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3.2 Surfaces

A NURBS surface is the generalization of the tensor-product B-spline surface. It is defined over the parametric variables u and v as

  equation89

A NURBS surface has (m+1)(n+1) control points tex2html_wrap_inline1855 and weights tex2html_wrap_inline1857 . Assuming basis functions along the two parametric axes of degree k-1 and l-1, respectively, the number of knots is (m+k+1)(n+l+1). The nondecreasing knot sequence is tex2html_wrap_inline1865 along the u-axis and tex2html_wrap_inline1869 along the v-axis. The parametric domain is tex2html_wrap_inline1873 and tex2html_wrap_inline1875 . If the end knots have multiplicity k and l in the u and v axis respectively, the surface patch will interpolate the four corners of the boundary control points.



Demetri Terzopoulos | Source Reference