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52-03.md
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------------------------ --------------------------------- --------------------
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[Previous](52-02.html) [Table of Contents](index.html) [Next](52-04.html)
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------------------------ --------------------------------- --------------------
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**LISTING 52.3 L52-3.C**
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/* Routines to perform incremental rotations around the three axes. */
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#include <math.h>
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#include “polygon.h”
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/* Concatenate a rotation by Angle around the X axis to transformation in
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XformToChange, placing the result back into XformToChange. */
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void AppendRotationX(Xform XformToChange, double Angle)
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{
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Fixedpoint Temp10, Temp11, Temp12, Temp20, Temp21, Temp22;
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Fixedpoint CosTemp = DOUBLE_TO_FIXED(cos(Angle));
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Fixedpoint SinTemp = DOUBLE_TO_FIXED(sin(Angle));
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/* Calculate the new values of the six affected matrix entries */
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Temp10 = FixedMul(CosTemp, XformToChange[1][0]) +
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FixedMul(-SinTemp, XformToChange[2][0]);
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Temp11 = FixedMul(CosTemp, XformToChange[1][1]) +
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FixedMul(-SinTemp, XformToChange[2][1]);
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Temp12 = FixedMul(CosTemp, XformToChange[1][2]) +
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FixedMul(-SinTemp, XformToChange[2][2]);
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Temp20 = FixedMul(SinTemp, XformToChange[1][0]) +
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FixedMul(CosTemp, XformToChange[2][0]);
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Temp21 = FixedMul(SinTemp, XformToChange[1][1]) +
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FixedMul(CosTemp, XformToChange[2][1]);
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Temp22 = FixedMul(SinTemp, XformToChange[1][2]) +
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FixedMul(CosTemp, XformToChange[2][2]);
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/* Put the results back into XformToChange */
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XformToChange[1][0] = Temp10; XformToChange[1][1] = Temp11;
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XformToChange[1][2] = Temp12; XformToChange[2][0] = Temp20;
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XformToChange[2][1] = Temp21; XformToChange[2][2] = Temp22;
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}
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/* Concatenate a rotation by Angle around the Y axis to transformation in
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XformToChange, placing the result back into XformToChange. */
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void AppendRotationY(Xform XformToChange, double Angle)
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{
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Fixedpoint Temp00, Temp01, Temp02, Temp20, Temp21, Temp22;
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Fixedpoint CosTemp = DOUBLE_TO_FIXED(cos(Angle));
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Fixedpoint SinTemp = DOUBLE_TO_FIXED(sin(Angle));
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/* Calculate the new values of the six affected matrix entries */
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Temp00 = FixedMul(CosTemp, XformToChange[0][0]) +
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FixedMul(SinTemp, XformToChange[2][0]);
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Temp01 = FixedMul(CosTemp, XformToChange[0][1]) +
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FixedMul(SinTemp, XformToChange[2][1]);
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Temp02 = FixedMul(CosTemp, XformToChange[0][2]) +
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FixedMul(SinTemp, XformToChange[2][2]);
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Temp20 = FixedMul(-SinTemp, XformToChange[0][0]) +
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FixedMul( CosTemp, XformToChange[2][0]);
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Temp21 = FixedMul(-SinTemp, XformToChange[0][1]) +
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FixedMul(CosTemp, XformToChange[2][1]);
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Temp22 = FixedMul(-SinTemp, XformToChange[0][2]) +
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FixedMul(CosTemp, XformToChange[2][2]);
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/* Put the results back into XformToChange */
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XformToChange[0][0] = Temp00; XformToChange[0][1] = Temp01;
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XformToChange[0][2] = Temp02; XformToChange[2][0] = Temp20;
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XformToChange[2][1] = Temp21; XformToChange[2][2] = Temp22;
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}
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/* Concatenate a rotation by Angle around the Z axis to transformation in
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XformToChange, placing the result back into XformToChange. */
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void AppendRotationZ(Xform XformToChange, double Angle)
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{
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Fixedpoint Temp00, Temp01, Temp02, Temp10, Temp11, Temp12;
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Fixedpoint CosTemp = DOUBLE_TO_FIXED(cos(Angle));
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Fixedpoint SinTemp = DOUBLE_TO_FIXED(sin(Angle));
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/* Calculate the new values of the six affected matrix entries */
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Temp00 = FixedMul(CosTemp, XformToChange[0][0]) +
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FixedMul(-SinTemp, XformToChange[1][0]);
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Temp01 = FixedMul(CosTemp, XformToChange[0][1]) +
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FixedMul(-SinTemp, XformToChange[1][1]);
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Temp02 = FixedMul(CosTemp, XformToChange[0][2]) +
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FixedMul(-SinTemp, XformToChange[1][2]);
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Temp10 = FixedMul(SinTemp, XformToChange[0][0]) +
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FixedMul(CosTemp, XformToChange[1][0]);
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Temp11 = FixedMul(SinTemp, XformToChange[0][1]) +
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FixedMul(CosTemp, XformToChange[1][1]);
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Temp12 = FixedMul(SinTemp, XformToChange[0][2]) +
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FixedMul(CosTemp, XformToChange[1][2]);
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/* Put the results back into XformToChange */
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XformToChange[0][0] = Temp00; XformToChange[0][1] = Temp01;
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XformToChange[0][2] = Temp02; XformToChange[1][0] = Temp10;
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XformToChange[1][1] = Temp11; XformToChange[1][2] = Temp12;
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}
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**LISTING 52.4 L52-4.C**
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/* Fixed point matrix arithmetic functions. */
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#include “polygon.h”
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/* Matrix multiplies Xform by SourceVec, and stores the result in DestVec.
