Matrix operations for HLSL

Matrix.hlsl

#ifndef __MATRIX_INCLUDED__
#define __MATRIX_INCLUDED__

#define IDENTITY_MATRIX float4x4(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1)

float4x4 inverse(float4x4 m) {
    float n11 = m[0][0], n12 = m[1][0], n13 = m[2][0], n14 = m[3][0];
    float n21 = m[0][1], n22 = m[1][1], n23 = m[2][1], n24 = m[3][1];
    float n31 = m[0][2], n32 = m[1][2], n33 = m[2][2], n34 = m[3][2];
    float n41 = m[0][3], n42 = m[1][3], n43 = m[2][3], n44 = m[3][3];

    float t11 = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44;
    float t12 = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44;
    float t13 = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44;
    float t14 = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34;

    float det = n11 * t11 + n21 * t12 + n31 * t13 + n41 * t14;
    float idet = 1.0f / det;

    float4x4 ret;

    ret[0][0] = t11 * idet;
    ret[0][1] = (n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44) * idet;
    ret[0][2] = (n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44) * idet;
    ret[0][3] = (n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43) * idet;

    ret[1][0] = t12 * idet;
    ret[1][1] = (n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44) * idet;
    ret[1][2] = (n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44) * idet;
    ret[1][3] = (n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43) * idet;

    ret[2][0] = t13 * idet;
    ret[2][1] = (n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44) * idet;
    ret[2][2] = (n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44) * idet;
    ret[2][3] = (n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43) * idet;

    ret[3][0] = t14 * idet;
    ret[3][1] = (n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34) * idet;
    ret[3][2] = (n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34) * idet;
    ret[3][3] = (n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33) * idet;

    return ret;
}

// http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/
float4 matrix_to_quaternion(float4x4 m)
{
    float tr = m[0][0] + m[1][1] + m[2][2];
    float4 q = float4(0, 0, 0, 0);

    if (tr > 0)
    {
        float s = sqrt(tr + 1.0) * 2; // S=4*qw 
        q.w = 0.25 * s;
        q.x = (m[2][1] - m[1][2]) / s;
        q.y = (m[0][2] - m[2][0]) / s;
        q.z = (m[1][0] - m[0][1]) / s;
    }
    else if ((m[0][0] > m[1][1]) && (m[0][0] > m[2][2]))
    {
        float s = sqrt(1.0 + m[0][0] - m[1][1] - m[2][2]) * 2; // S=4*qx 
        q.w = (m[2][1] - m[1][2]) / s;
        q.x = 0.25 * s;
        q.y = (m[0][1] + m[1][0]) / s;
        q.z = (m[0][2] + m[2][0]) / s;
    }
    else if (m[1][1] > m[2][2])
    {
        float s = sqrt(1.0 + m[1][1] - m[0][0] - m[2][2]) * 2; // S=4*qy
        q.w = (m[0][2] - m[2][0]) / s;
        q.x = (m[0][1] + m[1][0]) / s;
        q.y = 0.25 * s;
        q.z = (m[1][2] + m[2][1]) / s;
    }
    else
    {
        float s = sqrt(1.0 + m[2][2] - m[0][0] - m[1][1]) * 2; // S=4*qz
        q.w = (m[1][0] - m[0][1]) / s;
        q.x = (m[0][2] + m[2][0]) / s;
        q.y = (m[1][2] + m[2][1]) / s;
        q.z = 0.25 * s;
    }

    return q;
}

float4x4 m_scale(float4x4 m, float3 v)
{
    float x = v.x, y = v.y, z = v.z;

    m[0][0] *= x; m[1][0] *= y; m[2][0] *= z;
    m[0][1] *= x; m[1][1] *= y; m[2][1] *= z;
    m[0][2] *= x; m[1][2] *= y; m[2][2] *= z;
    m[0][3] *= x; m[1][3] *= y; m[2][3] *= z;

    return m;
}

float4x4 quaternion_to_matrix(float4 quat)
{
    float4x4 m = float4x4(float4(0, 0, 0, 0), float4(0, 0, 0, 0), float4(0, 0, 0, 0), float4(0, 0, 0, 0));

    float x = quat.x, y = quat.y, z = quat.z, w = quat.w;
    float x2 = x + x, y2 = y + y, z2 = z + z;
    float xx = x * x2, xy = x * y2, xz = x * z2;
    float yy = y * y2, yz = y * z2, zz = z * z2;
    float wx = w * x2, wy = w * y2, wz = w * z2;

