This paper proposesa new class of unit quaternion curves in SO(3). A general method is developed that transforms a curve in R3 (defined as a weighted sum of basis functions) into its unit quaternion analogue in SO(3). Applying the method to well-known spline curves (such as Bézier, Hermite, and B-spline curves), we are able to construct various unit quaternion curves which share many important ...

A T-conic (rational cubic with a quadratic denominator) spiral spline, with shape control parameters, will be discussed with the view to its application in Computer Graphics. An efficient scheme is presented which constructs a curve interpolating a set of given data points and allows subsequent interactive alteration of the shape of the curve by changing the shape control and shape preserving p...

This paper describes the design and implementation of a ROM-Less Direct Digital Frequency Synthesizer (DDS) using Bezier curve approximation. With Bezier curve approximation, phase values between 0 to π are mapped to sine amplitudes. Then, half wave symmetry of sine wave is exploited to construct full sine wave. The proposed approximation introduces maximum error of 7.9×10, which is equivalent ...

A novel modeling method for 3D curve welding seam is presented in this paper based on a welding robot for large workpiece. The 3D curve welding seam tracking is implemented by macro and micro motion which can control translational motion of torch in a large range and implement accurate seam tracking in small range. As such, the self-teaching seam model and real-time seam model are established t...

This paper is an overview of three spline approaches of degree one, two and three. It represents the review and comparative study of Linear, conic and cubic splines for the vectorization of outlines of the planar images. It has various phases including extracting outlines of images, detecting corner points from the detected outlines, and curve fitting. The idea of simulated annealing has been i...

introduction relative dose computation is a necessary step in radiation treatment planning. therefore, finding an approach that is both fast and accurate seems to be necessary. the purpose of this work was to investigate the feasibility of natural cubic spline to reconstruct dose maps for linear accelerator radiation treatment fields in comparison with those of the simulation. materials and met...

O. Ismail, Senior Member, IEEE Abstract— Fixed DP curve is a recent representation of the polynomial curves, proposed by Delgado and Pena in 2003. They introduced a new curve representation with linear computational complexity. An algorithmic approach to degree reduction of interval DP curve is presented in this paper. The four fixed Kharitonov's polynomials (four fixed DP curves) associated wi...