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    {
    Okay, this message is to Pedro Miguel Borges and Justin Greer and
    anybody else who wants to know a way to make DOOM graphics.  From this
    point on, everything you see came from the text file, not me:

    ******************************************************************************
    *                       'Doom' 3D Engine techniques                          *
    ******************************************************************************
    By Brian 'Neuromancer' Marshall
    (Email: brianm@vissci.demon.co.uk)

            This document is submitted subject to certain conditions:

    1. This Document is not in any way related to Id Software, and is
       not meant to be representive of their techniques : it is based
       upon my own investigations of a realtime 3d engine that produces
       a screen display similar to 'Doom' by Id software.

    2. I take no responsibility for any damange to data or computer equipment
       caused by attempts to implement these algorithms.

    3. Although I have made every attempt to ensure that this document is error
       free i take no responsability for any errors it may contain.

    4. Anyone is free to use this information as they wish, however I would
       appreciate being credited if the information has been useful.

    5. I take no responsability for the spelling or grammar.
       (My written english is none too good...so I won't take offence
        at any corrections: I am a programmer not a writer...)

            Right now that that little lot is out of the way I will start this
    document proper....

    1:  Definition of Terms
    ======================

            Throughout this document I will be making use of many graphical terms
    using my understanding of them as they apply to this algorithm. I will
    explain all the terms below. Feel free to skip this part....

    Texture:
            A texture for the purpose of this is a square image.

    U and V:
            U and V are the equivelants of x and y but are in texture space.
    ie They are the the two axies of the two dimensional texture.

    Screen:
            For my purposes 'screen' is the window we wish to fill: it doesn't
    have to be the whole screen.

    Affine Mapping:
            A affine mapping is a texture map where the texture is sampled
    in a linear fashion in both U and V.

    Biquadratic Mapping:
            A biquadratic mapping is a mapping where the texture is sampled
    along a curve in both U and V that approximates the perspective transform.
    This gives almost proper forshortening.

    Projective Mapping:
            A projective mapping is a mapping where a changing homogenous
    coordinated is added to the texture coordinateds to give (U,V,W) and
    a division is performed at every pixel. This is the mathematically and
    visual correct for of texture mapping for the square to quadrilateral
    mappings we are using.
            (As an aside it is possible to do a projective mapping without
    the divide (or 3 multiplies) but that is totally unrelated to the matter
    in hand...)

    Ray Casting:
            Ray Casting in this context is back-firing 'rays' along a two
    dinesional map. The rays do however follow heights... more on that later

    Sprite:
            A Sprite is a bitmap that is either a monster or an object. To
    put it another way it is anything that is not made out of wall or
    floor sectins.

    Sprite Scaling:
            By this I mean scaling a bitmap in either x or y or both.

    Right... Now thats over with onto the foundation:

    2:   Two Dimensional Ray Casting Techniques
    ===========================================

            In order to make this accessible to anyone I will start by
    explaining 2d raycasting as used in Wolfenstein 3d style games.

      2.1: Wolfenstien 3D Style Techniques...
      =======================================

              Wolfenstein 3d was a game that rocked the world (well me anyway!).
      It used a technique where you fire a ray accross a 2d grid based map to
      find all its walls and objects. The walls were then drawn vertically
      using sprite scaling techniques to simulate texture mapping.

              The tracing accross the map looked something like this;

            =============================================
            =   =   =   =   =   =  /=   =   =   =   =   =
            =   =   =   =   =   = / =   =   =   =   =   =
            =   =   =   =   =   =/  =   =   =   =   =   =
            ====================/========================
            =   =   =   =   =  /=   =   =   =   =   =   =
            =   =   =   =   = / =   =   =   =   =   =   =
            =   =   =   =   =/  =   =   =   =   =   =   =
            ================/============================
            =   =   =   =  /#   =   =   =   =   =   =   =
            =   =   =   = / #   =   =   =   =   =   =   =
            =   =   =   =/  #   =   =   =   =   =   =   =
            ============/===#########====================
            =   =   =  /=   =   =   #   =   =   =   =   =
            =   =   = / =   =   =   #   =   =   =   =   =
            =   =   =/  =   =   =   #   =   =   =   =   =
            ========/===============#====================
            =   =  /=   =   =   =   #   =   =   =   =   =
            =   = P =   =   =   =   #   =   =   =   =   =
            =   =  \=   =   =   =   #   =   =   =   =   =
            ========\===============#====================
            =   =   =\  =   =   =   #   =   =   =   =   =
            =   =   = \ =   =   =   #   =   =   =   =   =
            =   =   =  \=   =   =   #   =   =   =   =   =
            ============\=======#####====================
            =   =   =   =\  =   #   =   =   =   =   =   =
            =   =   =   = \ =   #   =   =   =   =   =   =
            =   =   =   =  \=   #   =   =   =   =   =   =
            ================\===#========================
            =   =   =   =   =\  #   =   =   =   =   =   =
            =   =   =   =   = \ #   =   =   =   =   =   =
            =   =   =   =   =  \#   =   =   =   =   =   =
            =============================================

