Comparison of interval methods for plotting algebraic curves

Computer Aided Geometric Design

Volumn 19, Issue 7, 2002, Pages 553-587

  Martin, Ralph ^a   Shou, Huahao ^b,c   Voiculescu, Irina ^d   Bowyer, Adrian ^e   Wang, Guojin ^b  

^a CARDIFF UNIVERSITY   (United Kingdom)

^b ZHEJIANG UNIVERSITY   (China)

^c ZHEJIANG UNIVERSITY OF TECHNOLOGY   (China)

^d UNIVERSITY OF OXFORD   (United Kingdom)

^e University of Bath   (United Kingdom)

Author keywords

Algebraic curves; Interval analysis; Range analysis; Subdivision

Indexed keywords

ALGEBRA; COMPUTATIONAL METHODS; COMPUTER AIDED DESIGN; FUNCTIONS; POLYNOMIALS; PROBLEM SOLVING;

COMPUTER AIDED GEOMETRICAL DESIGN (CAGD);

COMPUTATIONAL GEOMETRY;

EID: 0036647957     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(02)00146-2     Document Type: Article

References (36)

1. Ray tracing general parametric surfaces using interval arithmetic
2. Robust arithmetic for multivariate Bernstein-form polynomials
3. Interval methods in geometric modelling
4. The Bernstein form of a polynomial
5. A tracking algorithm for implicitly defined curves
6. Affine arithmetic and its applications to computer graphics
7. Interval arithmetic and recursive subdivision for implicit functions and constructive solid geometry
8. On the numerical condition of polynomials in Bernstein form
9. Algorithms for polynomials in Bernstein form
10. Surface intersection using affine arithmetic
11. Adaptive enumeration of implicit surfaces with affine arithmetic
12. Convergent bounds for the range of multivariate polynomials
13. A new method of evaluating compact geometric bounds for use in subdivision algorithms
14. Sampling of procedural shaders using affine arithmetic
15. Robust interval solid modeling. Part I. Representations
16. Robust interval solid modeling. Part II. Boundary evaluation
17. Bounds on a polynomial
18. Approximation by interval Bézier curves
19. Affine arithmetic in matrix form for algebraic curve drawing
20. Interval analysis for computer graphics
21. Quadtree algorithms for contouring functions of two variables
22. Interval methods in computer graphics
23. Distance approximations for rasterizing implicit curves
24. Rasterizing algebraic curves and surfaces
25. Approximation of measured data with interval B-splines
26. Interval and affine arithmetic for surface location of power- and Bernstein-form polynomials
27. Polynomial evaluation using affine arithmetic for curve drawing