An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Parametric keyframe interpolation incorporating kinetic adjustment and phrasing control
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Computer Methods for Mathematical Computations
Computer Methods for Mathematical Computations
Inbetweening for computer animation utilizing moving point constraints
SIGGRAPH '81 Proceedings of the 8th 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
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We are concerned in this paper with associations between spline curves that will hold at all inbetween positions when the control points of these curves are used as key points for animation or sweeping. It is established that any association between two spline curves that can be expressed as the equality of two linear mappings will hold throughout an inbetweening process provided the inbetweening trajectories are coordinated splines that uniquely interpolate the control-point key positions. Multiple associations are possible, so long as the basic requirements of linearity and coordination are observed.