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Re: pccm knot insertion question

Posted by Scott Schaefer on January 26, 2005 at 10:38:58:

In Reply to: pccm knot insertion question posted by soren on December 14, 2004 at 21:41:08:

: I am stuck. I am attempting to implement "Patching Catmull Clark Meshes" from siggraph 2000 by Jorg Peters. I dont understand the knot insertion step, which I am told is really easy.

: I need to insert three new knots at the endpoints to interpolate my nurbs patches. fine.

: I need to insert three new control points to preserve the relationship beween degree,ctrl, and knots. fine.

: what I dont understand are the rules for the new control points,

: Q0 = (P-1 + 4P0 + P1)/6
: Q1 = (P0 + 2P1)/3
: Q2 = P1
: Q3 = P2

: how can I use these in a control array that already contains P1, P2 ??? Isnt that a problem?

: I understand that when the spline function is evaluated, these guys will match up with P0, P0,P0, P0, but I feel like I am setting something up wrong, or miusunderstanding something.

I haven't read the paper recently. However, the rules that you specify look like the cubic B-spline subdivision limit mask (for the first point) with some end-point rule. Are these rules used on the boundary of the patch, perhaps?

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Comments:
: : I am stuck. I am attempting to implement "Patching Catmull Clark Meshes" from siggraph 2000 by Jorg Peters. I dont understand the knot insertion step, which I am told is really easy. : : I need to insert three new knots at the endpoints to interpolate my nurbs patches. fine. : : I need to insert three new control points to preserve the relationship beween degree,ctrl, and knots. fine. : : what I dont understand are the rules for the new control points, : : Q0 = (P-1 + 4P0 + P1)/6 : : Q1 = (P0 + 2P1)/3 : : Q2 = P1 : : Q3 = P2 : : how can I use these in a control array that already contains P1, P2 ??? Isnt that a problem? : : I understand that when the spline function is evaluated, these guys will match up with P0, P0,P0, P0, but I feel like I am setting something up wrong, or miusunderstanding something. : I haven't read the paper recently. However, the rules that you specify look like the cubic B-spline subdivision limit mask (for the first point) with some end-point rule. Are these rules used on the boundary of the patch, perhaps?

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