From the Wikipedia article: In the mathematical subfield of numerical analysis, de Boor's algorithm is a polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de Casteljau's algorithm for Bézier curves. The algorithm was devised by German-American mathematician Carl R. de Boor. Simplified, potentially faster variants of the de Boor algorithm have been created but they suffer from comparatively lower stability. That article offers what it calls a "naive" implementation def deBoor(k: int, x: int, t, c, p: int): """Evaluates S(x). Arguments --------- k: Index of knot interval that contains x. x: Position. t: Array of knot positions, needs to be padded as described above. c: Array of control points. p: Degree of B-spline. """ d = [c[j + k - p] for j in range(0, p + 1)] for r in range(1, p + 1): for j in range(p, r - 1, -1): alpha = (x - t[j + k - p]) / (t[j + 1 + k - r] - t[j + k - p]) d[j] = (1.0 - alpha) * d[j - 1] + alpha * d[j] return d[p] I have this problem: It looks like the c array goes out of bounds in the first line of code d = [c[j + k - p] for j in range(0, p + 1)] When generating the first point the first loop through range(0, p + 1) for a 3rd degree spline j = 0; k = 0; p = 3; so d[0] will be set to c[ -3 ] Question: How do I prevent attempts to access negative indices of c? Note 1: I tried checking for negative indices and accessing c[0] instead. The results look OK, but can this be correct? Side question, in this line alpha = (x - t[j + k - p]) / (t[j + 1 + k - r] - t[j + k - p]) should there not be a check to prevent divide by zero? Continue reading...
