LISTING 52.3 L52-3.C

/* 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 52.4 L52-4.C

/* 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 52.5 L52-5.C

/* 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);
   }
}