## A new method for drawing Algebraic Surfaces

### BibTeX

@MISC{_anew,

author = {},

title = {A new method for drawing Algebraic Surfaces},

year = {}

}

### OpenURL

### Abstract

R. The program produces a model of the surface which can be viewed using a general rendering package. The program has been specially designed to draw singular surfaces accurately and find all the components of the surface. There are many programs already existing which do this to a limited extent. Programs to draw surfaces of the type z = f(x; y) have been around for a number of years. CAD systems can draw specific types of algebraic surfaces but not normally singular ones. There are a few existing programs which draw general algebraic surfaces. Ray tracers [5] can be used to produce beautiful pictures of algebraic surface but they are slow and only gives the view from one direction. Other programs such the contour tracer written by the Geometry Supercomputer Project [2], produce good results but do not pay mush attention to singularities and may give topologically incorrect results.

### Citations

111 |
Singularity Theory I
- Arnold, Goryunov, et al.
- 1998
(Show Context)
Citation Context ...igmasz2) and E6, E7, E8 (normal forms x3 \Sigmasy4 \Sigmasz2, x3 + xy3 \Sigmasz2, and x3 + y5 \Sigmasz2) all have isolated singularities at the origin. Some of these surfaces are shown in Fig. 2. See =-=[1]-=- pp158-166 for a classification of germs of maps from R3 to R and [4] for a gentle introduction to Singularity theory. Figure 2. Zero contours of some of the standard germs Not all surfaces have isola... |

95 | Guaranteed ray intersections with implicit surfaces
- Kalra, Barr
- 1989
(Show Context)
Citation Context ...d for a number of years. CAD systems can draw specific types of algebraic surfaces but not normally singular ones. There are a few existing programs which draw general algebraic surfaces. Ray tracers =-=[5]-=- can be used to produce beautiful pictures of algebraic surface but they are slow and only gives the view from one direction. Other programs such the contour tracer written by the Geometry Supercomput... |

12 |
Surface Interrogations
- Geisow
- 1983
(Show Context)
Citation Context ...lynomials and a little differential geometry. The division of the surface into cells also plays an important part in the algorithm. Thanks must go to R. Martin who introduced me to A. Geisow's method =-=[3]-=- for drawing algebraic curves in the plane which is based on Bernstein polynomials, D. Marsh for useful conversations and an overview of possible techniques, C. Gibson for doubting whether it was poss... |

2 | Contour Tracing by - Dobkin, Levy, et al. - 1988 |

1 |
Zero set of Multivarient Polynomial Equations
- Milne
- 1991
(Show Context)
Citation Context ... help as the coefficients may have different signs even when the function has no solutions. Some other test, for example the generalization of Sterm sequences to two and three dimensions discussed in =-=[6]-=-, could be used to give a foolproof algorithm. We have not mentioned many of the subtleties of the implementation, which improve performance. For example the solutions on edges and faces are only foun... |