Name
Abstract | ||
|---|---|---|
In this paper we give a simple method for drawing a closed rational curve specified in terms of control points as two Bézier segments. The main result is the following:For every affine frame (r,s) (where r), for every rational curve F(t) specified over [r,s] by some control polygon (&bgr;0, …, &bgr;m) (where the &bgr;zero are weighted control points or control vectors), the control points (&thgr;0,… ,&thgr;m (w.r.t.[r,s]) of the rational curve G(t) = F4t are given by qi=-1 ibi, where 4:RP1→RP1 is the projectivity mapping [r,s] onto RP1−]r,s]. Thus, in order to draw the entire trace of the curve F over -∞,+∞ , we simply draw the curve segmentsF[(r,s]) and G([r,s]).The correctness of the method is established using a simple geometric argument about ways of partitioning the real projective line into two disjoint segments. Other known methods for drawing rational curves can be justified using similar geometric arguments. |
Year | DOI | Venue |
|---|---|---|
1999 | 10.1145/337680.337696 | ACM Trans. Graph. |
Keywords | DocType | Volume |
bézier curves,control points,de casteljau algorithm,rational curves,subdivision,weights | Journal | 18 |
Issue | ISSN | Citations |
4 | 0730-0301 | 1 |
PageRank | References | Authors |
0.38 | 5 | 1 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jean H. Gallier | 1 | 749 | 111.86 |