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| Content Provider | ACM Digital Library |
|---|---|
| Author | Pottmann, Helmut Hofer, Michael |
| Copyright Year | 2004 |
| Abstract | Variational interpolation in curved geometries has many applications, so there has always been demand for geometrically meaningful and efficiently computable $\textit{splines}$ in manifolds. We extend the definition of the familiar cubic spline curves and splines in tension, and we show how to compute these on parametric surfaces, level sets, triangle meshes, and point samples of surfaces. This list is more comprehensive than it looks, because it includes variational motion design for animation, and allows the treatment of obstacles via barrier surfaces. All these instances of the general concept are handled by the same geometric optimization algorithm, which minimizes an energy of curves on surfaces of arbitrary dimension and codimension. |
| Starting Page | 284 |
| Ending Page | 293 |
| Page Count | 10 |
| File Format | |
| ISSN | 07300301 |
| e-ISSN | 15577368 |
| DOI | 10.1145/1015706.1015716 |
| Volume Number | 23 |
| Issue Number | 3 |
| Journal | ACM Transactions on Graphics (TOG) |
| Language | English |
| Publisher | Association for Computing Machinery (ACM) |
| Publisher Date | 2004-08-01 |
| Publisher Place | New York |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Geometric optimization Motion design Obstacle avoidance Splines in manifolds Variational curve design |
| Content Type | Text |
| Resource Type | Article |
| Subject | Computer Graphics and Computer-Aided Design |
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