All Databases MacTech Vol 08-1992

3D Graphic Tools

Volume Number: 8

Issue Number: 1

Column Tag: Tools of the trade

Related Info: Quickdraw Color Quickdraw

3D Graphic Tools

High-performance 3D drawing & rendering in your programs

By David Harr, Alhambra, California

Note: Source code files accompanying article are located on MacTech CD-ROM or

source code disks.

Introduction

The Macintosh Toolbox provides good support for doing 2 dimensional computer

graphics in the form of QuickDraw. Basic QuickDraw (B&W) provides 6 geometric

primitives: line, rectangle, round-cornered rectangle, and circle, a polygon data

structure, and a region data structure, which allows the programmer to deal with

arbitrary areas and shapes. All of these can be drawn, outlined, filled, pattern filled,

resized and used as masks. Color QuickDraw adds the capabilities of drawing in color,

filling in color, using color patterns, palette animation, color masking, and provides

support for photo-realistic color and double-buffered on-screen animation.

With all of this attention to 2 dimensional graphics, however, Apple has been lax

in supporting the needs of those who are interested in doing 3 dimensional graphics and

modeling. The only support that Apple gives is in the form of a set of slow, buggy library

routines collectively known as Graf3D supplied in object form with MPW. The

“documentation” of Graf3D consists of eleven pages in an appendix at the back of the

MPW reference manual, Volume 1. This is a bare-bones listing of the routines and a

short explanation of the calling conventions, parameters and purpose of each routine.

Graf3D itself is a minimal effort in supporting 3d graphics. It provides only rotation,

scaling, translation, clipping, and 2d projection. There are no provisions for hidden

line removal, polygon fills, z-buffer rendering, light sources, or shading. It can be

used, at best, for wire-frame drawings.

3D Graphic Tools version 3.0, published by Micro System Options of Seattle,

Washington, is a set of routines written for programmers who wish to use

high-performance 3 dimensional drawing and rendering in their programs. The package

contains the source code for over 100 routines for 3D graphics. It provides a set of

tools for graphics programmers, and is a good basis for someone interested in writing

their own software for custom graphics applications.

This review discusses the C version of the package, which supports MPW C

version 3.0 and later, and THINK C version 4.05 and later. There is also a Pascal

version which is functionally identical to the C version and supports MPW Pascal

version 3.0 and later, and THINK Pascal version 3.01 and later.

Rendering Environment

All of the drawing in 3D Graphic Tools is done in a three dimensional extension of

the normal QuickDraw coordinate space. In other words, while most QuickDraw

operations take place in a plane with (-32000, -32000) in the top, left corner and

(32000, 32000) in the bottom, right corner, the coordinate space in 3D Graphic Tools

is a cube that is 64000 units on a side. This gives a space that is large enough for most

purposes, yet is small enough to allow the arithmetic operations to be carried out using

high speed integer mathematics.

Figure 1

By convention, the three axes of the coordinate system are labeled the x, y, and z

axes. The x and y axes are perpendicular to each other and lie in a horizontal plane,

while the z-axis is perpendicular to them both, and runs straight up and down. Each

axis runs from approximately -32000 to 32000, and each point in space has a unique

coordinate given by (x, y, z), where x, y, and z each represent the respective

coordinate of the three axes.

Mathematical Basis

Three dimensional rotations, transformations and scalings all involve

considerable linear algebra, so they require a lot of multiplication. In order to speed

the rendering of images and to make image manipulation as rapid as possible, it is

common to use fixed-point, or integer mathematics in the calculations, with some loss

in accuracy. 3D Graphic Tools supports a complete set of mathematical functions using

both the Fixed and Fract data types, as described in Inside Macintosh volumes I and IV.

These routines are not the routines included in the Macintosh ROMs, however. They are

hand-crafted assembly language routines that have been optimized for speed. On

average, the fixed math routines in 3D Graphic Tools are between 40% to 50% faster

than the Toolbox routines. This makes 3D Graphic Tools significantly faster than

Graf3D when performing line and point manipulation in three dimensions. In addition,

many of the conversion routines between types, such as frac2fix or fix2frac are

implemented as macros in 3D Graphic Tools, removing the overhead of a function call,

again adding to the speed of the package. In those situations where accuracy is

paramount, such as in zbuffer rendering, the routines revert to floating-point

mathematics, which is slower (e specially in those machines without a 68881/68882

FPU), but is more accurate.

Rendering Attributes

3D Graphic Tools has a full range of functions for performing three dimensional

image manipulation and rendering. These include basic operations such as rotations,

scalings, translations, and projections onto the two dimensional screen. In addition,

once a three dimensional scene has been constructed, it can be rendered to almost any

desired level of realism, from wire-frame drawings with no hidden line removal, to an

image incorporating such sophisticated techniques as multiple inde-pendent light

sources, shadows, specular highlighting, and texturing of objects. The only effort

required of the programmer is that they set the appropriate global variables.

