmed patch to blend between it and its neighbor patches. Using this method, solid objects bounded with bicubic Bézier patches can be G1 smoothed with bicubic patches. The operation is local. It provides designers with the facility to adjust the shape of a smoothed object interactively. The method can also be used for constructing smooth closed surfaces whose modeling is important for CAD/CG (cf. (Barnhill, 1985)).

AB - In this paper, a unified method for smoothing free-form surfaces with Bézier patches is presented. A non-smooth surface consisting of bicubic patches is turned into a G1 surface by the following process. Trim each patch along user-defined parameter lines using subdivision. Attach eight patches (one to each edge and one to each vertex) to each trimmed patch to blend between it and its neighbor patches. Using this method, solid objects bounded with bicubic Bézier patches can be G1 smoothed with bicubic patches. The operation is local. It provides designers with the facility to adjust the shape of a smoothed object interactively. The method can also be used for constructing smooth closed surfaces whose modeling is important for CAD/CG (cf. (Barnhill, 1985)).

KW - Bézier surfaces

KW - CAD/CG

KW - CAGD

KW - Computational geometry and object modeling-curve, surface, solid, and object representation

KW - Geometric continuity

KW - Smoothing

KW - Transition surfaces

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U2 - 10.1016/0167-8396(94)00003-B

DO - 10.1016/0167-8396(94)00003-B

M3 - 文章

AN - SCOPUS:0000208571

SN - 0167-8396

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SP - 231

EP - 249

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

IS - 3

ER -

Smoothing of free-form surfaces with Bézier patches

Abstract

Keywords

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