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A SIMPLE SHADING FOR COMPUTER DISPLAYED SURFACES

IP.com Disclosure Number: IPCOM000128593D
Original Publication Date: 1975-Dec-31
Included in the Prior Art Database: 2005-Sep-16
Document File: 4 page(s) / 19K

Publishing Venue

Software Patent Institute

Related People

G. T. Herman: AUTHOR [+4]

Abstract

This note proposes a simple way of removing: the axtifact caused by approximating curved surfaces with polygons i I n compUter-generated-three-dimensional display. The method is compared with Gouraud's continous,shading method.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

A SIMPLE SHADING FOR COMPUTER DISPLAYED SURFACES

G. T. Herman H. K. Liu

Technical Report Number 116

Send correspondence to:

Professor Gabor T. Herman Department of Computer Science State University of New York at Buffalo

4226 Ridge Lea Road Amherst, New York 14226

Abstract

This note proposes a simple way of removing: the axtifact caused by approximating curved surfaces with polygons i I n compUter-generated-three-dimensional display. The method is compared with Gouraud's continous,shading method.

Introduction

In order to achieve, a visually realistic representation of the surface of a three-dimensional object on a cathode-ray tube, one.has to solve the problems.of removing.the hidden parts of the.surface and shading its visible,parts. A commonly used approach which allows efficient solutions to both these problems is to approximate the surface so,that it is composed of planar polygons (2]. Lack of continuity in the shading across polygonal boundaries causes undesirable artifacts which can be removed by continuous shading procedures such as the one suggested by Gouraud [2].

In this note we discuss an extremely simple and efficient alternative method for removing the artifact mentioned above. In the application area which is our main concern our method is not only two orders of magnitude faster than.that of Gouraud's, but it also produces superior displays. In this application area the surface is approximated by a composition of squares, each one of which is parallel to one of three mutually perpendicular planes. In the next section we describe the,nature of our application area.

Three-Dimensional Reconstruction from Projections

The problem of reconstructing a three-dimensional object from a set of its two-dimensional projected images has arisen in fields ranging from electron microscopy to holographic inter- ferometry.. For example, in medicine we use an x-ray source to project the body onto the two- dimensional surface of a film. From a subset of all possible projections of a body, recon- struction algorithms (11 produce a three-dimensional array of numbers in which each number is

State University of New York at Buffalo Page 1 Dec 31, 1975

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A SIMPLE SHADING FOR COMPUTER DISPLAYED SURFACES

an estimate of the average density of the body in one of a set of equal, non-overlapping-cubes, called voxels (volume elements).

In order to see the shape of a particular organ,~a three-dimensional boundary detection algorithm has been devised (3]. This detects the organ's boundary surface and generates the description of the surface in terms of the square faces of the voxels.

An Example

For a demonstration of our ideas we use a plastic cast of an isolated c anine left ventricle with some beads inserted on the surface., Figure 1 shows a television image of this cast, blurred so as to make the resolution similar to that obtained in the reconstruction process.

A variant of t...