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    {
    From: PETER KOLDING
    Subj: 3D Graphics

    MB>  Hello, I'm trying to write a simple program that will plot points in three
    MB>  dimensions and allow you to rotate them,or view them from different
    angles.
    MB>  need a lot of help. I'm trying to make a data file of points in the format
    MB>  (x,y,z) and then have the program read the points in to display. So far no
    MB>  luck. If anyone has any code that is simple enough for me to understand I
    MB>  would appreciate it. Also if anyone has any code for doing fast vga
    MB>  animations(in assembly) could they please post it? Thanks in advance.
    }

    program boxrot;

    {PUBLIC DOMAIN  1993 Peter M. Gruhn}

    {Program draws a box on screen. Allows user to rotate the box around
     the three primary axes. Viewing transform is simple ignore z.}

    {I used _Computer_Graphics:_Principles_and_Practice_, Foley et al
     ISBN 0-201-12110-7 as a reference}

    {RUNNING:
     Borland Pascal 7. Should run on any graphics device supported by BGI.
     If you have smaller than 280 resolution, change '+200' to something
     smaller and/or change 75 to something smaller.

     Since this machine is
     not really set up for doing DOS graphics, I hard coded my BGI path, so
     you have to find 'initgraph' and change the bgi path to something that
     works on your machine. Try ''.

    {Okey dokey. This is kinda slow, and does a nice job of demonstrating the
     problems of repeatedly modifying the same data set. That is, the more and
     more you rotate the box, the more and more distorted it gets. This is
     because computers are not perfect at calculations, and all of those little
     errors add up quite quickly.

     It's because of that that I used reals, not reals. I used floating point
     because the guy doesn't know what is going on at all with 3d, so better to
     look at only the math that is really happening. Besides, I still have to
     think to use fixed point. Whaddaya want for .5 hour programming.

     DIRECTIONS:
       ',' - rotates around the x axis
       '.' - rotates around the y axis
       '/' - rotates around the z axis
       'q' - quits

       All rotations are done around global axes, not object axes.}

    uses graph,crt;

    const radtheta=1{degrees}*3.1415926535{radians}/180{per degrees};
          {sin and cos on computers are done in radians.}

    type tpointr=record   {Just a record to hold 3d points}
           x,y,z:real;
           end;

    var box:array[0..7] of tpointr;   {The box we will manipulate}
        c:char;                    {Our input mechanism}

    procedure init;
    var gd,gm:integer;
    {turns on graphics and creates a cube. Since the rotation routines
     rotate around the origin, I have centered the cube on the origin, so
     that it stays in place and only spins.} begin
      gd:=detect; initgraph(gd,gm,'d:\turbo\tp\');
      box[0].x:=-75;  box[0].y:=-75;  box[0].z:=-75;
      box[1].x:=75;   box[1].y:=-75;  box[1].z:=-75;
      box[2].x:=75;   box[2].y:=75;   box[2].z:=-75;
      box[3].x:=-75;  box[3].y:=75;   box[3].z:=-75;
      box[4].x:=-75;  box[4].y:=-75;  box[4].z:=75;
      box[5].x:=75;   box[5].y:=-75;  box[5].z:=75;
      box[6].x:=75;   box[6].y:=75;   box[6].z:=75;
      box[7].x:=-75;  box[7].y:=75;   box[7].z:=75; end;

    procedure myline(x1,y1,z1,x2,y2,z2:real); {Keeps the draw routine pretty.
    Pixels are integers, so I round. Since the
     cube is centered around 0,0 I move it over 200 to put it on screen.} begin
    {if you think those real mults are slow, here's some rounds too...}

