Algorithms for Graphics and Image Processing pp 299-316 | Cite as

# Surface Fitting and Surface Displaying

## Abstract

The display of the surface of a three-dimensional object is an important problem in applications of graphics systems where the goal is to provide the user with different views of a group of solid objects. Surface fitting is also necessary when the objects are given initially as sets of points. Surface fitting and displaying are also of interest in other areas. In computerized cartography or geography one deals with models of terrain that are expressed as mathematical surfaces. In picture processing and pattern recognition, surfaces enter into image analysis in at least two ways. First, one can think of a picture as a surface by using the brightness values for the third coordinate. Second, one may wish to consider the surfaces of the objects that appear in a picture. Then the segmentation problem (Chapter 4) is reduced to identifying groups of pixels that are images of a single surface.

### Keywords

Hull## Preview

Unable to display preview. Download preview PDF.

### Relevant Literature

- [13.BL]Blinn, J. F. “Computer Display of Curved Surfaces,”
*Ph.D. dissertation*, Dept. of Computer Science, University of Utah, 1978.Google Scholar - [13.BN]Blinn, J. F. and Newell, M. E. “Texture and Reflection in Computer Generated Images,”
*CACM*,**19**(1976), pp. 542–547.Google Scholar - [13.CT]Cook, R. L. and Torrance, K. E. “A Reflectance Model for Computer Graphics,”
*SIGGRAPH’81*, Dallas, Texas, (August 1981), pp. 307–316.Google Scholar - [13.FO]Forrest, A. R. “On Coons and Other Methods for the Representation of Curved Surfaces,”
*CGIP*,**1**(1972), pp. 341–359.MathSciNetGoogle Scholar - [13.GU]Guptill, A. L.
*Drawing with Pen and Ink*, revised edition, New York: Van Nostrand, 1968.Google Scholar - [13.HO]Horn, B. K. P. “Hill Shading and the Reflectance Map,”
*IEEE Proceedings*,**69**(1981), pp. 14–47.CrossRefGoogle Scholar - [13.LA]Lane, J. M.; Carpenter, L. C.; Whitted, T.; and Blinn, J. F. “Scan Line Methods for Displaying Parametrically Defined Surfaces,”
*CACM*,**23**(1980), pp. 23–34.Google Scholar - [13.LR]Lane, J. M. and Riesenfeld, R. F. “A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces,”
*IEEE Trans. on Pattern Analysis and Machine Intelligence*,**PAMI-2**(1980), pp. 35–46.CrossRefGoogle Scholar - [13.PH]Phong, B. T. “Illumination for Computer Generated Images,”
*CACM*,**18**(1975), pp. 311–317.Google Scholar - [13.SSS]Sutherland, I. E.; Sproull, R. F.; and Schumacker, R. A. “A Characterization of Ten Hidden-Surface Algorithms,”
*ACM Computing Surveys*,**6**(1974), pp. 1–55.CrossRefMATHGoogle Scholar - [13.WH]Whitted, T. “An Improved Illumination Model for Shaded Display,”
*CACM*,**23**(1980), pp. 343–349.Google Scholar