Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
On the curvature of curves and surfaces defined by normalforms
Computer Aided Geometric Design
Point inversion and projection for NURBS curve and surface: control polygon approach
Computer Aided Geometric Design
Computer Vision and Image Understanding
Distance extrema for spline models using tangent cones
GI '05 Proceedings of Graphics Interface 2005
A counterexample on point inversion and projection for NURBS curve
Computer Aided Geometric Design
Computing the minimum distance between a point and a NURBS curve
Computer-Aided Design
A torus patch approximation approach for point projection on surfaces
Computer Aided Geometric Design
Circular spline fitting using an evolution process
Journal of Computational and Applied Mathematics
A second order algorithm for orthogonal projection onto curves and surfaces
Computer Aided Geometric Design
Improved algorithms for the projection of points on NURBS curves and surfaces
Computer Aided Geometric Design
An example on approximation by fat arcs and fat biarcs
Computer-Aided Design
Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics
Computer-Aided Design
Critical point analysis using domain lifting for fast geometry queries
Computer-Aided Design
Algorithm for orthogonal projection of parametric curves onto B-spline surfaces
Computer-Aided Design
Continuous point projection to planar freeform curves using spiral curves
The Visual Computer: International Journal of Computer Graphics
Efficient point projection to freeform curves and surfaces
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
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This paper proposes a geometric iteration algorithm for computing point projection and inversion on planar parametric curves based on local biarc approximation. The iteration begins with initial estimation of the projection of the prescribed test point. For each iteration, we construct a biarc that locally approximates a segment on the original curve starting from the current projective point. Then we compute the projective point for the next iteration, as well as the parameter corresponding to it, by projecting the test point onto this biarc. The iterative process terminates when the projective point satisfies the required precision. Examples demonstrate that our algorithm converges faster and is less dependent on the choice of the initial value compared to the traditional geometric iteration algorithms based on single-point approximation.