            (#'s are walls, = is the grid....)

            This is just a case of firing a ray for each vertical
      line on the screen. This ray is traced accross the map to
      see where it crosses a grid boundry. Where it crosses a
      boundry you cjeck to see if there is a wall there we see how
      far away it it and draw a scaled vertical line from the texture
      on screen. The line we draw is selected from the texture by
      seeing where the line has intersected on the side of the square it
      hit.
            This is repeated with a ray for each vertical line on the
      screen that we wish to display.
            This is a very quick explaination of how it works missing
      out how the sprites are handled. If you want a more detailed
      explaination then I suggest getting acksrc.zip from
      ftp.funet.fi in /pub/msdos/games/programming

            This is someone's source for a Wolfenstien engine written
      in Borland C and Assembly language on the Pc.
            Its is not the fastest or best but has good documentation
      and solves similiar sprite probelms, distance probelms and has
      some much better explaination of the tracing technique tahn I have
      put here. I recommend to everyone interested taht you get a copy
      and have a thorough play around with it.
      (Even if you don't have a Pc: Everything but the drawing and video
       mode setting is done in 'C' so it should not be too hard to port
       ....)

      2.2 Ray Casting in the Doom Environment
      =======================================

            When you look at a screen from Doom you see floors, steps
      walls and lots of other trappings.
            You look out of windows and accross courtyards and you
      say WOW! what a great 3d game!!
            Then you fire your gun a baddie who's in line with you but
      above you and bang! he's a corpse.
            Then you climb up to the level where the corpse is and look
      out the window to where you were and you say Gosh! a 3d game!!

            Hmmm....

            Stop gawping at the graphics for a minute and look at the map
      screen. Nice line vectors. But isn't the map a bit simple???
            Notice how depite colours showing you that there are different
      heights. Then notice that despite the fact that there is NEVER a
      place where you can exist on two different levels. Smelling a little
      2d yet???
            Look where there are bridges (or sort of bridges) : managed to
      see under them yet??

            The whole point to this is that Doom is a 2D games just like
      its ancestor Wolfenstein but it has rather more advanced raycasting
      which does a very nice job of fooling the player into thinking its a
      3d game that shifting loads of polygons and back-culling, depth
      sorting etc...

            Right the explaination of how you turn a 2d map into the 3d
      doom screen is complex so if you are having difficulty try reading
      it a few times and if all else fails mail me....

      2.3 What is actually done!
      ==========================

            Right to start with the raycasting is started in the same
      way as Wolfenstien. That is find out where the player is in the 2d
      map and get a ray setup for the first vertical line on the screen.

            Now we have an extra stage from the Wolfenstein I described
      whcih involves a data srtucture that we will use later to actually
      draw the screen.

            In this data structure we start the ray off as at the bottom
      of the screen. This is shown in the diagram below;

            =================================
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =*                              =
            =================================

            Where the '=' show the boundry of the screen and '*' is the virtual
      position of the ray.

            Note: the Data structure is really two structures:
            One which is a set of list for each vertical 'scanline' and
            One which is a corresponding list for horizontal scanlines.

            Now we start tracing the ray. We skip accross the 2d map until
      we hit something interesting. By something interesting I mean something
      that is an actual wall or florr section edge.
            Right we have hit the edge of either a floor or wall section.
      We have several things to do know. These are;

            If it was a wall we hit:

      1: Find out how 'high' of screen this section of wall should be
         due to the distance it is accross the 2d map.
      2: Find out at what 'virtual height' it is: This is so that we can see
         where in the vertical scanline in comes for testing where to insert
         it and for clipping it.
      3: Test in our structure to see if you draw it or not.
         (This is done so that you can look through windows : how this works
          will become apparent later.)
      4: If any of the wall segment is visible then we find out where along
         the texture we have hit it and write into the structure the area of
         the screen it takes up as well as the texture, the point where we
         have hit the texture and the size it should be on screen. (This is
         so that we can draw it correctly even if the whole span is not on
         screen.

