An adaptive subdivision method for surface-fitting from sampled data
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Weighted bicubic spline interpolation to rapidly varying data
ACM Transactions on Graphics (TOG)
Geometric continuity, shape parameters, and geometric constructions for Catmull-Rom splines
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
Multiple-knot and rational cubic beta-splines
ACM Transactions on Graphics (TOG)
Rational continuity: parametric, geometric, and Frenet frame continuity of rational curves
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Knot insertion for Beta-spline curves and surfaces
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
Mathematical Methods for Curves and Surfaces
Geometric Continuity of Parametric Curves: Three Equivalent Characterizations
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
An analytical continuous-curvature path-smoothing algorithm
IEEE Transactions on Robotics
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Parametric spline curves are typically constructed so that the first n parametric derivatives agree where the curve segments abut. This type of continuity condition has become known as Cn or nth order parametric continuity. We show that the use of parametric continuity disallows many parametrizations which generate geometrically smooth curves. We define nth order geometric continuity (Gn), develop constraint equations that are necessary and sufficient for geometric continuity of curves, and show that geometric continuity is a relaxed for of parametric continuity. Gn continuity provides for the introduction of n quantities known as shape parameters which can be made available to a designer in a computer aided design environment to modify the shape of curves without moving control vertices. Several applications of the theory are discussed, along with topics of future research.