Approximate convolution with pairs of cubic Bézier LN curves

Authors:
Young Joon Ahn;Christoph M. Hoffmann
Affiliations:
Department of Mathematics Education, Chosun University, Gwangju 501-759, South Korea;Department of Computer Science, Purdue University, IN 47907, USA
Venue:
Computer Aided Geometric Design
Year:
2011

Citing 19
Cited 2

Analysis of the offset to a parabola

Computer Aided Geometric Design
An O(h2n) Hermite approximation for conic sections

Computer Aided Geometric Design
Polynomial/rational approximation of Minkowski sum boundary curves

Graphical Models and Image Processing
Hermite interpolation by piecewise polynomial surfaces with rational offsets

Computer Aided Geometric Design
Comparing Offset Curve Approximation Methods

IEEE Computer Graphics and Applications
Approximation of circular arcs and offset curves by Bézier curves of high degree

Journal of Computational and Applied Mathematics
Computing the convolution and the Minkowski sum of surfaces

Proceedings of the 21st spring conference on Computer graphics
Offset-rational sinusoidal spirals in Bézier form

Computer Aided Geometric Design
Minkowski sum boundary surfaces of 3D-objects

Graphical Models
Evaluating the boundary and covering degree of planar Minkowski sums and other geometrical convolutions

Journal of Computational and Applied Mathematics
Convolution surfaces of quadratic triangular Bézier surfaces

Computer Aided Geometric Design
Computing exact rational offsets of quadratic triangular Bézier surface patches

Computer-Aided Design
Preface: Pythagorean-hodograph curves and related topics

Computer Aided Geometric Design
On rationally supported surfaces

Computer Aided Geometric Design
PN surfaces and their convolutions with rational surfaces

Computer Aided Geometric Design
Equivolumetric offset surfaces

Computer Aided Geometric Design
Parameterizing surfaces with certain special support functions, including offsets of quadrics and rationally supported surfaces

Journal of Symbolic Computation
Partial degree formulae for plane offset curves

Journal of Symbolic Computation
Finding the best conic approximation to the convolution curve of two compatible conics based on Hausdorff distance

Computer-Aided Design

Exploring hypersurfaces with offset-like convolutions

Computer Aided Geometric Design
Geometric constraints on quadratic Bézier curves using minimal length and energy

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we present an approximation method for the convolution of two planar curves using pairs of compatible cubic Bezier curves with linear normals (LN). We characterize the necessary and sufficient conditions for two compatible cubic Bezier LN curves with the same linear normal map to exist. Using this characterization, we obtain the cubic spline approximation of the convolution curve. As illustration, we apply our method to the approximation of a font where the letters are constructed as the Minkowski sum of two planar curves. We also present numerical results using our approximation method for offset curves and compare our method to previous results.