Geometric modeling
Making the Oslo algorithm more efficient
SIAM Journal on Numerical Analysis
The NURBS book
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Projecting a test point to a NURBS curve finds theclosest point on the curve and point inversion finds thecorresponding parameter for this test point. This paperpresents an accurate and efficient method to solve both ofthese problems. We first subdivide the NURBS curves intoa set of Bézier curves using knot insertion. For pointprojection, we extract candidate Bézier subcurves basedon the relationship between the test point and the controlpolygon of the Bézier subcurve. For point inversion, weextract candidate Bézier subcurves based on the strongconvex hull property, and then find the approximatecandidate points and their corresponding parametervalues. Finally, by comparing the distances between thetest point and candidate points, we can find the closestpoint. We improve its accuracy by using the Newton-Raphsonmethod.