Analyzing surfaces: the truth about elimination theory
SCG '87 Proceedings of the third annual symposium on Computational geometry
Accurate Solid Modeling Using Polyhedral Approximations
IEEE Computer Graphics and Applications
Numerically stable implicitization of cubic curves
ACM Transactions on Graphics (TOG)
Comparison of various multivariate resultant formulations
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Implicitization of Parametric Curves by Matrix Annihilation
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
3D Reconstruction of parametric curves: recovering the control points
Machine Graphics & Vision International Journal
Cayley-Dixon projection operator for multi-univariate composed polynomials
Journal of Symbolic Computation
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
Cayley-Dixon resultant matrices of multi-univariate composed polynomials
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
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Classical algebraic geometry has been virtually ignored in computer-aided geometric design. However, because it deals strictly with algorithms, it is really more suited to this field than is modern algebraic geometry, which introduces abstractions far removed from the algorithmic nature of computer-aided design. This tutorial examines resultants, curve implicitization, curve inversion, and curve intersection. Discussion follows a series of examples simple enough for those with only a modest algebra background to follow.