Scan line methods for displaying parametrically defined surfaces
Communications of the ACM
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Virtual actors living in a real world
CA '95 Proceedings of the Computer Animation
Comparison of three curve intersection algorithms
Computer-Aided Design
Computing curve intersection by homotopy methods
Journal of Computational and Applied Mathematics
Tracking point-curve critical distances
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
SMI 2012: Full Curve intersection using hybrid clipping
Computers and Graphics
A geometric strategy for computing intersections of two spatial parametric curves
The Visual Computer: International Journal of Computer Graphics
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A new class of algorithms for the processing of parametrically defined curves is presented. All the algorithms are based on the 'divide and conquer' (subdivision) paradigm. An important feature which marks out this class of algorithms from earlier subdivision-based algorithms is that the curve is characterized algebraically and not geometrically. Curve shape properties needed for the processing tasks are derived from the algebraic form of the curve. As long as the necessary properties can be derived, any mathematical from of the curve may be used. In particular this paper considers polynominal curves represented in the rational quadratic, cubic or rational cubic form. Shape properties such as linearity and Euclidean bounds are derived and algorithms for drawing and curve-curve intersection are described.