/*
    None of this code has been made by me and just collected those snippets from many sources 
    across the internet. I haven't saved any of the original author names and all the credits 
    should go to them.

    HPlass (hermann.plass@gmail.com) - 2020
*/


/*
 * ████████╗██████╗  █████╗ ███╗   ██╗███████╗██████╗  ██████╗ ███████╗███████╗
 * ╚══██╔══╝██╔══██╗██╔══██╗████╗  ██║██╔════╝██╔══██╗██╔═══██╗██╔════╝██╔════╝
 *    ██║   ██████╔╝███████║██╔██╗ ██║███████╗██████╔╝██║   ██║███████╗█████╗
 *    ██║   ██╔══██╗██╔══██║██║╚██╗██║╚════██║██╔═══╝ ██║   ██║╚════██║██╔══╝
 *    ██║   ██║  ██║██║  ██║██║ ╚████║███████║██║     ╚██████╔╝███████║███████╗
 *    ╚═╝   ╚═╝  ╚═╝╚═╝  ╚═╝╚═╝  ╚═══╝╚══════╝╚═╝      ╚═════╝ ╚══════╝╚══════╝
 */

mat2 transpose(mat2 inMatrix) {
    vec2 i0 = inMatrix[0];
    vec2 i1 = inMatrix[1];

    mat2 outMatrix;
    outMatrix[0] = vec2(i0.x, i1.x);
    outMatrix[1] = vec2(i0.y, i1.y);

    return outMatrix;
}

mat3 transpose(mat3 inMatrix) {
    vec3 i0 = inMatrix[0];
    vec3 i1 = inMatrix[1];
    vec3 i2 = inMatrix[2];


    mat3 outMatrix;
  	outMatrix[0] = vec3(i0.x, i1.x, i2.x);
    outMatrix[1] = vec3(i0.y, i1.y, i2.y);
    outMatrix[2] = vec3(i0.z, i1.z, i2.z);

    return outMatrix;
}

mat4 transpose(mat4 inMatrix) {
    highp vec4 i0 = inMatrix[0];
    highp vec4 i1 = inMatrix[1];
    highp vec4 i2 = inMatrix[2];
    highp vec4 i3 = inMatrix[3];

    mat4 outMatrix;
    outMatrix[0] = vec4(i0.x, i1.x, i2.x, i3.x);
    outMatrix[1] = vec4(i0.y, i1.y, i2.y, i3.y);
    outMatrix[2] = vec4(i0.z, i1.z, i2.z, i3.z);
    outMatrix[3] = vec4(i0.w, i1.w, i2.w, i3.w);

    return outMatrix;
}


/*
 * ██╗███╗   ██╗██╗   ██╗███████╗██████╗ ███████╗███████╗
 * ██║████╗  ██║██║   ██║██╔════╝██╔══██╗██╔════╝██╔════╝
 * ██║██╔██╗ ██║██║   ██║█████╗  ██████╔╝███████╗█████╗
 * ██║██║╚██╗██║╚██╗ ██╔╝██╔══╝  ██╔══██╗╚════██║██╔══╝
 * ██║██║ ╚████║ ╚████╔╝ ███████╗██║  ██║███████║███████╗
 * ╚═╝╚═╝  ╚═══╝  ╚═══╝  ╚══════╝╚═╝  ╚═╝╚══════╝╚══════╝
 */

float inverse(float m) {
  return 1.0 / m;
}

mat2 inverse(mat2 m) {
 float det = (m[0][0]*m[1][1] - m[0][1]*m[1][0]);
  return mat2(m[1][1],-m[0][1],
             -m[1][0], m[0][0]) / det;
}

mat3 inverse(mat3 m) {
  float a00 = m[0][0], a01 = m[0][1], a02 = m[0][2];
  float a10 = m[1][0], a11 = m[1][1], a12 = m[1][2];
  float a20 = m[2][0], a21 = m[2][1], a22 = m[2][2];

  float b01 = a22 * a11 - a12 * a21;
  float b11 = -a22 * a10 + a12 * a20;
  float b21 = a21 * a10 - a11 * a20;

  float det = a00 * b01 + a01 * b11 + a02 * b21;

