Generalized scanning technique for display of parametrically defined surfaces
IEEE Computer Graphics and Applications
Adaptive forward differencing for rendering curves and surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
Real-time rendering of trimmed surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
On the stability of transformations between power and Bernstein polynomial forms
Computer Aided Geometric Design
Tessellation of trimmed NURB surfaces
Computer Aided Geometric Design
Rendering trimmed NURBS with adaptive forward differencing
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
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Three methods for evaluating the surface coordinates, first derivatives, and normal vectors of a NURB surface are compared. These methods include forward differencing, knot insertion, and a tow-stage Cox-de Boor technique. The computational complexity of each of these techniques is analyzed and summarized. The use of Hermite functions is shown to yield a poor approximation for the shading functions of a NURB surface. An improved method for computing derivatives by knot insertion is presented. An efficient algorithm for computing the foward difference matrix and a method for using foward differencing to compute the first derivatives of a NURB surface are also presented.