Smooth interpolation of orientations with angular velocity constraints using quaternions
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Visualizing quaternion rotation
ACM Transactions on Graphics (TOG)
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Spherical averages and applications to spherical splines and interpolation
ACM Transactions on Graphics (TOG)
Linear combination of transformations
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
General Construction of Time-Domain Filters for Orientation Data
IEEE Transactions on Visualization and Computer Graphics
Geometric design of motions constrained by a contacting surface pair
Computer Aided Geometric Design
"-Quaternion Splines for the Smooth Interpolation of Orientations
IEEE Transactions on Visualization and Computer Graphics
Energy-minimizing splines in manifolds
ACM SIGGRAPH 2004 Papers
Shape segmentation using local slippage analysis
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A variational approach to spline curves on surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Computer Aided Geometric Design
Bézier curves and C2 interpolation in Riemannian manifolds
Journal of Approximation Theory
Synthesis and evaluation of linear motion transitions
ACM Transactions on Graphics (TOG)
Spline joints for multibody dynamics
ACM SIGGRAPH 2008 papers
International Journal of Computer Mathematics
Metrics for 3D Rotations: Comparison and Analysis
Journal of Mathematical Imaging and Vision
A variational approach to spline curves on surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Computer Aided Geometric Design
Exponentials of skew-symmetric matrices and logarithms of orthogonal matrices
Journal of Computational and Applied Mathematics
Efficient Video Rectification and Stabilisation for Cell-Phones
International Journal of Computer Vision
Applications of conformal geometric algebra in computer vision and graphics
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
Fitting smoothing splines to time-indexed, noisy points on nonlinear manifolds
Image and Vision Computing
Solving inverse configuration space problems by adaptive sampling
Computer-Aided Design
On the Curve Reconstruction in Riemannian Manifolds
Journal of Mathematical Imaging and Vision
Lie-group interpolation and variational recovery for internal variables
Computational Mechanics
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We present an algorithm for generating a twice-differentiable curve on the rotation group SO(3) that interpolated a given ordered set of rotation matrices at their specified knot times. In our approach we regard SO(3) as a Lie group with a bi-invariant Riemannian metriac, and apply the coordinate-invariant methods of Riemannian geometry. The resulting rotation curve is easy to compute, invariant with respect to fixed and moving reference frames, and also approximately minimizes angular acceleration.