*******************************************************************************                       '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 thisdocument proper....1:  Definition of Terms======================        Throughout this document I will be making use of many graphical termsusing my understanding of them as they apply to this algorithm. I willexplain 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'thave to be the whole screen.Affine Mapping:        A affine mapping is a texture map where the texture is sampledin a linear fashion in both U and V.Biquadratic Mapping:        A biquadratic mapping is a mapping where the texture is sampledalong 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 homogenouscoordinated is added to the texture coordinateds to give (U,V,W) anda division is performed at every pixel. This is the mathematically andvisual correct for of texture mapping for the square to quadrilateralmappings we are using.        (As an aside it is possible to do a projective mapping withoutthe divide (or 3 multiplies) but that is totally unrelated to the matterin hand...)Ray Casting:        Ray Casting in this context is back-firing 'rays' along a twodinesional map. The rays do however follow heights... more on that laterSprite:        A Sprite is a bitmap that is either a monster or an object. Toput it another way it is anything that is not made out of wall orfloor 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 byexplaining 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 thana wall segment. Also note that a you exit a floor segment you may also hita wall segment.        Tracing the individual ray is continued until we hit a special kindof 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 earlyif we have found enough to fill the whole vertical scanline then we can stopwhenevr we have done this.        Next come a trick. I said we were tracing along a 2d map. Well Ilied a bit. There are (In my implementation at least..) TWO 2d maps. One isbasically from the floor along including all the 'floor' walls and everythingup to and including the walls that join onto the ceiling. The other mapis basically the ceiling (with anything coming down from the ceiling on itif you are doing this: this makes life a little more complex as I'll explainbelow..)        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 fromthe 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 builtout of walls jutting down from the ceiling. you have to decide whether todraw it or draw whatever was already in the scanline structure. This meanseither storing extra information in the buffer ie z coordinates or tracingalong both the ceiling and floor at the same time.... for most people I wouldsuggest 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 lotsof floor squares that aren't on screen. By tracing backwards you can keepgoing up the vertical scanline and you know that you are on the screen. Assoon as something goes off the top of the screen you can handle that and thenstop tracing.        Phew. has everyone got that???        Now we just go back and fire rays up the rest of the verticalscanlines. Easy!!???        At the end of this lot we have the necessary data in the two buffersto 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 raycastinga bit to subdivide the map... it helps with speed.        And don't forget the added complexity that walls aren't all at90 degrees to each other...3: Drawing the walls and Why it works!!=======================================        If you are familiar with Wolfenstein then please still read thisas it is esential background to understanding the floor routine.        As all of you probably know the walls are drawn by scaling the lineof the texture to the correct size for the screen. The information in thevertical buffer makes this easy. What you probably don't know is why thiscreates 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 ofsubdivision (The amount needed varies according to the angle the projectedsquare is at.). So why does the Doom technique work??        Well when we traced the rays we found out exactly where along theside 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 arecalculated correctly. This means that we have effecively subdivided thetexture along vertical scanlines and as the effective subdidvisons arecalculated 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 wallonly rotates about one axis and we have proper foreshortening.)        This knowlege helps us understand how to do the floors and whythat works.        We can now draw all the wall segments by just looking at the bufferand drawing the parts marked as walls.(Skiping where we put in the bits usedby 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 aboutwon for the floors.        We have the information needed to draw the floors from the horizontalbuffer.        All we have to do is look at the horizontal spans in the bufferand draw them in all.        Each of these spans has 2 end coordinates for which we haveexact texture coorinates. This tells us which line across the texturewe 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 alongwhich forshortening takes place is not involved (this is a fudge)we can step linearly along this line across the texture to approximatethe mapping. (This is far easier than a proper texture map).        This is effectivly a wall lying on its side which works as thetexture 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 thesame 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 areany sprites in the square. If there are you flag that sprite as visibleand add it to a list of visible sprites.When you have finished tracing and drawing the walls and floor youdepth sort the sprites and draw them from the back to the front. (paintersalgorithm). 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 markthem 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. Bythis 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 haveprepared the screen ready for drawing.        All we have to do is see how far away we are when we found eitherthe 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 fromthe map at the edges where you have hit something. As the map is 2D it iseasy to manage lighting, flickering etc.        For things like pools of light on the floor all you have to dois 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 thelighting goggles.7: Controlling the Baddies==========================                This is pretty easy: all you have to think about is moving andreacting on a 2d map. the only complications are things like the monsterslooking through windows and seeing a player but this all degenerates intoa simple 2d problem. Things like deciding whether the player has been hit orhas he/she hit a monster is just another case of firing a ray. (Or do itanother way...)8: Where next???================        Thats all folks... hopefully a useful and intersting insight intomy Doom engine works.        As to the question where next... well I already have some enhancementsto 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 newversion of this... but I cannot get into implimentation issues as allimplementation work is under copyright...        By the way if anyone out there implements this I'd love to herehow 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.'

Quote:Original post by Konfusius
I hope GD staff will not ban me for this, but anyway:

(This directly stolen from PCGPE)

-->>>SNIP

(and I snip again)