curve fitting - Why B-Spline are defined only where basis funcition sum to 1? -


i'm looking understand b-spline. don't understand why << curve defined order basis functions overlap>>, order degree+1 (for cubic order 4). found number equal order of basis functions overlap sum 1, , maybe linked fact curve start here.

the first phrase in:http://www-evasion.imag.fr/~francois.faure/doc/inventormentor/sgi_html/ch08.html in "knot sequence" section. pasted you:

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the definition of curve states, nurbs factors of basis function sum 1. outside interval, sum lower 1.

e.g. take 2 points p1 , p2 (and give them coordinates like). combination q = 0.5*p1 + 0.5 * p2 gives point q in middle of p1 , p2 (as 0.5 + 0.5 = 1). point q' = 0.2 * p1 + 0.2 * p2 sit? try out...


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