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A c²-continous b-spline quaternion curve interpolating a given sequence of solid orientations (1995).
| Content Provider | CiteSeerX |
|---|---|
| Author | Kim, Myoung-Jun Kim, Myung-Soo Shin, Sung Yong |
| Abstract | An algorithm is presented that constructs a C²-continuous B-spline quaternion curve which interpolates a given sequence of unit quaternions on the rotation group SO(3). The de Casteljau type construction method of B-spline curves can be extended to generate B-spline quaternion curves [Sch92]; however, the B-spline quaternion curves do not have C²-continuity in SO(3). The authors [KKS94a] recently suggested a new construction method that can extend a Bspline curve to a similar one in SO(3) while preserving the C^k-continuity of the B-spline curve. We adapt this method for the construction of a B-spline quaternion interpolation curve. Thus, the problem essentially reduces to the problem of finding the control points for the B-spline interpolation curve. However, due to the non-linearity of the associated constraint equations, it is non-trivial to compute the B-spline control points. We provide an efficient iterative refinement solution which can approximate the control points... |
| File Format | |
| Publisher Date | 1995-01-01 |
| Access Restriction | Open |
| Subject Keyword | Continous B-spline Quaternion Curve Solid Orientation Given Sequence Control Point B-spline Curve B-spline Quaternion Curve Similar One B-spline Control Point Casteljau Type Construction Method New Construction Method Continuous B-spline Quaternion Curve Unit Quaternion B-spline Interpolation Curve Bspline Curve Rotation Group Associated Constraint Equation Efficient Iterative Refinement Solution B-spline Quaternion Interpolation Curve |
| Content Type | Text |
