Parametric keyframe interpolation incorporating kinetic adjustment and phrasing control
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Interpolating splines with local tension, continuity, and bias control
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
An intelligent approach to discrete sampling of parametric curves
SAC '93 Proceedings of the 1993 ACM/SIGAPP symposium on Applied computing: states of the art and practice
Fast and accurate parametric curve length computation
Journal of Graphics Tools
Point-based methods for estimating the length of a parametric curve
Journal of Computational and Applied Mathematics
Transition Management for the Smooth Flight of a Small Autonomous Helicopter
Journal of Intelligent and Robotic Systems
Automatic generation of computeranimation: using AI for movie animation
Automatic generation of computeranimation: using AI for movie animation
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Specifying constraints on motion is simpler if the curve is parameterized by arc length, but many parametric curves of practical interest cannot be parameterized by arc length. An approximate numerical reparameterization technique that improves on a previous algorithm by using a different numerical integration procedure that recursively subdivides the curve and creates a table of the subdivision points is presented. The use of the table greatly reduces the computation required for subsequent arc length calculations. After table construction, the algorithm takes nearly constant time for each arc length calculation. A linear increase in the number of control points can result in a more than linear increase in computation. Examples of this type of behavior are shown.