            If it was a floor section that we hit:

      1: Find out where on the vertical line we are working the floor section
         that the ray has hit is. (We know the height of the the floor in the
         virtual map (2d) and we know the height of the player and the distance
         of the floor square from the player so it is easy).
         As a side effect of this we now know the U,V value where the ray has
         hit the floor square.

      2: Trace Accross the floor square till we hit the far edge of the floor
         square : we then workout where this is on the vertical scanline using
         the same technique as above. We now know the vertical span of the
         floor section, and where on the span it is.

      3: We check to see if the span is visible on the vertical span.
         If it is or part of it is used then we mark that part of the vertical
         scanline as used.
         We also have to make use of the horizontal buffer I mentioned. We
         insert into this in 2 places. The first is the x coordinate of where
         we hit the floor square into the y line where we where on the screen.
         Phew got that bit?? We also insert here the U,V value which we knew
         from the tracing. (I told you we'd need it later....)

            As you can see there's a little more to hiting a floor segment than
    a wall segment. Also note that a you exit a floor segment you may also hit
    a wall segment.

            Tracing the individual ray is continued until we hit a special kind
    of wall. This wall is marked as a wall that connects to the ceiling.
    This is one place to stop tracing this ray. However we can stop tracing early
    if we have found enough to fill the whole vertical scanline then we can stop
    whenevr we have done this.

            Next come a trick. I said we were tracing along a 2d map. Well I
    lied a bit. There are (In my implementation at least..) TWO 2d maps. One is
    basically from the floor along including all the 'floor' walls and everything
    up to and including the walls that join onto the ceiling. The other map
    is basically the ceiling (with anything coming down from the ceiling on it
    if you are doing this: this makes life a little more complex as I'll explain
    below..)
            Now when we have traced along the bottom map and hit a wall that
    connects to the ceiling then we go back and trace along the ceiling from
    the start to fill in the gaps. There is a problem with this however.
    The problem is when you have things like a monolith or something else built
    out of walls jutting down from the ceiling. you have to decide whether to
    draw it or draw whatever was already in the scanline structure. This means
    either storing extra information in the buffer ie z coordinates or tracing
    along both the ceiling and floor at the same time.... for most people I would
    suggest just not having anything jutting down from the ceiling.
            Also you could trace backwards instead of starting a new ray. This
    would be fasterfor many cases as you wouldn't be tracing through lots
    of floor squares that aren't on screen. By tracing backwards you can keep
    going up the vertical scanline and you know that you are on the screen. As
    soon as something goes off the top of the screen you can handle that and then
    stop tracing.

            Phew. has everyone got that???

            Now we just go back and fire rays up the rest of the vertical
    scanlines. Easy!!???

            At the end of this lot we have the necessary data in the two buffers
    to go back and draw the screen background.
    (There is one more thing done while tracing but I'll explain that later...)

            Oh... one other thing... you have may want to change the raycasting
    a bit to subdivide the map... it helps with speed.
            And don't forget the added complexity that walls aren't all at
    90 degrees to each other...

    3: Drawing the walls and Why it works!!
    =======================================

            If you are familiar with Wolfenstein then please still read this
    as it is esential background to understanding the floor routine.

            As all of you probably know the walls are drawn by scaling the line
    of the texture to the correct size for the screen. The information in the
    vertical buffer makes this easy. What you probably don't know is why this
    creates texture mapping that is good enough to fool us.

            The wall function is a Affine texture mapping. (well almost)
    Now affine texture mappings look abysmal unless you do quite a lot of
    subdivision (The amount needed varies according to the angle the projected
    square is at.). So why does the Doom technique work??

            Well when we traced the rays we found out exactly where along the
    side of the square we hit we were in relation to the width of the texture.
    This means that the top and bottom pixels of the scaled wall piece are
    calculated correctly. This means that we have effecively subdivided the
    texture along vertical scanlines and as the effective subdidvisons are
    calculated exactly with proper forshortening as a result of the tracing.
    So the ray casting has made the texture mapping easy for us.
            (We have enough subdivision by this scanline effect as the wall
    only rotates about one axis and we have proper foreshortening.)

