# DENTHOR/ASPHYXIA'S VGA TRAINERS GLENZING, FASTER POLYGONS, FIXED-POINT MATH

Well, this trainer is mainly on four things: glenzing, faster polygons, fixed-point math and assembler. The sample program is basically Part 9 rewritten to include the above. I’ll go through them in order, and hopefully you won’t have any hassles grasping the concepts.

Well, this trainer is mainly on four things: glenzing, faster polygons, fixed-point math and assembler. The sample program is basically Part 9 rewritten to include the above. I’ll go through them in order, and hopefully you won’t have any hassles grasping the concepts.

DENTHOR, coder for ... _____ _____ ____ __ __ ___ ___ ___ ___ __ _____ / _ \ / ___> | _ \ | |_| | \ \/ / \ \/ / | | / _ \ | _ | \___ \ | __/ | _ | \ / > < | | | _ | \_/ \_/ <_____/ |__| |__| |__| |__| /__/\__\ |__| \_/ \_/ smith9@batis.bis.und.ac.za The great South African Demo Team! Contact us for info/code exchange!

Grant Smith, alias Denthor of Asphyxia, wrote up several articles on the creation of demo effects in the 90s. I reproduce them here, as they offer so much insight into the demo scene of the time.

These articles apply some formatting to Denthor's original ASCII files, plus a few typo fixes.

## What is glenzing?

This is an easy one. Imagine, in a 3D object, that all the sides are made out of colored glass. That means that every time you look through a side, everything behind it is tinged in a certain color.

In ASCII:

So where the two sides overlap, the color values of the two sides are added. Easy huh? It is also easy to code. This is how you do it:

- Set up your palette to be a nice run of colors.
- Draw your first poly.
- While drawing poly 1, instead of plonking down a set pixel color, grab the background pixel, add 1 to it, then put the result down.
- Draw your second poly.
- While drawing poly 2, instead of plonking down a set pixel color, grab the background pixel, add 2 to it, then put the result down.
- and so forth.

So if the color behind poly 1 was 5, you would place pixel 6 down instead.

If you do this for every single pixel of every single side of your 3D object, you then have glenzing going. This is obviously slightly slower than just drawing an item straight, but in the sample program it goes quite quickly. This is because of the following sections.

## Faster polygons

In Part 9, you probably noticed that we were using a multiply for every single line of the poly that we drew. This is not good. Let’s find out how to speed it up, shall we?

With the multiply method, we went through every line, to find out the minimum x and maximum x value for that line.

How about if we found out all the min and max x’s for every line first, then just went through an array drawing them. We could do it by “scanning” each side in turn. Here is how we do it:

We go from point one to point two. For every single y we go down, we move a constant x value. This value is found like this:

Remember gradients? This is how you calculated the slope of a line *waaay* back in school. You never thought it would be any use, didn’t you?

Anyway, with this value, we can do the following:

and we will go through all the x-values we need for that line. Clever, huh?

Now for the clever bit. You have an array, from 0 to 199 (which is all the possible y-values your onscreen poly can have). Inside this is two values, which will be your min x and your max x. You start off with the min x being a huge number, and the max x being a low number. Then you scan a side. For each y, check to see if one of the following has happened:

- If the x value is smaller than the xmin value in your array, make the xmin value equal to the x value
- If the x value is larger than the xmax value in your array, make the xmax value equal to the x value

The loop now looks like this:

Easy? Do this for all four sides (you can change this for polys with different numbers of sides), and then you have all the x min and x max values you need to draw your polygon.

In the sample program, if you replaced the `Hline`

procedure with one that draws solid lines, you could use the given drawpoly for solids.

Even this procedure is sped up by the next section, on fixed point.

## What is fixed point?

Have you ever noticed how slow reals are? I mean *slooooow*. You can get a massive speed increase in most programs by replacing your reals with integers, words etc. But, I hear you cry, what happens to the much needed fraction bit after the decimal point? The answer? You keep it. Here’s how.

Let us say you have a word, which is 16 bits. If you want to use it as a fixed point value, you can separate it into 2 sections, one of which holds the whole value, and one which holds the fraction.

The number 6.5 would therefore be shown as follows:

128 is half (or .5) of 256, and in the case of the fraction section, 256 would equal one whole number.

So let us say we had `6.5 * 2`

. Using reals this would be a slow `mul`

, but with fixed point …

As you can see, we got the correct result! And in a fraction of the time that a multiplication of a real would have taken us. You can add and subtract fixed point values with no hassles, and multiply and divide them by normal values too. When you need the whole value section, you can just read the high byte, or do the following:

As you can see, the fraction is truncated. Obviously, the more bits you set aside for the fraction section, the more accurate your calculation is, but the lesser the maximum whole number you can have. For example, in the above numbers, the maximum value of your whole number was 256, a far cry from the 65,535 a normal (non fixed point) word’s maximum.

There are a lot of hassles using fixed point (go on, try shift a negative value), most of which have to do with the fact that you have severely decreased the maximum number you may have, but trust me, the speed increase is worth it (With long integers, and/or extended 386 registers, you can even have 16x16 fixed point, which means high accuracy and high maximum values)

Try write a program using fixed point. It is not difficult and you will get it perfect easily. Trust me, I’m a democoder ;-)

## Assembler

In the sample program I used one or two assembler commands that I havent discussed with you. Here they are:

For more info on shifting etc, re-read Part 7, it goes into the concept in detail.

The sample program is basically Part 9 rewritten. To see how the assembler stuff is working, do the following … Go into 50 line mode (-Much- easier to debug), then hit [Alt - D] then R. A little box with all your registers, segments etc and their values will pop up. Move it down to where you want it, then go back to the program screen (Hit Alt and its number together), and resize it so that you have both it and the register box onscreen at once (Alt - 5 to resize) … then use F4, F7 and F8 to trace though the program (you know how). The current value of the registers will always be in that box.

## In closing

Well, that is about it. The sample program may start as being a little intimidating to some when they first look at it, just remember to read it with Part 9, very little is different, it’s just with fixed point and a bit of assembler.