CaltechAUTHORS
A Caltech Library Service

# A scan line algorithm for displaying parametrically defined surfaces

Blinn, James F. (1978) A scan line algorithm for displaying parametrically defined surfaces. In: SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques. ACM , New York, NY, p. 27. https://resolver.caltech.edu/CaltechAUTHORS:20160613-163049392

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20160613-163049392

## Abstract

This paper presents a scan line algorithm for drawing picture of parametrically defined surfaces. A scan line algorithm is characterized by the order in which it generates the picture elements of the image. These are generated left to right, top to bottom in much the same was as a picture is scanned out on a TV screen. Parametrically defined surfaces are those generated by a set of bivariate functions defining the X, Y and Z position of points on the surface. The primary driving mechanism behind such an algorithm is the inversion of the functions used to define the surface. To keep the algorithm general enough to apply to a wide variety of functional forms, this inversion is done numerically. It is only required to provide mechanism for evaluating the function and its derivatives at any parametric location. The algorithm proceeds in two phases. First, a numerical search is made to find the local maxima of the Y definition function within the desired parameter ranges. These determine when portions of the surface first become visible as the scan plane progresses down the screen. Secondly, the actual scan conversion process is performed, maintaining a list of segments of the surface intersecting the current scan plane. As the scan plane passes local maxima of the Y function new segments are added to the list. In addition, any existing segments are updated to reflect their intersection with the updated scan plane. All intersection calculations are performed by a bivariate Newton-Raphson solution of the defining equations. If the solution does not converge, it is due to the scan plane passing a local minimum, causing segments to be deleted from the active list. Finally, within one scan line, an X scan must be performed to generate the Z information about the surface for each picture element. This is also performed by a bivariate Newton-Raphson iteration with a different set of defining functions.

Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/800248.807364DOIAbstract
http://dl.acm.org/citation.cfm?doid=965139.807364PublisherAbstract
Subject Keywords:Computer Graphics, Hidden Surface Elimination, Bicubic Patches, Numerical Inversion
Classification Code:CR Categories: 5.12, 5.13, 5.17, 5.4, 8.2
DOI:10.1145/800248.807364
Record Number:CaltechAUTHORS:20160613-163049392
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160613-163049392
Official Citation:James F. Blinn. 1978. A scan line algorithm for displaying parametrically defined surfaces. In Proceedings of the 5th annual conference on Computer graphics and interactive techniques (SIGGRAPH '78). ACM, New York, NY, USA, 27-. DOI=http://dx.doi.org/10.1145/800248.807364
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67895
Collection:CaltechAUTHORS
Deposited By:INVALID USER
Deposited On:14 Jun 2016 00:05