Geometric Parameters Based Cubic PH Curve Interpolation and Approximation ★

The Pythagorean-hodograph curves offer unique computational advantages in computer aided design and manufacturing. In this paper, geometric parameters based cubic PH curve interpolation and approximation algorithms are presented. The essential geometric parameters include the ratio ρ of the adjacent control polygon legs, the control polygon angle θ, the first control polygon leg L, the included angle δ between the first control polygon edge and the edge joining the origin O and the first control point, as well as the coefficient Dir of curve rotation. Furthermore the problem of PH curve approximation with endpoints interpolation to a cubic non-PH curve is studied, including the algorithms based on different geometric parameters input {δ, θ} , {ρ, θ} and {ρ, δ} respectively.