Adaptive forward differencing for rendering curves and surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Numerical recipes in C: the art of scientific computing
Numerical recipes in C: the art of scientific computing
The graphical processing of B-splines in a highly dynamic environment
The graphical processing of B-splines in a highly dynamic environment
Factoring a homogeneous transformation for a more efficient graphics pipeline
Computer Graphics Forum
Scan line methods for displaying parametrically defined surfaces
Communications of the ACM
Interactive display of large-scale NURBS models
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Interactive Display of Large NURBS Models
IEEE Transactions on Visualization and Computer Graphics
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Using formal analysis of parallel and perspective viewing transformation behavior, closed-form form expressions are obtained for immediate evaluation of maximum, minimum, and average scales at a given point in space. While these are constant for parallel transformations, they vary from point to point for perspective transformations. The average scale of a transformation is expressed in ways useful for heuristic computations. The expressions indicate how transformations perform in general without providing guarantees. It is shown that these results apply to the dynamic tessellation of curved surfaces. The maximum scale of a transformation across a bounded region can guarantee that one will meet postviewing approximation thresholds specified in display coordinates, based on derivative bounds precomputed in modeling coordinates.