_GRAPHICS PROGRAMMING COLUMN_
by Michael Abrash

[LISTING ONE]


/* 3D animation program to rotate 12 cubes. Uses fixed point. All C code 
tested with Borland C++ 3.0 in C compilation mode and the small model. */
#include <conio.h>
#include <dos.h>
#include "polygon.h"

/* Base offset of page to which to draw */
unsigned int CurrentPageBase = 0;
/* Clip rectangle; clips to the screen */
int ClipMinX = 0, ClipMinY = 0;
int ClipMaxX = SCREEN_WIDTH, ClipMaxY = SCREEN_HEIGHT;
static unsigned int PageStartOffsets[2] =
   {PAGE0_START_OFFSET,PAGE1_START_OFFSET};
int DisplayedPage, NonDisplayedPage;
int RecalcAllXforms = 1, NumObjects = 0;
Xform WorldViewXform;   /* initialized from floats */
/* Pointers to objects */
Object *ObjectList[MAX_OBJECTS];

void main() {
   int Done = 0, i;
   Object *ObjectPtr;
   union REGS regset;

   InitializeFixedPoint(); /* set up fixed-point data */
   InitializeCubes();    /* set up cubes and add them to object list; other 
                         objects would be initialized now, if there were any */
   Set320x240Mode(); /* set the screen to mode X */
   ShowPage(PageStartOffsets[DisplayedPage = 0]);
   /* Keep transforming the cube, drawing it to the undisplayed page,
      and flipping the page to show it */
   do {
      /* For each object, regenerate viewing info, if necessary */
      for (i=0; i<NumObjects; i++) {
         if ((ObjectPtr = ObjectList[i])->RecalcXform ||
               RecalcAllXforms) {
            ObjectPtr->RecalcFunc(ObjectPtr);
            ObjectPtr->RecalcXform = 0;
         }
      }
      RecalcAllXforms = 0;
      CurrentPageBase =    /* select other page for drawing to */
            PageStartOffsets[NonDisplayedPage = DisplayedPage ^ 1];
      /* For each object, clear the portion of the non-displayed page
         that was drawn to last time, then reset the erase extent */
      for (i=0; i<NumObjects; i++) {
         ObjectPtr = ObjectList[i];
         FillRectangleX(ObjectPtr->EraseRect[NonDisplayedPage].Left,
            ObjectPtr->EraseRect[NonDisplayedPage].Top,
            ObjectPtr->EraseRect[NonDisplayedPage].Right,
            ObjectPtr->EraseRect[NonDisplayedPage].Bottom,
            CurrentPageBase, 0);
         ObjectPtr->EraseRect[NonDisplayedPage].Left =
              ObjectPtr->EraseRect[NonDisplayedPage].Top = 0x7FFF;
         ObjectPtr->EraseRect[NonDisplayedPage].Right =
               ObjectPtr->EraseRect[NonDisplayedPage].Bottom = 0;
      }
      /* Draw all objects */
      for (i=0; i<NumObjects; i++)
         ObjectList[i]->DrawFunc(ObjectList[i]);
      /* Flip to display the page into which we just drew */
      ShowPage(PageStartOffsets[DisplayedPage = NonDisplayedPage]);
      /* Move and reorient each object */
      for (i=0; i<NumObjects; i++)
         ObjectList[i]->MoveFunc(ObjectList[i]);
      if (kbhit())
         if (getch() == 0x1B) Done = 1;   /* Esc to exit */
   } while (!Done);
   /* Return to text mode and exit */
   regset.x.ax = 0x0003;   /* AL = 3 selects 80x25 text mode */
   int86(0x10, &regset, &regset);
   exit(1);
}



[LISTING TWO]

/* Transforms all vertices in the specified polygon-based object into view 
space, then perspective projects them to screen space and maps them to screen 
coordinates, storing results in the object. Recalculates object->view 
transformation because only if transform changes would we bother 
to retransform the vertices. */
#include <math.h>
#include "polygon.h"

void XformAndProjectPObject(PObject * ObjectToXform)
{
   int i, NumPoints = ObjectToXform->NumVerts;
   Point3 * Points = ObjectToXform->VertexList;
   Point3 * XformedPoints = ObjectToXform->XformedVertexList;
   Point3 * ProjectedPoints = ObjectToXform->ProjectedVertexList;
   Point * ScreenPoints = ObjectToXform->ScreenVertexList;

