论文信息 - Bézier representation of epitrochoids and hypotrochoids

Bézier representation of epitrochoids and hypotrochoids

We developed a simple method to obtain the rational Bezier representation for segments of epitrochoids and hypotrochoids. This was achieved by adding two circular arcs expressed in Bernstein-like trigonometric basis functions, and considering the equivalence between this trigonometric form and the standard rational Bezier representation.

Javier Sánchez-Reyes

[1] Phillip Barkan,et al. Kinematics and Dynamics of Planar Machinery , 1979 .

[2] Javier Sánchez-Reyes. Higher-order Bézier circles , 1997, Comput. Aided Des..

[3] J. Stillwell,et al. Plane Algebraic Curves , 1986 .

[4] Les A. Piegl,et al. The NURBS Book , 1995, Monographs in Visual Communication.

[5] Javier Sánchez-Reyes,et al. Single-valued curves in polar coordinates , 1990, Comput. Aided Des..

[6] Tom Lyche,et al. Mathematical methods for curves and surfaces II : Lillehammer, 1997 , 1998 .

[7] Javier Sánchez-Reyes,et al. Harmonic rational Bézier curves, p-Bézier curves and trigonometric polynomials , 1998, Comput. Aided Geom. Des..

[8] R. C. Dix. Book Reviews : Kinematics and Dynamics of Planar Machinery: B. Paul, Prentice-Hall, Inc. Englewood Cliffs, New Jersey, 1979 , 1980 .