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matrix.cpp

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#include "StdAfx.h"
#include "matrix.h"

#define EPSILON 0.000001

// (mat11, mat12, mat13, mat14)     (mat0, mat4, mat8,  mat12)
// (mat21, mat22, mat23, mat24)  =  (mat1, mat5, mat9,  mat13)
// (mat31, mat32, mat33, mat34)     (mat2, mat6, mat10, mat14)
// (mat41, mat42, mat43, mat44)     (mat3, mat7, mat11, mat15)

Matrix4x4::Matrix4x4() {
        
        for(int i = 0; i < 4; i++) {
                for(int j=0;j < 4; j++) {
                        mat[i][j] = 0.0;
                }
        }
}

Matrix4x4::Matrix4x4(Matrix4x4 *matrix) {
        for(int i =0;i <4;i++)
                for(int j=0;j <4; j++)
                        mat[i][j] = matrix->mat[i][j];
}

Matrix4x4::Matrix4x4(float m11, float m12, float m13, float m14,
                                     float m21, float m22, float m23, float m24,
                                         float m31, float m32, float m33, float m34,
                                         float m41, float m42, float m43, float m44) {
        
        mat[0][0] = m11;
        mat[0][1] = m21;
        mat[0][2] = m31;
        mat[0][3] = m41;
        mat[1][0] = m12;
        mat[1][1] = m22;
        mat[1][2] = m32;
        mat[1][3] = m42;
        mat[2][0] = m13;
        mat[2][1] = m23;
        mat[2][2] = m33;
        mat[2][3] = m43;
        mat[3][0] = m14;
        mat[3][1] = m24;
        mat[3][2] = m34;
        mat[3][3] = m44;

}

void
Matrix4x4::identity() {
        for(int i =0; i < 4; i++)
                for(int j= 0;j < 4; j++)
                        mat[i][j] = 0.0;
        mat[0][0] = 1.0;
        mat[1][1] = 1.0;
        mat[2][2] = 1.0;
        mat[3][3] = 1.0;
}

const VECTOR
Matrix4x4::operator * (const VECTOR& vec) const {
        VECTOR result;
        result.x = mat[0][0]*vec.x + mat[1][0]*vec.y + mat[2][0] * vec.z + mat[3][0];
        result.y = mat[0][1]*vec.x + mat[1][1]*vec.y + mat[2][1] * vec.z + mat[3][1];
        result.z = mat[0][2]*vec.x + mat[1][2]*vec.y + mat[2][2] * vec.z + mat[3][2];
        return result;
}

void
Matrix4x4::transpose() {
        float tmp;
        for(int i = 0; i < 4; i++) {
                for(int j = 0; j < 4; j++) {
                        tmp = mat[i][j];
                        mat[i][j] = mat[j][i];
                        mat[j][i] = tmp;
                }
        }
}

/*
 * A function for creating a rotation matrix that rotates a vector called
 * "from" into another vector called "to".
 * Authors: Tomas Möller, John Hughes 1999
 */

void
Matrix4x4::rotation(VECTOR from, VECTOR to) {
        VECTOR v;
        float e, h, f;
        
        v = from.cross(to);
        e = from.dot(to);
        f = (e < 0)? -e:e;
        if (f > 1.0 - EPSILON) {
                VECTOR x;

                x.x = (from.x > 0.0) ? from.x : -from.x;
                x.y = (from.y > 0.0) ? from.y : -from.y;
                x.z = (from.z > 0.0) ? from.z : -from.z;

                if(x.x < x.y) {
                        if(x.x < x.z) {
                                x.x = 1.0;
                                x.y = x.z = 0.0;
                        } else {
                                x.z = 1.0; x.x = x.y = 0.0;
                        }
                }
                else {
                        if(x.y < x.z) {
                                x.y = 1.0; x.x = x.z = 0.0;
                        } else {
                                x.z = 1.0; x.x = x.y = 0.0;
                        }
                }