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Multiplies a 4x4 matrix times a 4x1 matrix; the result is a 4x1 matrix. Cheats
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by assuming the W coord is 1 and bottom row of matrix is 0 0 0 1, and doesn't
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bother to set the W coordinate of the destination. */
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void XformVec(Xform WorkingXform, Fixedpoint *SourceVec,
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Fixedpoint *DestVec)
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{
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int i;
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for (i=0; i<3; i++)
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DestVec[i] = FixedMul(WorkingXform[i][0], SourceVec[0]) +
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FixedMul(WorkingXform[i][1], SourceVec[1]) +
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FixedMul(WorkingXform[i][2], SourceVec[2]) +
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WorkingXform[i][3]; /* no need to multiply by W = 1 */
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}
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/* Matrix multiplies SourceXform1 by SourceXform2 and stores result in
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DestXform. Multiplies a 4x4 matrix times a 4x4 matrix; result is a 4x4 matrix.
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Cheats by assuming bottom row of each matrix is 0 0 0 1, and doesn't bother
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to set the bottom row of the destination. */
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void ConcatXforms(Xform SourceXform1, Xform SourceXform2,
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Xform DestXform)
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{
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int i, j;
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for (i=0; i<3; i++) {
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for (j=0; j<4; j++)
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DestXform[i][j] =
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FixedMul(SourceXform1[i][0], SourceXform2[0][j]) +
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FixedMul(SourceXform1[i][1], SourceXform2[1][j]) +
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FixedMul(SourceXform1[i][2], SourceXform2[2][j]) +
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SourceXform1[i][3];
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}
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}
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**LISTING 52.5 L52-5.C**
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/* Set up basic data that needs to be in fixed point, to avoid data
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definition hassles. */
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#include “polygon.h”
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/* All vertices in the basic cube */
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static IntPoint3 IntCubeVerts[NUM_CUBE_VERTS] = {
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{15,15,15},{15,15,-15},{15,-15,15},{15,-15,-15},
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{-15,15,15},{-15,15,-15},{-15,-15,15},{-15,-15,-15} };
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/* Transformation from world space into view space (no transformation,
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currently) */
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static int IntWorldViewXform[3][4] = {
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{1,0,0,0}, {0,1,0,0}, {0,0,1,0}};
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void InitializeFixedPoint()
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{
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int i, j;
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for (i=0; i<3; i++)
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for (j=0; j<4; j++)
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WorldViewXform[i][j] = INT_TO_FIXED(IntWorldViewXform[i][j]);
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for (i=0; i<NUM_CUBE_VERTS; i++) {
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CubeVerts[i].X = INT_TO_FIXED(IntCubeVerts[i].X);
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CubeVerts[i].Y = INT_TO_FIXED(IntCubeVerts[i].Y);
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CubeVerts[i].Z = INT_TO_FIXED(IntCubeVerts[i].Z);
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}
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}
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------------------------ --------------------------------- --------------------
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[Previous](52-02.html) [Table of Contents](index.html) [Next](52-04.html)
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------------------------ --------------------------------- --------------------
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* * * * *
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Graphics Programming Black Book © 2001 Michael Abrash
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