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Attention:

This material is copyright  1995-1997 Chris Hecker. All rights

reserved.

You have permission to read this article for your own education. You

do not have permission to put it on your website (but you may link

to my main page, below), or to put it in a book, or hand it out to your

class or your company, etc. If you have any questions about using

this article, send me email. If you got this article from a web page

that was not mine, please let me know about it.

Thank you, and I hope you enjoy the article,

Chris Hecker

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PS. The email address at the end of the article is incorrect. Please

use [email protected] for any correspondence.

Perspective Texture

Mapping, Part II:

Rasterization

BEHIND THE SCREEN

id I say I’d be doing two

columns? Silly me—I meant

four or five columns. Our

topic, perspective texture

mapping, is so huge I don’t

know what I was thinking

when I said we could cover it

completely in two columns.

Luckily, the topic has enough variety

that it should keep everyone glued to

these pages for the duration.

In Part 1, we covered most of the

math behind the perspective projection

and triangle gradients (those neat num-

bers that let us interpolate without

recalculating at each scanline), and we

quickly went over polygon fill conven-

tions and stepping on pixel centers.

That’s a lot of information for a single

article. In fact, there’s so much material

still to cover I’m not even going to

summarize my last article beyond say-

ing, “Read it.” If you haven’t read Part

I, you’ll still get a lot out of Part II, but

you might have trouble seeing how this

information fits in perspective (cough).

This time around we’re going to

focus on the triangle rasterization stage,

and we’ll expand on the math for the

fill convention we derived last issue.

As I did last time, I encourage you

to get out a piece of graph paper and

join in the fun. Speaking for myself, I

find it impossible to learn math with-

out scribbling all over the place.

If you don’t like math, well, com-

puter graphics is math for the most

part, so I’m not sure what to tell you.

My goal is to describe the math in an

accessible way, but I’m not going to

hide the fact that math underlies every-

thing about computer graphics, espe-

cially three dimensional computer

graphics. If you like programming you

will definitely like math...heck, math’s

even better than computer program-

ming because there are no compiler or

operating system bugs! (Of course,

there’s no compiler or operating system

to tell you when you’ve done something

wrong, either.)

Raster Blaster

When I say rasterization, I mean taking

the continuous geometric triangle—

defined by its vertices—and displaying

it on the monitor’s discrete display grid,

or “raster.” The rule we defined for

doing this is called a top-left fill con-

vention, where we light all pixels that

are strictly inside the polygon bound-

aries and any pixels that are exactly on

the polygon boundary if they’re on the

top or left edges (remember, pixels are

boxes with a center, not just points).

Figure 1 shows this fill convention in

GAME DEVELOPER • JUNE/JULY 1995

Figure 1. The Fill Convention

109876543210

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