   /* Recalculate the object->view transform */
   ConcatXforms(WorldViewXform, ObjectToXform->XformToWorld, 
                                                 ObjectToXform->XformToView);
   /* Apply that new transformation and project the points */
   for (i=0; i<NumPoints; i++, Points++, XformedPoints++,
         ProjectedPoints++, ScreenPoints++) {
      /* Transform to view space */
      XformVec(ObjectToXform->XformToView, (Fixedpoint *) Points,
            (Fixedpoint *) XformedPoints);
      /* Perspective-project to screen space */
      ProjectedPoints->X =
            FixedMul(FixedDiv(XformedPoints->X, XformedPoints->Z),
            DOUBLE_TO_FIXED(PROJECTION_RATIO * (SCREEN_WIDTH/2)));
      ProjectedPoints->Y =
            FixedMul(FixedDiv(XformedPoints->Y, XformedPoints->Z),
            DOUBLE_TO_FIXED(PROJECTION_RATIO * (SCREEN_WIDTH/2)));
      ProjectedPoints->Z = XformedPoints->Z;
      /* Convert to screen coordinates. The Y coord is negated to flip from 
      increasing Y being up to increasing Y being down, as expected by polygon 
      filler. Add in half the screen width and height to center on screen */
      ScreenPoints->X = ((int) ((ProjectedPoints->X +
            DOUBLE_TO_FIXED(0.5)) >> 16)) + SCREEN_WIDTH/2;
      ScreenPoints->Y = (-((int) ((ProjectedPoints->Y +
            DOUBLE_TO_FIXED(0.5)) >> 16))) + SCREEN_HEIGHT/2;
   }
}


[LISTING THREE]

/* Routines to perform incremental rotations around the three axes. */
#include <math.h>
#include "polygon.h"

/* Concatenate a rotation by Angle around the X axis to transformation in 
 XformToChange, placing the result back into XformToChange. */
void AppendRotationX(Xform XformToChange, double Angle)
{
   Fixedpoint Temp10, Temp11, Temp12, Temp20, Temp21, Temp22;
   Fixedpoint CosTemp = DOUBLE_TO_FIXED(cos(Angle));
   Fixedpoint SinTemp = DOUBLE_TO_FIXED(sin(Angle));

   /* Calculate the new values of the six affected matrix entries */
   Temp10 = FixedMul(CosTemp, XformToChange[1][0]) +
         FixedMul(-SinTemp, XformToChange[2][0]);
   Temp11 = FixedMul(CosTemp, XformToChange[1][1]) +
         FixedMul(-SinTemp, XformToChange[2][1]);
   Temp12 = FixedMul(CosTemp, XformToChange[1][2]) +
         FixedMul(-SinTemp, XformToChange[2][2]);
   Temp20 = FixedMul(SinTemp, XformToChange[1][0]) +
         FixedMul(CosTemp, XformToChange[2][0]);
   Temp21 = FixedMul(SinTemp, XformToChange[1][1]) +
         FixedMul(CosTemp, XformToChange[2][1]);
   Temp22 = FixedMul(SinTemp, XformToChange[1][2]) +
         FixedMul(CosTemp, XformToChange[2][2]);
   /* Put the results back into XformToChange */
   XformToChange[1][0] = Temp10; XformToChange[1][1] = Temp11;
   XformToChange[1][2] = Temp12; XformToChange[2][0] = Temp20; 
   XformToChange[2][1] = Temp21; XformToChange[2][2] = Temp22;
}
/* Concatenate a rotation by Angle around the Y axis to transformation in 
  XformToChange, placing the result back into XformToChange. */
void AppendRotationY(Xform XformToChange, double Angle)
{
   Fixedpoint Temp00, Temp01, Temp02, Temp20, Temp21, Temp22;
   Fixedpoint CosTemp = DOUBLE_TO_FIXED(cos(Angle));
   Fixedpoint SinTemp = DOUBLE_TO_FIXED(sin(Angle));

