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How to Solve a Cubic Equation, Part 2: The 11 Case

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James F. BlinnAuthors Info & Claims

IEEE Computer Graphics and Applications, Volume 26, Issue 4

Pages 90 - 100

https://doi.org/10.1109/MCG.2006.81

Published: 01 July 2006 Publication History

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Abstract

Jim Blinn discusses a good practical closed-form solution process for cubic equations and makes some observations about the relation between iterative and closed-form solutions.

References

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M. Livio, The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry, Simon and Schuster, 2005.

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F. Acton, Real Computing Made Real, Princeton Univ. Press, 1996, pp. 29–32.

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C. Loop and J.F. Blinn, Real-Time GPU Rendering of Piecewise Algebraic Surfaces, to be published in Proc. Siggraph, ACM Press, 2006.

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J.F. Blinn, Jim Blinn's Corner: Notation, Notation, Notation, Morgan Kauffman, 2003, pp. 262–263.

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J.F. Blinn, "How to Solve a Quadratic Equation," IEEE Computer Graphics and Applications, vol. 25, no. 6, pp. 76–79.

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N.J. Higham, Accuracy and Stability of Numerical Algorithms, SIAM, 2002, pp. 479–481.

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D. Herbison-Evans, "Solving Quartics and Cubics for Graphics," Graphics Gems V, A.W. Paeth, ed., AP Professional, 1995, pp. 11–12.

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W.H. Press et al., Numerical Recipes in C++, Cambridge Univ. Press, 2002, pp. 190–191.

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Cited By

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Yuksel C(2022)High-Performance Polynomial Root Finding for GraphicsProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/35438655:3(1-15)Online publication date: 27-Jul-2022
https://dl.acm.org/doi/10.1145/3543865
Nehab DHoppe H(2008)Random-access rendering of general vector graphicsACM SIGGRAPH Asia 2008 papers10.1145/1457515.1409088(1-10)Online publication date: 10-Dec-2008
https://dl.acm.org/doi/10.1145/1457515.1409088
Qin ZMcCool MKaplan CHaines EMcGuire M(2008)Precise vector textures for real-time 3D renderingProceedings of the 2008 symposium on Interactive 3D graphics and games10.1145/1342250.1342281(199-206)Online publication date: 15-Feb-2008
https://dl.acm.org/doi/10.1145/1342250.1342281
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How to Solve a Cubic Equation, Part 2: The 11 Case

Recommendations

How to Solve a Cubic Equation, Part 1: The Shape of the Discriminant

Jim Blinn begins a discussion on solving cubic equations.
How to Solve a Cubic Equation, Part 4: The 111 Case

Jim Blinn continues his discussion on solving cubic equations
How to Solve a Cubic Equation, Part 3: General Depression and a New Covariant

Jim Blinn continues his discussion on solving cubic equations.

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cover image IEEE Computer Graphics and Applications

IEEE Computer Graphics and Applications Volume 26, Issue 4

July 2006

99 pages

ISSN:0272-1716

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IEEE Computer Society Press

Washington, DC, United States

Publication History

Published: 01 July 2006

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Yuksel C(2022)High-Performance Polynomial Root Finding for GraphicsProceedings of the ACM on Computer Graphics and Interactive Techniques10.1145/35438655:3(1-15)Online publication date: 27-Jul-2022
https://dl.acm.org/doi/10.1145/3543865
Nehab DHoppe H(2008)Random-access rendering of general vector graphicsACM SIGGRAPH Asia 2008 papers10.1145/1457515.1409088(1-10)Online publication date: 10-Dec-2008
https://dl.acm.org/doi/10.1145/1457515.1409088
Qin ZMcCool MKaplan CHaines EMcGuire M(2008)Precise vector textures for real-time 3D renderingProceedings of the 2008 symposium on Interactive 3D graphics and games10.1145/1342250.1342281(199-206)Online publication date: 15-Feb-2008
https://dl.acm.org/doi/10.1145/1342250.1342281
Blinn J(2006)How to Solve a Cubic Equation, Part 3IEEE Computer Graphics and Applications10.1109/MCG.2006.12926:6(92-102)Online publication date: 1-Nov-2006
https://dl.acm.org/doi/10.1109/MCG.2006.129

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Recommendations

How to Solve a Cubic Equation, Part 1: The Shape of the Discriminant

How to Solve a Cubic Equation, Part 4: The 111 Case

How to Solve a Cubic Equation, Part 3: General Depression and a New Covariant

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