A general construction scheme for unit quaternion curves with simple high order derivatives
Explore this paper's citation graph
Summary
A general method is developed that transforms a curve in 3 (defined as a weighted sum of basis functions) into its unit quaternion analogue in 3 , and this method is applied to well-known spline curves to construct various unitquaternion curves which share many important differential properties with their original curves.
- Type
- article
- Published
- 1995-09-15
- Cited by
- 263
- References
- 18
- OpenAlex
- https://openalex.org/W2012294177
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:1029131
Keywords
Citation, Order (exchange), Computer science, Simple (philosophy), Unit (ring theory)
References
- Optimal Spacecraft Rotational Maneuvers
- Models and Techniques in Computer Animation
- Visualization of moving objects using dual quaternion curves
- Optimal Continuous Torque Attitude Maneuvers
- A recursive evaluation algorithm for a class of Catmull-Rom splines
- Interpolating solid orientations with circular blending quaternion curves
- A Compact Differential Formula for the First Derivative of a Unit Quaternion Curve
- A C/sup 2/-continuous B-spline quaternion curve interpolating a given sequence of solid orientations
- Animating rotation with quaternion curves
- A Practical Guide to Splines
- Smooth interpolation of orientations with angular velocity constraints using quaternions
- Elements of Quaternions
- Quaternion Calculus for Animation
- Orientation interpolation in quaternion space using spherical biarcs
- VIII.4 – USING GEOMETRIC CONSTRUCTIONS TO INTERPOLATE ORIENTATION WITH QUATERNIONS
- Smooth Interpolation of Orientations
Cited by
- Quaternion Gauss Maps and Optimal Framings of Curves and Surfaces
- A framework for learning photographic composition preferences from gameplay data
- Déplacement d'un manequin virtuel dans un environnement encombré : simulation de mouvement en intégrant les contraintes d'équilibre
- Bangenerering för industrirobot med 6 frihetsgrader
- Réduction de dimension pour l'animation de personnages
- Automatic 5-axis NC toolpath generation
- Continuous-Time Estimation of Attitude Using B-Splines on Lie Groups
- The exponential map for the group of similarity transformations and applications to motion interpolation
- C2 spherical Bézier splines
- A new closed-form approach to absolute orientation
- Relative continuous-time SLAM
- Biomechanical modeling and control of the human body for computer animation
- The De Casteljau Algorithm on Lie Groups and Spheres
- A new type of free-form curve given by an integral form
- Generation of spherical non-uniform rational basis spline curves and its application in five-axis machining
- Spherical parabolic blends for robot workspace trajectories
- On-line locomotion generation based on motion blending
- General Construction of Time-Domain Filters for Orientation Data
- Practical Parameterization of Rotations Using the Exponential Map
- Cn interpolation on smooth manifolds with one-parameter transformations
Related papers
- Obtaining Triplet from Quaternions
- A Unified Approach: Split Quaternions with Quaternion Coefficients and Quaternions with Dual Coefficients
- Modeling and control for a quadrotor UAV based on quaternion
- Quaternions in molecular modeling.
- On Generalized Tetranacci Quaternions
- A simple improved iteration scheme for electronic structure calculations