    m[0][0] = 1.0 - (yy + zz);
    m[0][1] = xy - wz;
    m[0][2] = xz + wy;

    m[1][0] = xy + wz;
    m[1][1] = 1.0 - (xx + zz);
    m[1][2] = yz - wx;

    m[2][0] = xz - wy;
    m[2][1] = yz + wx;
    m[2][2] = 1.0 - (xx + yy);

    m[3][3] = 1.0;

    return m;
}

float4x4 m_translate(float4x4 m, float3 v)
{
    float x = v.x, y = v.y, z = v.z;
    m[0][3] = x;
    m[1][3] = y;
    m[2][3] = z;
    return m;
}

float4x4 compose(float3 position, float4 quat, float3 scale)
{
    float4x4 m = quaternion_to_matrix(quat);
    m = m_scale(m, scale);
    m = m_translate(m, position);
    return m;
}

void decompose(in float4x4 m, out float3 position, out float4 rotation, out float3 scale)
{
    float sx = length(float3(m[0][0], m[0][1], m[0][2]));
    float sy = length(float3(m[1][0], m[1][1], m[1][2]));
    float sz = length(float3(m[2][0], m[2][1], m[2][2]));

    // if determine is negative, we need to invert one scale
    float det = determinant(m);
    if (det < 0) {
        sx = -sx;
    }

    position.x = m[3][0];
    position.y = m[3][1];
    position.z = m[3][2];

    // scale the rotation part

    float invSX = 1.0 / sx;
    float invSY = 1.0 / sy;
    float invSZ = 1.0 / sz;

    m[0][0] *= invSX;
    m[0][1] *= invSX;
    m[0][2] *= invSX;

    m[1][0] *= invSY;
    m[1][1] *= invSY;
    m[1][2] *= invSY;

    m[2][0] *= invSZ;
    m[2][1] *= invSZ;
    m[2][2] *= invSZ;

    rotation = matrix_to_quaternion(m);

    scale.x = sx;
    scale.y = sy;
    scale.z = sz;
}

float4x4 axis_matrix(float3 right, float3 up, float3 forward)
{
    float3 xaxis = right;
    float3 yaxis = up;
    float3 zaxis = forward;
    return float4x4(
		xaxis.x, yaxis.x, zaxis.x, 0,
		xaxis.y, yaxis.y, zaxis.y, 0,
		xaxis.z, yaxis.z, zaxis.z, 0,
		0, 0, 0, 1
	);
}

// http://stackoverflow.com/questions/349050/calculating-a-lookat-matrix
float4x4 look_at_matrix(float3 forward, float3 up)
{
    float3 xaxis = normalize(cross(forward, up));
    float3 yaxis = up;
    float3 zaxis = forward;
    return axis_matrix(xaxis, yaxis, zaxis);
}

float4x4 look_at_matrix(float3 at, float3 eye, float3 up)
{
    float3 zaxis = normalize(at - eye);
    float3 xaxis = normalize(cross(up, zaxis));
    float3 yaxis = cross(zaxis, xaxis);
    return axis_matrix(xaxis, yaxis, zaxis);
}

float4x4 extract_rotation_matrix(float4x4 m)
{
    float sx = length(float3(m[0][0], m[0][1], m[0][2]));
    float sy = length(float3(m[1][0], m[1][1], m[1][2]));
    float sz = length(float3(m[2][0], m[2][1], m[2][2]));

    // if determine is negative, we need to invert one scale
    float det = determinant(m);
    if (det < 0) {
        sx = -sx;
    }

    float invSX = 1.0 / sx;
    float invSY = 1.0 / sy;
    float invSZ = 1.0 / sz;

    m[0][0] *= invSX;
    m[0][1] *= invSX;
    m[0][2] *= invSX;
    m[0][3] = 0;

    m[1][0] *= invSY;
    m[1][1] *= invSY;
    m[1][2] *= invSY;
    m[1][3] = 0;

    m[2][0] *= invSZ;
    m[2][1] *= invSZ;
    m[2][2] *= invSZ;
    m[2][3] = 0;

    m[3][0] = 0;
    m[3][1] = 0;
    m[3][2] = 0;
    m[3][3] = 1;

    return m;
}

#endif // __MATRIX_INCLUDED__