SuperHack/SuperHack CD.bin/CODING/DEMOS/OTLIGHT.ZIP/LIGHT.DOC

Text File | 1996-10-18 | 8.6 KB | 223 lines

                     - THE OUTLAW TRIAD DEMO-SERIES -

───────────────────────────────■ PART XII ■───────────────────────────────────

                         Written by : Inopia/OT
                         Edited by  : Vulture/OT
                         Topic      : Improved flatshading

──────────────────────────────■ Introduction ■────────────────────────────────

 Welcome to the Outlaw Triad demo-series! In these series we will be talking
 about programming demo-effects in either pascal or assembler. Theory behind
 the effects shall be discussed while a full sourcecode is also provided.
 So... it's time to move on to some serious math. We will implement improved
 flatshading now. I (Inopia) got a lot of these things from an article written
 by STO/THECLAN, in Insight#1 magazine, and I read PC Underground. Be sure to
 get them if you want to learn more about programming 3d. Here we go!

─────────────────────────────────■ Theory ■───────────────────────────────────

 - VECTORS -

 Okay, first we need to discuss vectors. A vector is a kind of arrow, with a
 starting point, a direction and a length. We use 3D vectors, so we define a
 vector with X,Y,Z. A vector is noted like this:

      =Vx
     V=Vy
      =Vz

 Ok, a triangle has three coordinates. But we need two vectors to do our
 calculations with. Let's define those vectors with some vector substraction:

  V1 = P2 - P1
  V2 = P3 - P1

 You need to substract all seperate components (x,y,z) from eachother here.
 So x-x, y-y and z-z. P1,P2 and P3 are the 3d triangle coordinates. V1 and
 V2 are the vectors we are going to do some calculating with.

 - VECTORS AND LIGHT -

 Now we need to find out a vector, in a right angle to the triangle. This is
 needed to determine the color of the face. Picture this: you have a postcard,
 a shiny postcard which you got from your girlfriend, who was on vacation in
 Singapore (without you, cos your car broke down). You hold it into the light.
 If you hold it like this...

 1.  |<------------------------------
     |
     |
     |                                 Lightbeam
     |
     |
     |<------------------------------

  Postcard

 There is a lot of light falling onto the card. But if you hold it like this:

 2.  \<------------------------------
      \
       \
        \                              Lightbeam
         \
          \<-------------------------

 There is LESS light falling onto the card! Let's find out how we can
 calculate this. Let's bring up that card again:


   |
   |                                     \
   |                                               V
   |                                       \     /
   |
 --|----------- V                            \ /
   |
   |                                         / \
   |
   |                                       /     \
   |
   |                                               \

  1.                                 2.

 As you can see I created a line through the middle of the card, IN A RIGHT
 ANGLE TO THE CARD. This line is called the normal. Let's shine some light
 on this, shall we?

   |    <----------------
   |                                     \<-------------------
   |
   |                                       \     /
   |
 --|-----------      beam                    \ /
   |
   |                                         / \
   |
   |                                       /     \
   |
   |    <----------------                          \<---------

   1.                                 2.

 In the first picture, the normal and the lightbeam have THE SAME ANGLE WITH
 THE POSTCARD! This means there's a full amount of light shining on the card.
 In the second picture however, the two angles differ. The angle between the
 lightsource and the normal is larger than zero. If we can find this angle
 (between the normal and the lightsource) we can find out how much light is
 shining onto the postcard, and in our case, the polygon in 3d space!!!

 - CROSSPRODUCT - DOTPRODUCT -

 To find the normal, we must we take the crossproduct of the two vectors we
 calculated before. This will leave us with just one vector. This vector is
 a right angle with the two other vectors, and thus in a right angle with the
 triangle.