  return mat3(b01, (-a22 * a01 + a02 * a21), (a12 * a01 - a02 * a11),
              b11, (a22 * a00 - a02 * a20), (-a12 * a00 + a02 * a10),
              b21, (-a21 * a00 + a01 * a20), (a11 * a00 - a01 * a10)) / det;
}

mat4 inverse(mat4 m) {
  float
      a00 = m[0][0], a01 = m[0][1], a02 = m[0][2], a03 = m[0][3],
      a10 = m[1][0], a11 = m[1][1], a12 = m[1][2], a13 = m[1][3],
      a20 = m[2][0], a21 = m[2][1], a22 = m[2][2], a23 = m[2][3],
      a30 = m[3][0], a31 = m[3][1], a32 = m[3][2], a33 = m[3][3],

      b00 = a00 * a11 - a01 * a10,
      b01 = a00 * a12 - a02 * a10,
      b02 = a00 * a13 - a03 * a10,
      b03 = a01 * a12 - a02 * a11,
      b04 = a01 * a13 - a03 * a11,
      b05 = a02 * a13 - a03 * a12,
      b06 = a20 * a31 - a21 * a30,
      b07 = a20 * a32 - a22 * a30,
      b08 = a20 * a33 - a23 * a30,
      b09 = a21 * a32 - a22 * a31,
      b10 = a21 * a33 - a23 * a31,
      b11 = a22 * a33 - a23 * a32,

      det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;

  return mat4(
      a11 * b11 - a12 * b10 + a13 * b09,
      a02 * b10 - a01 * b11 - a03 * b09,
      a31 * b05 - a32 * b04 + a33 * b03,
      a22 * b04 - a21 * b05 - a23 * b03,
      a12 * b08 - a10 * b11 - a13 * b07,
      a00 * b11 - a02 * b08 + a03 * b07,
      a32 * b02 - a30 * b05 - a33 * b01,
      a20 * b05 - a22 * b02 + a23 * b01,
      a10 * b10 - a11 * b08 + a13 * b06,
      a01 * b08 - a00 * b10 - a03 * b06,
      a30 * b04 - a31 * b02 + a33 * b00,
      a21 * b02 - a20 * b04 - a23 * b00,
      a11 * b07 - a10 * b09 - a12 * b06,
      a00 * b09 - a01 * b07 + a02 * b06,
      a31 * b01 - a30 * b03 - a32 * b00,
      a20 * b03 - a21 * b01 + a22 * b00) / det;
}


/*
 * ██████╗  ██████╗ ████████╗ █████╗ ████████╗███████╗
 * ██╔══██╗██╔═══██╗╚══██╔══╝██╔══██╗╚══██╔══╝██╔════╝
 * ██████╔╝██║   ██║   ██║   ███████║   ██║   █████╗
 * ██╔══██╗██║   ██║   ██║   ██╔══██║   ██║   ██╔══╝
 * ██║  ██║╚██████╔╝   ██║   ██║  ██║   ██║   ███████╗
 * ╚═╝  ╚═╝ ╚═════╝    ╚═╝   ╚═╝  ╚═╝   ╚═╝   ╚══════╝
 */
 
vec4 rotateX (vec4 vertex, float degrees){
    float alpha = degrees * PI / 180.0;
    float sina = sin(alpha);
	float cosa = sin(alpha);
    mat2 m = mat2(cosa, -sina, sina, cosa);
    return vec4( m * vertex.yz, vertex.xw).zyxw;
}

vec4 rotateY (vec4 vertex, float degrees){
    float alpha = degrees * PI / 180.0;
    float sina = sin(alpha);
	float cosa = sin(alpha);
    mat2 m = mat2(cosa, -sina, sina, cosa);
    return vec4( m * vertex.xz, vertex.yw).xzyw;
}

vec4 rotateZ (vec4 vertex, float degrees){
    float alpha = degrees * PI / 180.0;
    float sina = sin(alpha);
	float cosa = sin(alpha);
    mat2 m = mat2(cosa, -sina, sina, cosa);
    return vec4( m * vertex.xy, vertex.zw).xyzw;
}