Program To Implement 3D Rotation About An Arbitrary Axis

#include<iostream.h>

#include<math.h>

#include<conio.h>

 //using namespace std;

 typedef struct {

    float x;

    float y;

    float z;

}Point;

Point points;

 float rotationMatrix[4][4];

float inputMatrix[4][1] = {0.0, 0.0, 0.0, 0.0};

float outputMatrix[4][1] = {0.0, 0.0, 0.0, 0.0};

 void showPoint(){

    cout<<"("<<outputMatrix[0][0]<<","<<outputMatrix[1][0]<<","<<outputMatrix[2][0]<<")"<<endl;

}

 void multiplyMatrix()

{

    for(int i = 0; i < 4; i++ ){

            for(int j = 0; j < 1; j++){

                outputMatrix[i][j] = 0;

                for(int k = 0; k < 4; k++){

                        outputMatrix[i][j] += rotationMatrix[i][k] * inputMatrix[k][j];

                }

            }

    }

}

void setUpRotationMatrix(float angle, float u, float v, float w)

{

    float L = (u*u + v * v + w * w);

    angle = angle * M_PI / 180.0; //converting to radian value

    float u2 = u * u;

    float v2 = v * v;

    float w2 = w * w;

    rotationMatrix[0][0] = (u2 + (v2 + w2) * cos(angle)) / L;

    rotationMatrix[0][1] = (u * v * (1 - cos(angle)) - w * sqrt(L) * sin(angle)) / L;

    rotationMatrix[0][2] = (u * w * (1 - cos(angle)) + v * sqrt(L) * sin(angle)) / L;

    rotationMatrix[0][3] = 0.0;

    rotationMatrix[1][0] = (u * v * (1 - cos(angle)) + w * sqrt(L) * sin(angle)) / L;

    rotationMatrix[1][1] = (v2 + (u2 + w2) * cos(angle)) / L;

    rotationMatrix[1][2] = (v * w * (1 - cos(angle)) - u * sqrt(L) * sin(angle)) / L;

    rotationMatrix[1][3] = 0.0;

    rotationMatrix[2][0] = (u * w * (1 - cos(angle)) - v * sqrt(L) * sin(angle)) / L;

    rotationMatrix[2][1] = (v * w * (1 - cos(angle)) + u * sqrt(L) * sin(angle)) / L;

    rotationMatrix[2][2] = (w2 + (u2 + v2) * cos(angle)) / L;

    rotationMatrix[2][3] = 0.0;

    rotationMatrix[3][0] = 0.0;

    rotationMatrix[3][1] = 0.0;

    rotationMatrix[3][2] = 0.0;

    rotationMatrix[3][3] = 1.0;

}

int main()

{

    float angle;

    float u, v, w;

    clrscr();

    cout<<" PROGRAM FOR THE ROTATION \n";

    cout<<" Enter the initial point you want to transform:";

    cin>>points.x>>points.y>>points.z;

    inputMatrix[0][0] = points.x;

    inputMatrix[1][0] = points.y;

    inputMatrix[2][0] = points.z;

    inputMatrix[3][0] = 1.0;

    cout<<" Enter axis vector: ";

    cin>>u>>v>>w;

    cout<<" Enter the rotating angle in degree: ";

    cin>>angle;

    setUpRotationMatrix(angle, u, v, w);

    multiplyMatrix();

    showPoint();

    return 0;

}