Analysis of the offset to a parabola
Computer Aided Geometric Design
Minimal energy surfaces using parametric splines
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
Adaptive subdivision and the length and energy of Be´zier curves
Computational Geometry: Theory and Applications
Energy formulations of A-splines
Computer Aided Geometric Design
Planar G2 transition with a fair Pythagorean hodograph quintic curve
Journal of Computational and Applied Mathematics
Geometric Hermite curves with minimum strain energy
Computer Aided Geometric Design
Sketch-Based Interfaces and Modeling (SBIM): Sketching piecewise clothoid curves
Computers and Graphics
Complex rational Bézier curves
Computer Aided Geometric Design
The elastic bending energy of pythagorean-hodograph curves
Computer Aided Geometric Design
Technical Section: A blending interpolator with value control and minimal strain energy
Computers and Graphics
Proceedings of the 2010 ACM Symposium on Applied Computing
Hermite interpolation by hypocycloids and epicycloids with rational offsets
Computer Aided Geometric Design
Path planning for deformable linear objects
IEEE Transactions on Robotics
Approximate convolution with pairs of cubic Bézier LN curves
Computer Aided Geometric Design
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This paper derives expressions for the arc length and the bending energy of quadratic Bezier curves. The formulas are in terms of the control point coordinates. For fixed start and end points of the Bezier curve, the locus of the middle control point is analyzed for curves of fixed arc length or bending energy. In the case of arc length this locus is convex. For bending energy it is not. Given a line or a circle and fixed end points, the locus of the middle control point is determined for those curves that are tangent to a given line or circle. For line tangency, this locus is a parallel line. In the case of the circle, the locus can be classified into one of six major types. In some of these cases, the locus contains circular arcs. These results are then used to implement fast algorithms that construct quadratic Bezier curves tangent to a given line or circle, with given end points, that minimize bending energy or arc length.