   /* Calculate the new values of the six affected matrix entries */
   Temp00 = FixedMul(CosTemp, XformToChange[0][0]) +
         FixedMul(SinTemp, XformToChange[2][0]);
   Temp01 = FixedMul(CosTemp, XformToChange[0][1]) +
         FixedMul(SinTemp, XformToChange[2][1]);
   Temp02 = FixedMul(CosTemp, XformToChange[0][2]) +
         FixedMul(SinTemp, XformToChange[2][2]);
   Temp20 = FixedMul(-SinTemp, XformToChange[0][0]) +
         FixedMul( CosTemp, XformToChange[2][0]);
   Temp21 = FixedMul(-SinTemp, XformToChange[0][1]) +
         FixedMul(CosTemp, XformToChange[2][1]);
   Temp22 = FixedMul(-SinTemp, XformToChange[0][2]) +
         FixedMul(CosTemp, XformToChange[2][2]);
   /* Put the results back into XformToChange */
   XformToChange[0][0] = Temp00; XformToChange[0][1] = Temp01;
   XformToChange[0][2] = Temp02; XformToChange[2][0] = Temp20;
   XformToChange[2][1] = Temp21; XformToChange[2][2] = Temp22;
}

/* Concatenate a rotation by Angle around the Z axis to transformation in 
  XformToChange, placing the result back into XformToChange. */
void AppendRotationZ(Xform XformToChange, double Angle)
{
   Fixedpoint Temp00, Temp01, Temp02, Temp10, Temp11, Temp12;
   Fixedpoint CosTemp = DOUBLE_TO_FIXED(cos(Angle));
   Fixedpoint SinTemp = DOUBLE_TO_FIXED(sin(Angle));

   /* Calculate the new values of the six affected matrix entries */
   Temp00 = FixedMul(CosTemp, XformToChange[0][0]) +
         FixedMul(-SinTemp, XformToChange[1][0]);
   Temp01 = FixedMul(CosTemp, XformToChange[0][1]) +
         FixedMul(-SinTemp, XformToChange[1][1]);
   Temp02 = FixedMul(CosTemp, XformToChange[0][2]) +
         FixedMul(-SinTemp, XformToChange[1][2]);
   Temp10 = FixedMul(SinTemp, XformToChange[0][0]) +
         FixedMul(CosTemp, XformToChange[1][0]);
   Temp11 = FixedMul(SinTemp, XformToChange[0][1]) +
         FixedMul(CosTemp, XformToChange[1][1]);
   Temp12 = FixedMul(SinTemp, XformToChange[0][2]) +
         FixedMul(CosTemp, XformToChange[1][2]);
   /* Put the results back into XformToChange */
   XformToChange[0][0] = Temp00; XformToChange[0][1] = Temp01;
   XformToChange[0][2] = Temp02; XformToChange[1][0] = Temp10;
   XformToChange[1][1] = Temp11; XformToChange[1][2] = Temp12;
}



[LISTING FOUR]

/* Fixed point matrix arithmetic functions */
#include "polygon.h"

/* Matrix multiplies Xform by SourceVec, and stores the result in DestVec. 
Multiplies a 4x4 matrix times a 4x1 matrix; the result is a 4x1 matrix. Cheats 
by assuming the W coord is 1 and bottom row of matrix is 0 0 0 1, and doesn't 
bother to set the W coordinate of the destination */
void XformVec(Xform WorkingXform, Fixedpoint *SourceVec,
   Fixedpoint *DestVec)
{
   int i;

   for (i=0; i<3; i++)
      DestVec[i] = FixedMul(WorkingXform[i][0], SourceVec[0]) +
            FixedMul(WorkingXform[i][1], SourceVec[1]) +
            FixedMul(WorkingXform[i][2], SourceVec[2]) +
            WorkingXform[i][3];   /* no need to multiply by W = 1 */
}

/* Matrix multiplies SourceXform1 by SourceXform2 and stores result in 
 DestXform. Multiplies a 4x4 matrix times a 4x4 matrix; result is a 4x4 matrix.
 Cheats by assuming bottom row of each matrix is 0 0 0 1, and doesn't bother 
 to set the bottom row of the destination */
void ConcatXforms(Xform SourceXform1, Xform SourceXform2,
   Xform DestXform)
{
   int i, j;

   for (i=0; i<3; i++) {
      for (j=0; j<4; j++)
         DestXform[i][j] =
               FixedMul(SourceXform1[i][0], SourceXform2[0][j]) +
               FixedMul(SourceXform1[i][1], SourceXform2[1][j]) +
               FixedMul(SourceXform1[i][2], SourceXform2[2][j]) +
               SourceXform1[i][3];
   }
}



[LISTING FIVE]

/* Set up basic data that needs to be in fixed point, to avoid data
   definition hassles. */
#include "polygon.h"

