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Re: Non-uniform b-splines

Posted by Scott Schaefer on January 31, 2005 at 19:21:27:

In Reply to: Re: Non-uniform b-splines posted by donkey on January 27, 2005 at 09:00:49:

: That message didn't show up the way I wrote it. What I wanted to say was that I can't use values for the curve parameter, u, where:

: u < U[3]

: or

: u < U[n+1]

: : Hi,

: : This question isn't really about subdivision, but maybe someone here still knows the answer. I'm also sorry if the question is stupid, since I'm pretty new to the whole thing.

: : I'm trying to define and draw non-uniform b-splines. And it works out rather fine. With Cox-deBoor recursion I can generate both uniform and non-uniform curves, closed or open. The problem comes with the parameter value.

: : If I have a knot-sequence U {0, 1, 2, .., n+4} and some control points P[0], P[1], .., P[n] for cubic spline-segments, I can't use parametervalues, u, where u U[n+1]. When I do, the resulting values goes towards 0 for every control point. The visual result is for every set of knots and control points a curve that starts and ends in origo.

For cubic B-splines each control point is associated with 3 knot values. If your not values are u0...u_n+1 and control points p_1...p_n, then p_i is associated with the knot vector {u_i-1,u_i,u_i+1}. In this situation, you should be able to evaluate from u_2 to u_n-1. In practice, people ususally put a triple knot at the end points to force interpolation of the first and last control points.

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: : That message didn't show up the way I wrote it. What I wanted to say was that I can't use values for the curve parameter, u, where: : : u < U[3] : : or : : u < U[n+1] : : : Hi, : : : This question isn't really about subdivision, but maybe someone here still knows the answer. I'm also sorry if the question is stupid, since I'm pretty new to the whole thing. : : : I'm trying to define and draw non-uniform b-splines. And it works out rather fine. With Cox-deBoor recursion I can generate both uniform and non-uniform curves, closed or open. The problem comes with the parameter value. : : : If I have a knot-sequence U {0, 1, 2, .., n+4} and some control points P[0], P[1], .., P[n] for cubic spline-segments, I can't use parametervalues, u, where u U[n+1]. When I do, the resulting values goes towards 0 for every control point. The visual result is for every set of knots and control points a curve that starts and ends in origo. : For cubic B-splines each control point is associated with 3 knot values. If your not values are u0...u_n+1 and control points p_1...p_n, then p_i is associated with the knot vector {u_i-1,u_i,u_i+1}. In this situation, you should be able to evaluate from u_2 to u_n-1. In practice, people ususally put a triple knot at the end points to force interpolation of the first and last control points.

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