To describe the tool path of a CNC machine, it is often necessary to approximate curves by G1 arc splines with the number of arc segments as small as possible. Ahn et al. have proposed an iterative algorithm for approximating quadratic Be

The polygonal approximation problem is a primary problem in computer graphics, pattern recognition, CAD/CAM, etc. In R2, the cone intersection method (CIM) is one of the most e

A method for constructing a cubic Pythagorean hodograph (PH) curve (called a Tschirnhausen cubic curve as well) satisfying unbalanced Hermite interpolation conditions is presented. The resultant curve interpolates two given end points, and has a given vector as the tangent vector at the starting point. The generation method is based on complex number calculation. Resultant curves are represented in a B

Meek and Walton discussed the approximation of discrete data by G1 arc splines in 1992. For a biarc from the start point A to the end point B, they assumed that the sum of two counterclockwise angles of the two arcs was equal to the sum of the counterclockwise angle from the start tangent vector to the vector B-A and that from the vector B-A to the terminal tangent vector. In this note, we show that the relation can be relaxed by the addition or subtraction of 2π.

The highlight line model is a powerful tool in assessing the quality of a surface. Efficient highlight line generation is especially important for an interactive design environment. In this paper, a method for dynamic generation of highlight lines on a locally deforming NURBS surface is presented. The method generates frames of the deforming surface and the corresponding highlight lines by directly modifying the current highlight lines using a Taylor expansion technique, instead of going through a tracing process. The highlight lines computation process adopted here enables a unified distance surface to generate all highlight lines in the highlight line family. The computation process is facilitated by looking up pre-calculated information of the tessellation mesh and an indexing technique for the distance surface. The indexing technique is presented to determine when the highlight line model should be re-generated and, to facilitate the highlight line re-generation process. The new technique is suitable for interactive design environments and animation applications as the updating process takes only one subtraction and one vector inner product to get the new parameters for each new node.