/* All vertices in the basic cube */
static IntPoint3 IntCubeVerts[NUM_CUBE_VERTS] = {
   {15,15,15},{15,15,-15},{15,-15,15},{15,-15,-15},
   {-15,15,15},{-15,15,-15},{-15,-15,15},{-15,-15,-15} };
/* Transformation from world space into view space (no transformation,
   currently) */
static int IntWorldViewXform[3][4] = {
   {1,0,0,0}, {0,1,0,0}, {0,0,1,0}};

void InitializeFixedPoint()
{
   int i, j;

   for (i=0; i<3; i++)
      for (j=0; j<4; j++)
         WorldViewXform[i][j] = INT_TO_FIXED(IntWorldViewXform[i][j]);
   for (i=0; i<NUM_CUBE_VERTS; i++) {
      CubeVerts[i].X = INT_TO_FIXED(IntCubeVerts[i].X);
      CubeVerts[i].Y = INT_TO_FIXED(IntCubeVerts[i].Y);
      CubeVerts[i].Z = INT_TO_FIXED(IntCubeVerts[i].Z);
   }
}


[LISTING SIX]

/* Rotates and moves a polygon-based object around the three axes.
   Movement is implemented only along the Z axis currently. */
#include "polygon.h"

void RotateAndMovePObject(PObject * ObjectToMove)
{
   if (--ObjectToMove->RDelayCount == 0) {   /* rotate */
      ObjectToMove->RDelayCount = ObjectToMove->RDelayCountBase;
      if (ObjectToMove->Rotate.RotateX != 0.0)
         AppendRotationX(ObjectToMove->XformToWorld,
               ObjectToMove->Rotate.RotateX);
      if (ObjectToMove->Rotate.RotateY != 0.0)
         AppendRotationY(ObjectToMove->XformToWorld,
               ObjectToMove->Rotate.RotateY);
      if (ObjectToMove->Rotate.RotateZ != 0.0)
         AppendRotationZ(ObjectToMove->XformToWorld,
               ObjectToMove->Rotate.RotateZ);
      ObjectToMove->RecalcXform = 1;
   }
   /* Move in Z, checking for bouncing and stopping */
   if (--ObjectToMove->MDelayCount == 0) {
      ObjectToMove->MDelayCount = ObjectToMove->MDelayCountBase;
      ObjectToMove->XformToWorld[2][3] += ObjectToMove->Move.MoveZ;
      if (ObjectToMove->XformToWorld[2][3]>ObjectToMove->Move.MaxZ)
         ObjectToMove->Move.MoveZ = 0; /* stop if close enough */
      ObjectToMove->RecalcXform = 1;
   }
}



[LISTING SEVEN]

/* Draws all visible faces in specified polygon-based object. Object must have 
previously been transformed and projected, so that ScreenVertexList array is 
filled in. */
#include "polygon.h"

void DrawPObject(PObject * ObjectToXform)
{
   int i, j, NumFaces = ObjectToXform->NumFaces, NumVertices;
   int * VertNumsPtr;
   Face * FacePtr = ObjectToXform->FaceList;
   Point * ScreenPoints = ObjectToXform->ScreenVertexList;
   long v1, v2, w1, w2;
   Point Vertices[MAX_POLY_LENGTH];
   PointListHeader Polygon;

   /* Draw each visible face (polygon) of the object in turn */
   for (i=0; i<NumFaces; i++, FacePtr++) {
      NumVertices = FacePtr->NumVerts;
      /* Copy over the face's vertices from the vertex list */
      for (j=0, VertNumsPtr=FacePtr->VertNums; j<NumVertices; j++)
         Vertices[j] = ScreenPoints[*VertNumsPtr++];
      /* Draw only if outside face showing (if the normal to the
         polygon points toward viewer; that is, has a positive Z component) */
      v1 = Vertices[1].X - Vertices[0].X;
      w1 = Vertices[NumVertices-1].X - Vertices[0].X;
      v2 = Vertices[1].Y - Vertices[0].Y;
      w2 = Vertices[NumVertices-1].Y - Vertices[0].Y;
      if ((v1*w2 - v2*w1) > 0) {
         /* It is facing the screen, so draw */
         /* Appropriately adjust the extent of the rectangle used to
            erase this object later */
         for (j=0; j<NumVertices; j++) {
            if (Vertices[j].X >
                  ObjectToXform->EraseRect[NonDisplayedPage].Right)
               if (Vertices[j].X < SCREEN_WIDTH)
                  ObjectToXform->EraseRect[NonDisplayedPage].Right =
                        Vertices[j].X;
               else ObjectToXform->EraseRect[NonDisplayedPage].Right =
                     SCREEN_WIDTH;
            if (Vertices[j].Y >
                  ObjectToXform->EraseRect[NonDisplayedPage].Bottom)
               if (Vertices[j].Y < SCREEN_HEIGHT)
                  ObjectToXform->EraseRect[NonDisplayedPage].Bottom =
                        Vertices[j].Y;
               else ObjectToXform->EraseRect[NonDisplayedPage].Bottom=
                     SCREEN_HEIGHT;
            if (Vertices[j].X <
                  ObjectToXform->EraseRect[NonDisplayedPage].Left)
               if (Vertices[j].X > 0)
                  ObjectToXform->EraseRect[NonDisplayedPage].Left =
                        Vertices[j].X;
               else ObjectToXform->EraseRect[NonDisplayedPage].Left=0;
            if (Vertices[j].Y <
                  ObjectToXform->EraseRect[NonDisplayedPage].Top)
               if (Vertices[j].Y > 0)
                  ObjectToXform->EraseRect[NonDisplayedPage].Top =
                        Vertices[j].Y;
               else ObjectToXform->EraseRect[NonDisplayedPage].Top=0;
         }
         /* Draw the polygon */
         DRAW_POLYGON(Vertices, NumVertices, FacePtr->Color, 0, 0);
      }
   }
}