The basic data unit in 3D Graphic Tools is the patch. A patch is a set of vertices

and facets that determines the shape of the object that the patch represents [see listing

1]. In addition to this shape information, however, the patch also contains an extensive

set of rendering attributes that are needed when making use of the more sophisticated

rendering options in the package. The rendering information associated with a patch is

used to determine the effect of illumination on the object. Some of the information is

also used to add texture and supply visual effects to the surface of the object.

Each vertex is defined by the coordinate (x, y, z) that it occupies in space and a

number in the vertex list. Thus, vertex 7 might be at (17, 23, 48). Each facet is

defined by a list of vertices, which are referenced by number, not by coordinate. This

list is arranged so that the vertices are listed counterclockwise in order. The reason

that each vertex is addressed by number is so that if an object is translated, rotated, or

scaled, the changes need only be made to the master list of vertices, and all facets of the

patch will automatically be correctly positioned. This is much faster than stepping

through each facet and individually repositioning each vertex in that way, because each

facet shares at least two vertices with other facets in the same object.

The ambience, diffusion, and reflection coefficients all control how light

reflecting off the object is treated. The reflection coefficients consist of three numbers

in the range 0 to 65535. Each controls what percentage of the red, green and blue light

is reflected from the object. A coefficient of 0 indicates 0%, 32767 is 50%, and

65535 is 100% reflection. When using the zbuffer rendering, then the ambience and

diffusion coefficients come into play also. If there is ambient light, then the ambience

coefficient determines what percentage of that light is reflected from the object, while

the diffusion coefficient determines what percentage of the light is reflected uniformly

in all directions.

The specular index, the specularity and transparency coefficients all determine

the quality of the illumination of the object. The transparency coefficient determines

the percentage of the background color which is added to the final color of the object. If

it is 0, then the object is opaque, and none of the background color is added, whereas if

it is 1, then the object is invisible, and its color is 100% determined by the

background color. The specular index and the specular coefficient are related and

determine how shiny the object is and how that shininess is distributed across the

surface of the object.

In addition to all of these rendering options for the patch, there are also several

miscellaneous attributes. There are three attributes that are specifically concerned

with lighting effects. If a patch is declared as a light source, then it emanates light of the

color determined by the reflection coefficients. If the ambient effect and distance effect

booleans are set, then the ambient light is added directly to the light reaching the

viewer’s eye, causing more distant objects to become grayed out. The farther away an

object is, the lower the intensity of the light reaching the viewer’s eye, causing more

distant objects to become darker. There are also three attributes that are used to

determine how the object is rendered. If the framed boolean is set, then all facets are

drawn with the edges in a different color than the facet itself. The color to draw the

edges in is given in the frameColor field. If the pattern boolean is set, then the facet is

drawn with a QuickDraw color pattern inside. Related to the pattern boolean is the

grayscale boolean, which fills the facet with one of 65 gray levels ranging from white

to black.

Advanced Options

In order to give the objects displayed a more photo-realistic look, 3D Graphic

Tools also has several advanced rendering options. These options, although they increase

the time required to display the scene, do not require nearly as much time as

full-blown ray traces, yet they provide a level of realism approaching that of ray

tracing. These advanced functions include texture mapping, anti- aliasing, and shadows.

Texture mapping is one of the most impressive features of the package. It allows

the programmer to add any one of six “textures” to an object. Each texturemap may be

rotated, scaled, or translated to produce interesting effects when projected onto the

object. The first of the six texture types is not really a texture at all, it is a PICT file of

the programmer’s choosing that will be placed onto the object in much the same way as

if the PICT were projected onto the object by a movie projector or slide projector.

However, it is also possible for the PICT to be repeated in every facet of the object,

causing it to appear again and again. In addition, the PICT can be enlarged or reduced to

any desired extent. Three more “naturalistic” textures include wood, rock, and bumps.

These have other attributes such as grain and roughness to make them even more

versatile.

Anti- aliasing is a technique that is used to soften and smooth the appearance of

the object. There are several algorithms used in computer graphics for anti- aliasing.

The one used in 3D Graphic Tools is to create a 3 X 3 convolution matrix of the selected

pixel and the eight pixels surrounding it, and then use that matrix to get a weighted

average of the color of the pixels. This color is then used to determine the displayed

color in the pixel. The main use for this technique is to soften the edges of facets in the

object. Once an object is rendered, if edge anti- aliasing is enabled, then each visible

facet in an object is processed a second time, but only the edge pixels are redrawn. In

addition, it is possible to apply anti- aliasing to a rectangular portion of an image,

allowing anti- aliasing to work either on any portion or the entirety of a rendered

image.

Shadows are the result of a reduction in illumination intensity caused by the

presence of an object between a light source and another object. The object between the

light source and the second object will cast a shadow on the far object. The degree to

which the illumination is reduced is a function of the transparency of the interposing

object. The more opaque the interposing object is, the less light reaches the far object.

This is the model that 3D Graphic Tools uses to generate shadows. This model does have

one limitation. If there are multiple objects between a light source and the far object,

only the first object encountered will be used to cast a shadow.