Surface design based on direct curvature editing

Abstract

This paper presents a novel method for modifying the shapes of existing uniform bi-cubic B-spline surfaces by interactively editing the curvatures along isoparametric curves. The method allows us to edit the curvatures of the two intersecting isoparametric curves at each knot with specified positions, unit tangents, and unit normals. The user adjusts the radii of circles, representing the radii of curvature in the u and v isoparametric directions directly via a GUI without having to work with control points and knots. Such shape specifications are converted into iterative repositionings of the control points on the basis of geometrical rules. Using these point-based curvature-editing techniques, we successfully embedded log-aesthetic curves into existing surfaces along their isoparametric curves. Moreover, we were able to distribute the cross curvature with log-aesthetic variation along the isoparametric curves. We applied our technique to the design of automobile hood surfaces to demonstrate the effectiveness of our algorithms.