[LISTING EIGHT]

/* Initializes the cubes and adds them to the object list. */
#include <stdlib.h>
#include <math.h>
#include "polygon.h"

#define ROT_6  (M_PI / 30.0)     /* rotate 6 degrees at a time */
#define ROT_3  (M_PI / 60.0)     /* rotate 3 degrees at a time */
#define ROT_2  (M_PI / 90.0)     /* rotate 2 degrees at a time */
#define NUM_CUBES 12             /* # of cubes */
Point3 CubeVerts[NUM_CUBE_VERTS]; /* set elsewhere, from floats */
/* Vertex indices for individual cube faces */
static int Face1[] = {1,3,2,0};
static int Face2[] = {5,7,3,1};
static int Face3[] = {4,5,1,0};
static int Face4[] = {3,7,6,2};
static int Face5[] = {5,4,6,7};
static int Face6[] = {0,2,6,4};
static int *VertNumList[]={Face1, Face2, Face3, Face4, Face5, Face6};
static int VertsInFace[]={ sizeof(Face1)/sizeof(int),
   sizeof(Face2)/sizeof(int), sizeof(Face3)/sizeof(int),
   sizeof(Face4)/sizeof(int), sizeof(Face5)/sizeof(int),
   sizeof(Face6)/sizeof(int) };
/* X, Y, Z rotations for cubes */
static RotateControl InitialRotate[NUM_CUBES] = {
   {0.0,ROT_6,ROT_6},{ROT_3,0.0,ROT_3},{ROT_3,ROT_3,0.0},
   {ROT_3,-ROT_3,0.0},{-ROT_3,ROT_2,0.0},{-ROT_6,-ROT_3,0.0},
   {ROT_3,0.0,-ROT_6},{-ROT_2,0.0,ROT_3},{-ROT_3,0.0,-ROT_3},
   {0.0,ROT_2,-ROT_2},{0.0,-ROT_3,ROT_3},{0.0,-ROT_6,-ROT_6},};
static MoveControl InitialMove[NUM_CUBES] = {
   {0,0,80,0,0,0,0,0,-350},{0,0,80,0,0,0,0,0,-350},
   {0,0,80,0,0,0,0,0,-350},{0,0,80,0,0,0,0,0,-350},
   {0,0,80,0,0,0,0,0,-350},{0,0,80,0,0,0,0,0,-350},
   {0,0,80,0,0,0,0,0,-350},{0,0,80,0,0,0,0,0,-350},
   {0,0,80,0,0,0,0,0,-350},{0,0,80,0,0,0,0,0,-350},
   {0,0,80,0,0,0,0,0,-350},{0,0,80,0,0,0,0,0,-350}, };
/* Face colors for various cubes */
static int Colors[NUM_CUBES][NUM_CUBE_FACES] = {
   {15,14,12,11,10,9},{1,2,3,4,5,6},{35,37,39,41,43,45},
   {47,49,51,53,55,57},{59,61,63,65,67,69},{71,73,75,77,79,81},
   {83,85,87,89,91,93},{95,97,99,101,103,105},
   {107,109,111,113,115,117},{119,121,123,125,127,129},
   {131,133,135,137,139,141},{143,145,147,149,151,153} };
/* Starting coordinates for cubes in world space */
static int CubeStartCoords[NUM_CUBES][3] = {
   {100,0,-6000},  {100,70,-6000}, {100,-70,-6000}, {33,0,-6000},
   {33,70,-6000},  {33,-70,-6000}, {-33,0,-6000},   {-33,70,-6000},
   {-33,-70,-6000},{-100,0,-6000}, {-100,70,-6000}, {-100,-70,-6000}};
/* Delay counts (speed control) for cubes */
static int InitRDelayCounts[NUM_CUBES] = {1,2,1,2,1,1,1,1,1,2,1,1};
static int BaseRDelayCounts[NUM_CUBES] = {1,2,1,2,2,1,1,1,2,2,2,1};
static int InitMDelayCounts[NUM_CUBES] = {1,1,1,1,1,1,1,1,1,1,1,1};
static int BaseMDelayCounts[NUM_CUBES] = {1,1,1,1,1,1,1,1,1,1,1,1};

