Hi there! It's been quite a long time (again) since the last tutorial … I'll bet some of you had given up one me

Today is my 21st birthday, so I decided it would be the perfect time to finish up this trainer which I have been meaning to send out for weeks. It's on texure mapping. I know, I know, I said light sourcing, then gourad, then texture mapping, but I got enough mail (a deluge in fact ;) telling me to do texure mapping…

I'll be using the code from Tut 20 quite extensively, so make sure you know whats going on in there… well, on with the show!

BTW, I've improved my web page quite a bit… give it a visit, I want to really ramp up that hit count :)

If you would like to contact me, or the team, there are many ways you can do it :

            1) Write a message to Grant Smith/Denthor/Asphyxia in private mail on the ASPHYXIA BBS.
            2) Write to :  Grant Smith
                           P.O.Box 270 Kloof
                           3640
                           Natal
                           South Africa
            3) Call me (Grant Smith) at (031) 73 2129 (leave a message if you call during work hours). Call +27-31-73-2129 if you call from outside South Africa. (It's YOUR phone bill ;-))
            4) Write to denthor@goth.vironix.co.za in E-Mail.
            5) Write to asphyxia@beastie.cs.und.ac.za to get to all of us at once.

http://www.vironix.co.za/~grants

ftp://ftp.eng.ufl.edu/pub/msdos/demos/code/graph/tutor

There are two things you should know before we begin.

Firstly, I am cheating. The texture mapping I am going to show you is not perspective-correct, with clever divides for z-placement etc. This method looks almost as good and is quite a bit faster too.

Secondly, you will find it all rather easy. The reason for this is that it's all rather simple. I first made the routine by sitting down with some paper and a pencil and had it on the machine in a few hours. A while later when people on the net started discussing their methods, they were remarkably similar.

Let me show you what I mean.

Let us assume you have a texture of 128×128 (a straight array of bytes [0..127, 0..127]) which you want to map onto the side of a polygon. The problem of course being that the polygon can be all over the place, with one side longer then the other etc.

Our first step is to make sure we know which end is up… let me demonstrate…

                      1
                    +
                 /    \
              /         \
          4 +            +  2
              \        /
                \   /
                  +
                  3

Let us say that the above is the chosen polygon. We have decided that point 1 is the top left, point 3 is bottom right. This means that

  1 - 2   is the top of the texture
  2 - 3   is the right of the texture
  3 - 4   is the bottom of the texture
  4 - 1   is the left of the texture

The same polygon, but rotated :

                      3
                    +
                 /    \
              /         \
          2 +            +  4
              \        /
                \   /
                  +
                  1

Although the positions of the points are different, point 1 is still the top left of our texture.

Okay, so now you have four points and know which one of them is also the top left of our texture. What next?

If you think back to our tutorial on polygons, you will remember we draw it scanline by scanline. We do texture mapping the same way.

Lets look at that picture again :

                      1
                    +
               a /    \  b
              /         \
          4 +            +  2
              \        /
                \   /
                  +
                  3

We know that point 1 is at [0,0] in our texture. Point 2 is at [127,0], Point 3 is at [127,127], and Point 4 is at [0,127].

The clever bit, and the entire key to texture mapping, is making the logical leap that precisely half way between Point 1 and Point 2 (b), we are at [64,0] in our texture. (a) is in the same manner at [0,64].

That's it. All we need to know per y scanline is :

The starting position on the x axis of the polgon line
The position on the x in the texture map referenced by that point
The position on the y in the texture map referenced by that point

The ending position on the x axis of the polgon line
The position on the x in the texture map referenced by that point
The position on the y in the texture map referenced by that point

Let me give you an example. Let's sat that (a) and (b) from the above picture are on the same y scanline. We know that the x of that scanline is (say) 100 pixels at the start and 200 pixels at the end, making it's width 100 pixels.

We know that on the left hand side, the texture is at [0,64], and at the right hand side, the texture is at [64,0]. In 100 pixels we have to traverse our texture from [0,64] to [64,0].

Assume at the start we have figured out the starting and ending points in the texture

  textureX = 0;
  textureY = 64;
  textureEndX = 64;
  textureEndY = 0;
 
  dx := (TextureEndX-TextureX)/(maxx-minx);
  dy := (TextureEndY-TextureY)/(maxx-minx);
  for loop1 := minx to maxx do BEGIN
    PutPixel (loop1, ypos, texture [textureX, textureY], VGA);
    textureX = textureX + dx;
    textureY = textureY + dy;
  END;

Do the above for all the scanlines, and you have a texture mapped polygon! It's that simple.

We find our beginning and ending positions in the usual fasion. We know that Point 1 is [0,0]. We know that Point 2 is [127,0]. We know the number of scanlines on the y axis between Point 1 and Point 2.

  textureDX = 127/abs (point2.y - point1.y)

We run though all the y scanlines, starting from [0,0] and adding the above formula to the X every time. When we hit the last scanline, we will be at point [127,0] in the texure.

Repeat for all four sides, and you have the six needed variables per scanline.

As you can see, texture mapping (this type at least) is quite easy, and produces quite a good result. You will however notice a bit of distortion if you bring the polygon too close. This can be fixed by a) Subdividing the polygon, so the one is made up of four or more smaller polygons. Much bigger, but works; b) Using more accurate fixed point; or c) Figuring out perspective correct texture mapping, mapping along constant-z lines etc.

When people write me, they often refer to my “tutes”. This stems back to Mark Feldman calling them such in the PCGPE. I always though a “tute” was something you did with your car to gain someones attention. I dunno, maybe its an Australian thing

I have been coding almost exclusively in C/C++ for the past year or so. Sorry guys, thats all they will pay me for ;) Anyway, the trainers will continue to be in Pascal for ease of understanding by beginners, but if someone (*ahem* Snowman) doesn't start converting them to C soon, I will do it myself. He also corrected any mistakes I made while he was converting, so I'd prefer he did it (sort of a proofreader after release…)

Send me presents! It's my birthday!

Byeeeee…

Denthor 16-04-96