Name
Title | ||
|---|---|---|
A general construction scheme for unit quaternion curves with simple high order derivatives |
Abstract | ||
|---|---|---|
This paper proposes a new class of unit quaternion curves in 3 . A general method is developed that transforms a curve in 3 (de- fined as a weighted sum of basis functions) into its unit quaternion analogue in 3 . Applying the method to well-known spline curves (such as Bezier, Hermite, and B-spline curves), we a re able to construct various unit quaternion curves which share many im- portant differential properties with their original curve s. Many of our naive common beliefs in geometry break down even in the simple non-Euclidean space 3 or 3 . For exam- ple, the de Casteljau type construction of cubic B-spline qu aternion curves does not preserve 2-continuity (10). Through the use of decomposition into simple primitive quaternion curves, our quater- nion curves preserve most of the algebraic and differential properties of the original spline curves. |
Year | DOI | Venue |
|---|---|---|
1995 | 10.1145/218380.218486 | SIGGRAPH |
Keywords | Field | DocType |
unit quaternion curve,orientation,hermite,rotation,quaternion,general construction scheme,b-spline,be´zier,simple high order derivative,euclidean space,b spline | B-spline,Spline (mathematics),Family of curves,Algebraic number,Mathematical analysis,Quaternion,Hermite polynomials,Basis function,Artificial intelligence,Computer vision,Pure mathematics,Hurwitz quaternion,Mathematics | Conference |
ISBN | Citations | PageRank |
0-89791-701-4 | 82 | 10.17 |
References | Authors | |
8 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Myoung-jun Kim | 1 | 141 | 19.56 |
| Myung-soo Kim | 2 | 149 | 29.02 |
| Sung Yong Shin | 3 | 1904 | 168.33 |