void InitializeCubes()
{
   int i, j, k;
   PObject *WorkingCube;

   for (i=0; i<NUM_CUBES; i++) {
      if ((WorkingCube = malloc(sizeof(PObject))) == NULL) {
         printf("Couldn't get memory\n"); exit(1); }
      WorkingCube->DrawFunc = DrawPObject;
      WorkingCube->RecalcFunc = XformAndProjectPObject;
      WorkingCube->MoveFunc = RotateAndMovePObject;
      WorkingCube->RecalcXform = 1;
      for (k=0; k<2; k++) {
         WorkingCube->EraseRect[k].Left =
            WorkingCube->EraseRect[k].Top = 0x7FFF;
         WorkingCube->EraseRect[k].Right = 0;
         WorkingCube->EraseRect[k].Bottom = 0;
      }
      WorkingCube->RDelayCount = InitRDelayCounts[i];
      WorkingCube->RDelayCountBase = BaseRDelayCounts[i];
      WorkingCube->MDelayCount = InitMDelayCounts[i];
      WorkingCube->MDelayCountBase = BaseMDelayCounts[i];
      /* Set the object->world xform to none */
      for (j=0; j<3; j++)
         for (k=0; k<4; k++)
            WorkingCube->XformToWorld[j][k] = INT_TO_FIXED(0);
      WorkingCube->XformToWorld[0][0] = 
         WorkingCube->XformToWorld[1][1] =
         WorkingCube->XformToWorld[2][2] =
         WorkingCube->XformToWorld[3][3] = INT_TO_FIXED(1);
      /* Set the initial location */
      for (j=0; j<3; j++) WorkingCube->XformToWorld[j][3] =
            INT_TO_FIXED(CubeStartCoords[i][j]);
      WorkingCube->NumVerts = NUM_CUBE_VERTS;
      WorkingCube->VertexList = CubeVerts;
      WorkingCube->NumFaces = NUM_CUBE_FACES;
      WorkingCube->Rotate = InitialRotate[i];
      WorkingCube->Move.MoveX = INT_TO_FIXED(InitialMove[i].MoveX);
      WorkingCube->Move.MoveY = INT_TO_FIXED(InitialMove[i].MoveY);
      WorkingCube->Move.MoveZ = INT_TO_FIXED(InitialMove[i].MoveZ);
      WorkingCube->Move.MinX = INT_TO_FIXED(InitialMove[i].MinX);
      WorkingCube->Move.MinY = INT_TO_FIXED(InitialMove[i].MinY);
      WorkingCube->Move.MinZ = INT_TO_FIXED(InitialMove[i].MinZ);
      WorkingCube->Move.MaxX = INT_TO_FIXED(InitialMove[i].MaxX);
      WorkingCube->Move.MaxY = INT_TO_FIXED(InitialMove[i].MaxY);
      WorkingCube->Move.MaxZ = INT_TO_FIXED(InitialMove[i].MaxZ);
      if ((WorkingCube->XformedVertexList =
            malloc(NUM_CUBE_VERTS*sizeof(Point3))) == NULL) {
         printf("Couldn't get memory\n"); exit(1); }
      if ((WorkingCube->ProjectedVertexList =
            malloc(NUM_CUBE_VERTS*sizeof(Point3))) == NULL) {
         printf("Couldn't get memory\n"); exit(1); }
      if ((WorkingCube->ScreenVertexList =
            malloc(NUM_CUBE_VERTS*sizeof(Point))) == NULL) {
         printf("Couldn't get memory\n"); exit(1); }
      if ((WorkingCube->FaceList =
            malloc(NUM_CUBE_FACES*sizeof(Face))) == NULL) {
         printf("Couldn't get memory\n"); exit(1); }
      /* Initialize the faces */
      for (j=0; j<NUM_CUBE_FACES; j++) {
         WorkingCube->FaceList[j].VertNums = VertNumList[j];
         WorkingCube->FaceList[j].NumVerts = VertsInFace[j];
         WorkingCube->FaceList[j].Color = Colors[i][j];
      }
      ObjectList[NumObjects++] = (Object *)WorkingCube;
   }
}