    {hey, you may wonder, what happened to the stinking z coordinate? Ah, says I,
     this is the simplest of 3d viewing transforms. You just take the z coord out
     of things and boom. Looking straight down the z axis on the object. If I get
     inspired, I will add simple perspective transform to these.} {There, got
    inspired. Made mistakes. Foley et al are not very good at
     tutoring perspective and I'm kinda ready to be done and post this.}
      line(round(x1)+200,round(y1)+200,
           round(x2)+200,round(y2)+200);
    end;

    procedure draw;
    {my model is hard coded. No cool things like vertex and edge and face
     lists.}

    begin
      myline(box[0].x,box[0].y,box[0].z, box[1].x,box[1].y,box[1].z);
      myline(box[1].x,box[1].y,box[1].z, box[2].x,box[2].y,box[2].z);
      myline(box[2].x,box[2].y,box[2].z, box[3].x,box[3].y,box[3].z);
      myline(box[3].x,box[3].y,box[3].z, box[0].x,box[0].y,box[0].z);

      myline(box[4].x,box[4].y,box[4].z, box[5].x,box[5].y,box[5].z);
      myline(box[5].x,box[5].y,box[5].z, box[6].x,box[6].y,box[6].z);
      myline(box[6].x,box[6].y,box[6].z, box[7].x,box[7].y,box[7].z);
      myline(box[7].x,box[7].y,box[7].z, box[4].x,box[4].y,box[4].z);

      myline(box[0].x,box[0].y,box[0].z, box[4].x,box[4].y,box[4].z);
      myline(box[1].x,box[1].y,box[1].z, box[5].x,box[5].y,box[5].z);
      myline(box[2].x,box[2].y,box[2].z, box[6].x,box[6].y,box[6].z);
      myline(box[3].x,box[3].y,box[3].z, box[7].x,box[7].y,box[7].z);

      myline(box[0].x,box[0].y,box[0].z, box[5].x,box[5].y,box[5].z);
      myline(box[1].x,box[1].y,box[1].z, box[4].x,box[4].y,box[4].z); end;

    procedure rotx;
    {if you know your matrix multiplication, the following equations
     are derived from

     [x   [ 1  0  0  0   [x',y',z',1]
      y     0  c -s  0 =
      z     0  s  c  0
      1]    0  0  0  1]
    }
    var i:integer;
    begin
      setcolor(0);
      draw;
      for i:=0 to 7 do
        begin
        box[i].x:= box[i].x;
        box[i].y:= box[i].y*cos(radTheta) + box[i].z*sin(radTheta);
        box[i].z:=-box[i].y*sin(radTheta) + box[i].z*cos(radTheta);
        end;
      setcolor(15);
      draw;
    end;

    procedure roty;
    {if you know your matrix multiplication, the following equations
     are derived from
     [x   [ c  0  s  0   [x',y',z',1]
      y     0  1  0  0 =
      z    -s  0  c  0
      1]    0  0  0  1]
    }
    var i:integer;
    begin
      setcolor(0);
      draw;
      for i:=0 to 7 do
        begin
        box[i].x:= box[i].x*cos(radTheta) - box[i].z*sin(radTheta);
        box[i].y:= box[i].y;
        box[i].z:= box[i].x*sin(radTheta) + box[i].z*cos(radTheta);
        end;
      setcolor(15);
      draw;
    end;

    procedure rotz;
    {if you know your matrix multiplication, the following equations
     are derived from

     [x   [ c -s  0  0   [x',y',z',1]
      y     s  c  0  0 =
      z     0  0  1  0
      1]    0  0  0  1]
    }
    var i:integer;
    begin
      setcolor(0);
      draw;
      for i:=0 to 7 do
        begin
        box[i].x:= box[i].x*cos(radTheta) + box[i].y*sin(radTheta);
        box[i].y:=-box[i].x*sin(radTheta) + box[i].y*cos(radTheta);
        box[i].z:= box[i].z;
        end;
      setcolor(15);
      draw;
    end;

    begin
      init;
      setcolor(14); draw;
      repeat
        c:=readkey;
        case c of
          ',' : rotx;
          '.' : roty;
          '/' : rotz;
          else {who gives a};
          end; {case}
      until c='q';
      closegraph;
    end.

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