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By Patria Dobbins

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This method is also known as "Zebra analysis". Technical specifications A NURBS curve is defined by its order, a set of weighted control points, and a knot vector. NURBS curves and surfaces are generalizations of both B-splines and Bézier curves and surfaces, the primary difference being the weighting of the control points which makes NURBS curves rational (non-rational B-splines are a special case of rational B-splines). Whereas Bézier curves evolve into only one parametric direction, usually called s or u, NURBS surfaces evolve into two parametric directions, called s and t or u and v.

These patches should be fitted together in such a way that the boundaries are invisible. This is mathematically expressed by the concept of geometric continuity. Higher-level tools exist which benefit from the ability of NURBS to create and establish geometric continuity of different levels: Positional continuity (G0) holds whenever the end positions of two curves or surfaces are coincidental. The curves or surfaces may still meet at an angle, giving rise to a sharp corner or edge and causing broken highlights.

Curvature The most important property in differential geometry is the curvature κ. ) and relations between the first and second derivative, and thus, the precise curve shape. Having determined the derivatives it is easy to compute or approximated as the arclength from the second derivate κ = | r''(so) | . The direct computation of the curvature κ with these equations is the big advantage of parameterized curves against their polygonal representations. Example: a circle Non-rational splines or Bézier curves may approximate a circle, but they cannot represent it exactly.

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