[LISTING NINE]

; 386-specific fixed point multiply and divide.
; C near-callable as: Fixedpoint FixedMul(Fixedpoint M1, Fixedpoint M2);
;                 Fixedpoint FixedDiv(Fixedpoint Dividend, Fixedpoint Divisor);
; Tested with TASM 3.0.
        .model small
        .386
        .code
        public  _FixedMul,_FixedDiv
; Multiplies two fixed-point values together.
FMparms struc
        dw      2 dup(?)        ;return address & pushed BP
M1      dd      ?
M2      dd      ?
FMparms ends
        align   2
_FixedMul       proc    near
        push    bp
        mov     bp,sp
        mov     eax,[bp+M1]
        imul    dword ptr [bp+M2] ;multiply
        add     eax,8000h       ;round by adding 2^(-16)
        adc     edx,0           ;whole part of result is in DX
        shr     eax,16          ;put the fractional part in AX
        pop     bp
        ret
_FixedMul       endp
; Divides one fixed-point value by another.
FDparms struc
        dw      2 dup(?)        ;return address & pushed BP
Dividend dd     ?
Divisor  dd     ?
FDparms ends
        align   2
_FixedDiv       proc    near
        push    bp
        mov     bp,sp
        sub     cx,cx           ;assume positive result
        mov     eax,[bp+Dividend]
        and     eax,eax         ;positive dividend?
        jns     FDP1            ;yes
        inc     cx              ;mark it's a negative dividend
        neg     eax             ;make the dividend positive
FDP1:   sub     edx,edx         ;make it a 64-bit dividend, then shift
                                ; left 16 bits so that result will be in EAX
        rol     eax,16          ;put fractional part of dividend in
                                ; high word of EAX
        mov     dx,ax           ;put whole part of dividend in DX
        sub     ax,ax           ;clear low word of EAX
        mov     ebx,dword ptr [bp+Divisor]
        and     ebx,ebx         ;positive divisor?
        jns     FDP2            ;yes
        dec     cx              ;mark it's a negative divisor
        neg     ebx             ;make divisor positive
FDP2:   div     ebx             ;divide
        shr     ebx,1           ;divisor/2, minus 1 if the divisor is
        adc     ebx,0           ; even
        dec     ebx
        cmp     ebx,edx         ;set Carry if remainder is at least
        adc     eax,0           ; half as large as the divisor, then
                                ; use that to round up if necessary
        and     cx,cx           ;should the result be made negative?
        jz      FDP3            ;no
        neg     eax             ;yes, negate it
FDP3:   mov     edx,eax         ;return result in DX:AX; fractional
                                ; part is already in AX
        shr     edx,16          ;whole part of result in DX
        pop     bp
        ret
_FixedDiv       endp
        end



[LISTING TEN]

/* POLYGON.H: Header file for polygon-filling code, also includes
   a number of useful items for 3D animation. */
#define MAX_OBJECTS  100   /* max simultaneous # objects supported */
#define MAX_POLY_LENGTH 4  /* four vertices is the max per poly */
#define SCREEN_WIDTH 320
#define SCREEN_HEIGHT 240
#define PAGE0_START_OFFSET 0
#define PAGE1_START_OFFSET (((long)SCREEN_HEIGHT*SCREEN_WIDTH)/4)
#define NUM_CUBE_VERTS 8              /* # of vertices per cube */
#define NUM_CUBE_FACES 6              /* # of faces per cube */
/* Ratio: distance from viewpoint to projection plane / width of
   projection plane. Defines the width of the field of view. Lower
   absolute values = wider fields of view; higher values = narrower */
#define PROJECTION_RATIO -2.0 /* negative because visible Z
                                 coordinates are negative */
/* Draws the polygon described by the point list PointList in color
   Color with all vertices offset by (X,Y) */
#define DRAW_POLYGON(PointList,NumPoints,Color,X,Y)          \
   Polygon.Length = NumPoints; Polygon.PointPtr = PointList; \
   FillConvexPolygon(&Polygon, Color, X, Y);
#define INT_TO_FIXED(x) (((long)(int)x) << 16)
#define DOUBLE_TO_FIXED(x) ((long) (x * 65536.0 + 0.5))