            This knowlege helps us understand how to do the floors and why
    that works.

            We can now draw all the wall segments by just looking at the buffer
    and drawing the parts marked as walls.(Skiping where we put in the bits used
    by the floor/ceiling bits: we draw them later.)

    4:  Drawing the Floor/Ceiling and why it works!
    ===============================================

            If you have grasped why the walls work then you have just about
    won for the floors.
            We have the information needed to draw the floors from the horizontal
    buffer.
            All we have to do is look at the horizontal spans in the buffer
    and draw them in all.
            Each of these spans has 2 end coordinates for which we have
    exact texture coorinates. This tells us which line across the texture
    we have to step along to do an Affine or linear mapping.
            This is shown below;

            =================================
            =                               =
            =                               =
            =                               =
            =                               = U1,V1 (exit)
            =                              **
            =                           *** =
            =                        ***    =
            =                     ***       =
            =                  ***          =
            =               ***             =
            =            ***                =
            =         ***                   =
            =       **                      =
            =     **                        =
            =   **                          =
            = **                            =
      U0,V0 **                              =
    (entry) =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =                               =
            =================================

    (apologies for the wonky line: it should be straight!!)

            Now...as the end coordinates are correct and the axis along
    which forshortening takes place is not involved (this is a fudge)
    we can step linearly along this line across the texture to approximate
    the mapping. (This is far easier than a proper texture map).
            This is effectivly a wall lying on its side which works as the
    texture coordinates at the ends of the span have been calculated correctly.
    This is a benefit of the raycasting we used to find everything.
            Easy huh??

    5: Sprites
    ==========

            The Sprites are really quite easy to do. The basic technique is the
    same as used in Wolfenstein 3d.
            This is done as follows:

    When you enter a 'square' on the floor map you test to see if there are
    any sprites in the square. If there are you flag that sprite as visible
    and add it to a list of visible sprites.

    When you have finished tracing and drawing the walls and floor you
    depth sort the sprites and draw them from the back to the front. (painters
    algorithm). The only complication in drawing them is that you have to check
    buffer that has the walls in, in order to clip the sprites correctly.

            (If you're interested in Doom you can occasionally see large
    explosions (ie BFG) slip partially behind a wall segment.)

            On possibly faster way of handling the sprites would be to mark
    them like wall segments as you find them in the buffer. The only (ONLY!)
    complication to this approach is that sprites can have holes in them. By
    this I mean things like the gap between an arm and a leg which should be
    the background colour.

    6: Lighting and Depth Cueing
    ============================

            Lighting and Depth Cueing fits nicely in with the way that we have
    prepared the screen ready for drawing.
            All we have to do is see how far away we are when we found either
    the floor or wall section and set the light level according to the distance.
            The other thing that is applied is a light level. This is taken from
    the map at the edges where you have hit something. As the map is 2D it is
    easy to manage lighting, flickering etc.
            For things like pools of light on the floor all you have to do
    is subdivide that patch of floor so that you can set the bit under the
    skylight to a lighter colour. Its also very easy to frig this for the
    lighting goggles.

    7: Controlling the Baddies
    ==========================

            This is pretty easy: all you have to think about is moving and
    reacting on a 2d map. the only complications are things like the monsters
    looking through windows and seeing a player but this all degenerates into
    a simple 2d problem. Things like deciding whether the player has been hit or
    has he/she hit a monster is just another case of firing a ray. (Or do it
    another way...)

    8: Where next???
    ================

            Thats all folks... hopefully a useful and intersting insight into
    my Doom engine works.
            As to the question where next... well I already have some enhancements
    to my Doom enigine and others are in the works...

    Some of what you may eventually see are:

            Proper lighting (I have done this already...its easier than you
                            think)
            Non-Vertical walls (i.e. Aliens style corridors...)
            Orgranic Walls (i.e. Curved like the Aliens nest...)
            Fractal Landscapes (This one is still very much a theory but how
                            about being able to go outside and walk up and down
                            hills etc??)

            If there are bits people are really shaky about I may post a new
    version of this... but I cannot get into implimentation issues as all
    implementation work is under copyright...

            By the way if anyone out there implements this I'd love to here
    how you get on...

            Anyone got any comments or any other interesting algorithms???

    Brian 'Neuromancer' Marshall         'When do graphics not look like graphics?
    ( Email: brianm@vissci.demon.co.uk )  :when we get it RIGHT.'

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