International Journal of Geometric Methods in Modern Physics · 2019 · 23 citations · 12 references
ArchitectureComputer ScienceDesignComputational GeometryComputer-aided DesignGeometric ModelingCurve InterpolationCurve ModelingGeometry ProcessingShape InterpolationSurface DesignSurface InterpolationBezier Curve InterpolationBezier SurfacesControl PointsGeometric InterpolationInvariantsMotion InterpolationSpherical CurvesTransference Principles
This paper considers a kind of design of a ruled surface. The design interconnects some concepts from the fields of computer-aided geometric design (CAGD) and kinematics. Dual unit spherical Bézier-like curves on the dual unit sphere (DUS) are obtained by a novel method with respect to the control points. A dual unit spherical Bézier-like curve corresponds to a ruled surface by using Study’s transference principle and closed ruled surfaces are determined via control points and also, integral invariants of these surfaces are investigated. Finally, the results are illustrated by several examples and the motion interpolation was shown as an embodiment of this method.
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Animating rotation with quaternion curves
Ken Shoemake · ACM SIGGRAPH Computer Graphics · 1985 · 1.7K citations
Geometric Construction of Be´zier Motions
Q. J. Ge, Bahram Ravani · Journal of Mechanical Design · 1994 · 99 citations