  V3 = V1 * V2

  V3x = V1y * V2z - V1z * V2y
  V3y = V1z * V2x - V1x * V2z
  V3z = V1x * V2y - V1y * V2x

 There is just one slight problem. These values can vary in size, according
 to the size of the triangle. We want to get em to be in -1 to 1, so that
 we can adjust the size to anything we want. As said before, a vector also
 has a size. One can easily calulate the size of a vector like this:

  length = sqrt (V3x * V3x + V3y * V3y + V3z * V3z)

 To shrink a vector to a length of 1, we devide all components of the vector
 by the length of the vector:

  V3x = V3x / length
  V3y = V3y / length
  V3z = V3z / length

 We also multiply these values with the maximum number of colors you reserved
 for the shading. Check the source to see what I mean. Anyhow, V3 holds the
 normalvector of the triangle.

 Now we need to come up with a lightsource. Well, the lightsource is easy:
 it's defined by you. Mostly, the light is coming from the viewer, so the
 lightsource would be:

        0
    LS  0
       -1

 You see? This is a 3d vector also. Now, one more formula coming up...
 The dotproduct. This formula returns a value which is equal to the cosine
 of the angle between the lightsource and the triangle. You use the normal
 you just calculated and the lightvector for the calculation.

  DP = V3x * LSx + V3y * LSy + V3z * LSz

 Now, if we take the dotproduct of the normal and the lightvector like
 stated here, we've calculated the exact color of the face. Draw it and
 you're done! Phew! Pretty complicated math but well worth the effort.
 Again, check out the source to see how it can be done.

 This method is a lot better than just using the avarage z-value of a poly
 to calculate the color. You can use this method for more complicated objects
 as well. If you know how to handle 3DS objects, you could try this method
 on those objects. Go for it!

 - OPTIMIZATION TIPS -

 - Well, as you might have guessed, it's impossible to get an engine running
   fast when you've got all those SQRT's to execute. The solution: calculate
   all facenormals once, and then just rotate 'em just like the vertices.
 - There are faces you can't see. Ofcourse you don't have to draw them. Here's
   a neat trick for that: whenever the Z-value of a facenormal is smaller than
   zero, don't draw it! Makes the engine running a LOT faster.
   (note: we will implement this effect in a future trainer)
 - How can we avoid the lightsource vector and the dotproduct? Like this, we
   take the Z-value of the facenormal, and adjust it a bit, so that it will
   fit into the amount of colors you want. The only problem is you can't have
   a variable lightsource. If you still wanna have that effect, try rotating
   the normal vectors over other angles than the vertices, or don't rotate
   the vertices at all (although I think an object that's not moving looks
   very DULL!).

 There are probably some untrue things in here so if you know better mail me.
 (mail me or OT for any other reason). Catch ya later!

       -Inopia/Outlaw Triad-

───────────────────────────────■ Distro Sites ■───────────────────────────────

 Call our distribution sites! All our releases are available at:

  BlueNose      World HQ          [phone]
  The Force     Distrosite        [phone]
  Bugs'R'Us     Distrosite        [phone]    More distros wanted!
  The 7 Angels  Distrosite        [phone]    (preferably outside
  ShockWave     South African HQ  [phone]     of the Netherlands)
  Society HQ    United States HQ  +1  [phone]
  ACe World     Brazilian HQ      [phone]
  Corps Elite   Canadian HQ      +403 (ITS)-PRIVATE

 Also check the major FTP/WWW sites for Outlaw Triad productions.

──────────────────────────────────■ Contact ■─────────────────────────────────

 Want to contact Outlaw Triad for some reason? You can reach us at our
 distrosites in Holland. Or if you have e-mail access, mail us:

   Vulture   (coder/pr)   [e-mail]
   Inopia    (coder)      [e-mail]

 Our internet homepage:

   http://www.tem.nhl.nl/~comma400/vulture.html

 These internet adresses should be valid at least till june 1997.

──────────────────────────────────────────────────────────────────────────────

  Quote: Time is the best teacher. Unfortunately, it kills all its students.