Generating B-spline curves with points, normals and curvature constraints: A constructive approach

Abdulwahed Abbas; Ahmad Nasri; Takashi Maekawa

doi:10.1007/s00371-010-0441-2

Generating B-spline curves with points, normals and curvature constraints: A constructive approach

Abdulwahed Abbas^*, Ahmad Nasri, Takashi Maekawa

^*Corresponding author for this work

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

21 Citations (Scopus)

Abstract

This paper presents a constructive method for generating a uniform cubic B-spline curve interpolating a set of data points simultaneously controlled by normal and curvature constraints. By comparison, currently published methods have addressed one or two of those constraints (point, normal or cross-curvature interpolation), but not all three constraints simultaneously with C2 continuity. Combining these constraints provides better control of the generated curve in particular for feature curves on free-form surfaces. Our approach is local and provides exact interpolation of these constraints.

Original language	English
Pages (from-to)	823-829
Number of pages	7
Journal	Visual Computer
Volume	26
Issue number	6-8
DOIs	https://doi.org/10.1007/s00371-010-0441-2
Publication status	Published - 2010 Jun 1
Externally published	Yes

Keywords

B-splines curves and surfaces
Curvature
Fitting
Interpolation
Limit curve and surface
Normal
Recursive subdivision

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Computer Graphics and Computer-Aided Design

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10.1007/s00371-010-0441-2

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abstract = "This paper presents a constructive method for generating a uniform cubic B-spline curve interpolating a set of data points simultaneously controlled by normal and curvature constraints. By comparison, currently published methods have addressed one or two of those constraints (point, normal or cross-curvature interpolation), but not all three constraints simultaneously with C2 continuity. Combining these constraints provides better control of the generated curve in particular for feature curves on free-form surfaces. Our approach is local and provides exact interpolation of these constraints.",

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author = "Abdulwahed Abbas and Ahmad Nasri and Takashi Maekawa",

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T1 - Generating B-spline curves with points, normals and curvature constraints

T2 - A constructive approach

AU - Abbas, Abdulwahed

AU - Nasri, Ahmad

AU - Maekawa, Takashi

PY - 2010/6/1

Y1 - 2010/6/1

N2 - This paper presents a constructive method for generating a uniform cubic B-spline curve interpolating a set of data points simultaneously controlled by normal and curvature constraints. By comparison, currently published methods have addressed one or two of those constraints (point, normal or cross-curvature interpolation), but not all three constraints simultaneously with C2 continuity. Combining these constraints provides better control of the generated curve in particular for feature curves on free-form surfaces. Our approach is local and provides exact interpolation of these constraints.

AB - This paper presents a constructive method for generating a uniform cubic B-spline curve interpolating a set of data points simultaneously controlled by normal and curvature constraints. By comparison, currently published methods have addressed one or two of those constraints (point, normal or cross-curvature interpolation), but not all three constraints simultaneously with C2 continuity. Combining these constraints provides better control of the generated curve in particular for feature curves on free-form surfaces. Our approach is local and provides exact interpolation of these constraints.

KW - B-splines curves and surfaces

KW - Curvature

KW - Fitting

KW - Interpolation

KW - Limit curve and surface

KW - Normal

KW - Recursive subdivision

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DO - 10.1007/s00371-010-0441-2

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VL - 26

SP - 823

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JO - Visual Computer

JF - Visual Computer

IS - 6-8

ER -

Generating B-spline curves with points, normals and curvature constraints: A constructive approach

Abstract

Keywords

ASJC Scopus subject areas

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