Smooth interpolation of orientations with angular velocity constraints using quaternions
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Through-the-lens camera control
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
A general construction scheme for unit quaternion curves with simple high order derivatives
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Fast construction of accurate quaternion splines
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Motion Smoothing Using Wavelets
Journal of Intelligent and Robotic Systems
"-Quaternion Splines for the Smooth Interpolation of Orientations
IEEE Transactions on Visualization and Computer Graphics
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
On parametric smoothness of generalised B-spline curves
Computer Aided Geometric Design
An impulsive noise reduction agent for rigid body motion data using B-spline wavelets
Expert Systems with Applications: An International Journal
On parametric smoothness of generalised B-spline curves
Computer Aided Geometric Design
A generative theory of shape
Interpolating solid orientations with a C² -continuous B-spline quaternion curve
Edutainment'07 Proceedings of the 2nd international conference on Technologies for e-learning and digital entertainment
On the Curve Reconstruction in Riemannian Manifolds
Journal of Mathematical Imaging and Vision
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An algorithm is presented that constructs a C/sup 2/-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; however, the B-spline quaternion curves do not have C/sup 2/-continuity in SO(3). The authors recently suggested a new construction method that can extend a B-spline curve to a similar one in SO(3) while preserving the C/sup 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 very precisely.