/**
 * Apply a transform to the given AABB.
 *
 * @param starting the AABB transformation will be applied to
 * @param transformMatrix the transform to be applied to all vertices of the AABB, given as a 4x4 matrix
 * @return thetransformed AABB
 */
AABB transformAABB(const AABB starting, const mat4 transformMatrix) {
    vec4 v[8] = {
        transformMatrix * vec4(starting.position.x, starting.position.y, starting.position.z, 1),
        transformMatrix * vec4(starting.position.x, starting.position.y, starting.position.z + starting.dimensions.z, 1),
        transformMatrix * vec4(starting.position.x, starting.position.y + starting.dimensions.y, starting.position.z, 1),
        transformMatrix * vec4(starting.position.x, starting.position.y + starting.dimensions.y, starting.position.z + starting.dimensions.z, 1),
        transformMatrix * vec4(starting.position.x + starting.dimensions.x, starting.position.y, starting.position.z, 1),
        transformMatrix * vec4(starting.position.x + starting.dimensions.x, starting.position.y, starting.position.z + starting.dimensions.z, 1),
        transformMatrix * vec4(starting.position.x + starting.dimensions.x, starting.position.y + starting.dimensions.y, starting.position.z, 1),
        transformMatrix * vec4(starting.position.x + starting.dimensions.x, starting.position.y + starting.dimensions.y, starting.position.z + starting.dimensions.z, 1),
    };

    float maxX = minusInfinity, maxY = minusInfinity, maxZ=minusInfinity, minX=infinity, minY=infinity, minZ=infinity;

    for (uint i = 0; i < 8; ++i) {
        maxX = (v[i].x > maxX) ? v[i].x : maxX;
        maxY = (v[i].y > maxY) ? v[i].y : maxY;
        maxZ = (v[i].z > maxZ) ? v[i].z : maxZ;
        minX = (v[i].x < minX) ? v[i].x : minX;
        minY = (v[i].y < minY) ? v[i].y : minY;
        minZ = (v[i].z < minZ) ? v[i].z : minZ;
    }

    return AABB(vec4(minX, minY, minZ, 1), vec4(maxX-minX, maxY-minY, maxZ-minZ, 0));
}