Planar two-point G1 Hermite interpolating log-aesthetic spirals

Authors:
D. S. Meek;T. Saito;D. J. Walton;N. Yoshida
Affiliations:
Department of Computer Science, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2;Bio-Applications and Systems Engineering, Tokyo University of Agriculture Technology, 2-24-16 Naka-cho Koganei, Tokyo 184-8588, Japan;Department of Computer Science and St. Paul's College, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2;Nihon University, 1-2-1 Izumi-cho Narashino, Chiba, 275-8575, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

Log-aesthetic spirals are currently being studied as fair curves that can be used in computer aided design. A family of planar log-aesthetic spirals that include a point of zero curvature is used in this paper. The two-point G^1 Hermite data that is considered has some restrictions on the angles. This paper proves that for any member of the family, a unique segment of that spiral can be found that matches given two-point G^1 Hermite data.