New computer methods for global optimization
New computer methods for global optimization
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Honest plotting, global extrema, and interval arithmetic
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
An accurate algorithm for rasterizing algebraic curves
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Distance approximations for rasterizing implicit curves
ACM Transactions on Graphics (TOG)
From honest to intelligent plotting
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Topologically reliable display of algebraic curves
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Performance of Various Computers Using Standard Linear Equations Software
Performance of Various Computers Using Standard Linear Equations Software
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Resolution independent curve rendering using programmable graphics hardware
ACM SIGGRAPH 2005 Papers
Useful computations need useful numbers
ACM Communications in Computer Algebra
A New Framework for Sharp and Efficient Resolution of NCSP with Manifolds of Solutions
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
ACM Transactions on Graphics (TOG)
EGSR'04 Proceedings of the Fifteenth Eurographics conference on Rendering Techniques
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This paper presents a series of new algorithms for reliably graphing two-dimensional implicit equations and inequalities. A clear standard for interpreting the graphs generated by two-dimensional graphing software is introduced and used to evaluate the presented algorithms. The first approach presented uses a standard interval arithmetic library. This approach is shown to be faulty; an analysis of the failure reveals a limitation of standard interval arithmetic. Subsequent algorithms are developed in parallel with improvements and extensions to the interval arithmetic used by the graphing algorithms. Graphs exhibiting a variety of mathematical and artistic phenomena are shown to be graphed correctly by the presented algorithms. A brief comparison of the final algorithm presented to other graphing algorithms is included.