typedef long Fixedpoint;
typedef Fixedpoint Xform[3][4];
/* Describes a single 2D point */
typedef struct { int X; int Y; } Point;
/* Describes a single 3D point in homogeneous coordinates; the W
   coordinate isn't present, though; assumed to be 1 and implied */
typedef struct { Fixedpoint X, Y, Z; } Point3;
typedef struct { int X; int Y; int Z; } IntPoint3;
/* Describes a series of points (used to store a list of vertices that
   describe a polygon; each vertex is assumed to connect to the two
   adjacent vertices; last vertex is assumed to connect to first) */
typedef struct { int Length; Point * PointPtr; } PointListHeader;
/* Describes the beginning and ending X coordinates of a single
   horizontal line */
typedef struct { int XStart; int XEnd; } HLine;
/* Describes a Length-long series of horizontal lines, all assumed to
   be on contiguous scan lines starting at YStart and proceeding
   downward (used to describe a scan-converted polygon to the
   low-level hardware-dependent drawing code) */
typedef struct { int Length; int YStart; HLine * HLinePtr;} HLineList;
typedef struct { int Left, Top, Right, Bottom; } Rect;
/* Structure describing one face of an object (one polygon) */
typedef struct { int * VertNums; int NumVerts; int Color; }  Face;
typedef struct { double RotateX, RotateY, RotateZ; } RotateControl;
typedef struct { Fixedpoint MoveX, MoveY, MoveZ, MinX, MinY, MinZ,
   MaxX, MaxY, MaxZ; } MoveControl;
/* Fields common to every object */
#define BASE_OBJECT                                              \
   void (*DrawFunc)();     /* draws object */                    \
   void (*RecalcFunc)();   /* prepares object for drawing */     \
   void (*MoveFunc)();     /* moves object */                    \
   int RecalcXform;        /* 1 to indicate need to recalc */    \
   Rect EraseRect[2];      /* rectangle to erase in each page */
/* Basic object */
typedef struct { BASE_OBJECT } Object;
/* Structure describing a polygon-based object */
typedef struct {
   BASE_OBJECT
   int RDelayCount, RDelayCountBase; /* controls rotation speed */
   int MDelayCount, MDelayCountBase; /* controls movement speed */
   Xform XformToWorld;        /* transform from object->world space */
   Xform XformToView;         /* transform from object->view space */
   RotateControl Rotate;      /* controls rotation change over time */
   MoveControl Move;          /* controls object movement over time */
   int NumVerts;              /* # vertices in VertexList */
   Point3 * VertexList;       /* untransformed vertices */
   Point3 * XformedVertexList;   /* transformed into view space */
   Point3 * ProjectedVertexList; /* projected into screen space */
   Point * ScreenVertexList;     /* converted to screen coordinates */
   int NumFaces;              /* # of faces in object */
   Face * FaceList;           /* pointer to face info */
} PObject;

extern void XformVec(Xform, Fixedpoint *, Fixedpoint *);
extern void ConcatXforms(Xform, Xform, Xform);
extern int FillConvexPolygon(PointListHeader *, int, int, int);
extern void Set320x240Mode(void);
extern void ShowPage(unsigned int);
extern void FillRectangleX(int, int, int, int, unsigned int, int);
extern void XformAndProjectPObject(PObject *);
extern void DrawPObject(PObject *);
extern void AppendRotationX(Xform, double);
extern void AppendRotationY(Xform, double);
extern void AppendRotationZ(Xform, double);
extern near Fixedpoint FixedMul(Fixedpoint, Fixedpoint);
extern near Fixedpoint FixedDiv(Fixedpoint, Fixedpoint);
extern void InitializeFixedPoint(void);
extern void RotateAndMovePObject(PObject *);
extern void InitializeCubes(void);
extern int DisplayedPage, NonDisplayedPage, RecalcAllXforms;
extern int NumObjects;
extern Xform WorldViewXform;
extern Object *ObjectList[];
extern Point3 CubeVerts[];