                VECTOR u = x - from;
                VECTOR w = x - to;

                float c1 = 2.0 / u.dot(u);
                float c2 = 2.0 / w.dot(w);
                float c3 = c1 * c2 * u.dot(w);

                float u_h[3];
                float w_h[3];

                u_h[0] = u.x;
                u_h[1] = u.y;
                u_h[2] = u.z;

                w_h[0] = w.x;
                w_h[1] = w.y;
                w_h[2] = w.z;


                for(int i = 0; i < 3; i++) {
                        for(int j = 0; j < 3; j++) {
                                mat[i][j] = -c1 * u_h[i] * u_h[j] - c2 * w_h[i]*w_h[j] + c3 * w_h[i] * u_h[j];
                        }
                        mat[i][i] += 1.0;
                }
        }
        else
        {
                h = (1.0 - e)/(v.dot(v));
    
                mat[0][0] = e + h*v.x * v.x; 
                mat[0][1] = h*v.x*v.y - v.z;     
                mat[0][2] = h*v.x*v.z + v.y;
                mat[0][3] = 0.0f;

                mat[1][0] = h*v.x*v.y + v.z;  
                mat[1][1] = e + h * v.y * v.y; 
                mat[1][2] = h*v.y*v.z - v.x;
                mat[1][3] = 0.0f;

                mat[2][0] = h*v.x*v.z - v.y;  
                mat[2][1] = h*v.y*v.z + v.x;     
                mat[2][2] = e + h*v.z * v.z;
                mat[2][3] = 0.0f;

                mat[3][0] = 0.0f;
                mat[3][1] = 0.0f;
                mat[3][2] = 0.0f;
                mat[3][3] = 1.0f;
        }
}

void
Matrix4x4::rotateX(float alpha) {
        float cosa = cos(alpha);
        float sina = sin(alpha);

        mat[0][0] = 1.0f;
        mat[0][1] = 0.0f;
        mat[0][2] = 0.0f;
        mat[0][3] = 0.0f;

        mat[1][0] = 0.0f;
        mat[1][1] = cosa;
        mat[1][2] = sina;
        mat[1][3] = 0.0f;

        mat[2][0] = 1.0f;
        mat[2][1] = -sina;
        mat[2][2] = cosa;
        mat[2][3] = 0.0f;

        mat[3][0] = 0.0f;
        mat[3][1] = 0.0f;
        mat[3][2] = 0.0f;
        mat[3][3] = 1.0f;
}

void
Matrix4x4::rotateY(float alpha) {
        float cosa = cos(alpha);
        float sina = sin(alpha);

        mat[0][0] = cosa;
        mat[0][1] = 0.0f;
        mat[0][2] = -sina;
        mat[0][3] = 0.0f;

        mat[1][0] = 0.0f;
        mat[1][1] = 1.0f;
        mat[1][2] = 0.0f;
        mat[1][3] = 0.0f;

        mat[2][0] = sina;
        mat[2][1] = 0.0f;
        mat[2][2] = cosa;
        mat[2][3] = 0.0f;

        mat[3][0] = 0.0f;
        mat[3][1] = 0.0f;
        mat[3][2] = 0.0f;
        mat[3][3] = 1.0f;
}

void
Matrix4x4::rotateZ(float alpha) {
        float cosa = cos(alpha);
        float sina = sin(alpha);

        mat[0][0] = cosa;
        mat[0][1] = sina;
        mat[0][2] = 0.0f;
        mat[0][3] = 0.0f;

        mat[1][0] = -sina;
        mat[1][1] = cosa;
        mat[1][2] = 0.0f;
        mat[1][3] = 0.0f;

        mat[2][0] = 0.0f;
        mat[2][1] = 0.0f;
        mat[2][2] = 1.0f;
        mat[2][3] = 0.0f;

        mat[3][0] = 0.0f;
        mat[3][1] = 0.0f;
        mat[3][2] = 0.0f;
        mat[3][3] = 1.0f;
}

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