libcruft-util/matrix.cpp

 /****************************************************************************
                              __         .__  .__  .__                  .___
   ___________ ___.__. _______/  |______  |  | |  | |__| ______ ____   __| _/
 _/ ___\_  __ <   |  |/  ___/\   __\__  \ |  | |  | |  |/  ___// __ \ / __ |
 \  \___|  | \/\___  |\___ \  |  |  / __ \|  |_|  |_|  |\___ \\  ___// /_/ |
  \___  >__|   / ____/____  > |__| (____  /____/____/__/____  >\___  >____ |
      \/       \/         \/            \/                  \/     \/     \/

  Copyright:
    Danny Robson, 2011
 *****************************************************************************/

#include "matrix.hpp"

#include "debug.hpp"

#include <cstring>

using namespace util;


void
matrix::scale (double x, double y, double z) {
    check_hard (is_affine ());
    values[0][0] *= x;
    values[1][1] *= y;
    values[2][2] *= z;
}


void
matrix::translate (double x, double y, double z) {
    check_hard (is_affine ());
    values[0][3] += x;
    values[1][3] += y;
    values[2][3] += z;
}


matrix
matrix::inverse (void) const {
    return matrix(*this).invert ();
}


matrix&
matrix::invert (void) {
    check_hard (is_affine ());

    // inv ([ M b ]  == [ inv(M) -inv(M).b ]
    //      [ 0 1 ])    [     0       1

    // Invert the 3x3 M
    double A = (values[1][1] * values[2][2] - values[1][2] * values[2][1]);
    double B = (values[1][2] * values[2][0] - values[1][0] * values[2][2]);
    double C = (values[1][0] * values[2][1] - values[1][1] * values[2][0]);

    double D = (values[0][2] * values[2][1] - values[0][1] * values[2][2]);
    double E = (values[0][0] * values[2][2] - values[0][2] * values[2][0]);
    double F = (values[2][0] * values[0][1] - values[0][0] * values[2][1]);

    double G = (values[0][1] * values[1][2] - values[0][2] * values[1][1]);
    double H = (values[0][2] * values[1][0] - values[0][0] * values[1][2]);
    double K = (values[0][0] * values[1][1] - values[0][1] * values[1][0]);

    double det = values[0][0] * A + values[0][1] * B + values[0][2] * C;
    check_neq (det, 0.0);

    values[0][0] = A / det;
    values[0][1] = D / det;
    values[0][2] = G / det;
    values[1][0] = B / det;
    values[1][1] = E / det;
    values[1][2] = H / det;
    values[2][0] = C / det;
    values[2][1] = F / det;
    values[2][2] = K / det;

    // Multiply the b
    double b0 = - values[0][0] * values[0][3] - values[0][1] * values[1][3] - values[0][2] * values[2][3];
    double b1 = - values[1][0] * values[0][3] - values[1][1] * values[1][3] - values[1][2] * values[2][3];
    double b2 = - values[2][0] * values[0][3] - values[2][1] * values[1][3] - values[2][2] * values[2][3];

    values[0][3] = b0;
    values[1][3] = b1;
    values[2][3] = b2;

    return *this;
}


matrix
matrix::operator* (const matrix &rhs) const {
    matrix m;
    memset (m.values, 0, sizeof (m.values));

    for (unsigned i = 0; i < 4; ++i)
        for (unsigned j = 0; j < 4; ++j)
            for (unsigned k = 0; k < 4; ++k)
                m.values[i][j] += values[i][k] * rhs.values[k][j];

    return m;
}


util::point
matrix::to_local (const util::point &p) const {
    check_soft (is_affine ());

    return { p.x * values[0][0] + p.y * values[0][1] + p.z * values[0][2]  + values[0][3],
             p.x * values[1][0] + p.y * values[1][1] + p.z * values[1][2]  + values[1][3],
             p.x * values[2][0] + p.y * values[2][1] + p.z * values[2][2]  + values[2][3] };
}


util::point
matrix::to_global (const util::point &p) const {
    return inverse ().to_local (p);
}



bool
matrix::is_affine (void) const {
    return exactly_equal (values[3][0], 0.0) &&
           exactly_equal (values[3][1], 0.0) &&
           exactly_equal (values[3][2], 0.0) &&
           exactly_equal (values[3][3], 1.0);
}


const matrix
matrix::IDENTITY = { { { 1.0, 0.0, 0.0, 0.0 },
                       { 0.0, 1.0, 0.0, 0.0 },
                       { 0.0, 0.0, 1.0, 0.0 },
                       { 0.0, 0.0, 0.0, 1.0 } } };


const matrix
matrix::ZEROES = { { { 0.0, 0.0, 0.0, 0.0 },
                     { 0.0, 0.0, 0.0, 0.0 },
                     { 0.0, 0.0, 0.0, 0.0 },
                     { 0.0, 0.0, 0.0, 0.0 } } };


std::ostream&
operator<< (std::ostream &os, const matrix &m) {
    os << "{ {" << m.values[0][0] << ", " << m.values[0][1] << ", " << m.values[0][2] << ", " << m.values[0][3] << "}, "
       <<   "{" << m.values[1][0] << ", " << m.values[1][1] << ", " << m.values[1][2] << ", " << m.values[1][3] << "}, "
       <<   "{" << m.values[2][0] << ", " << m.values[2][1] << ", " << m.values[2][2] << ", " << m.values[2][3] << "}, "
       <<   "{" << m.values[3][0] << ", " << m.values[3][1] << ", " << m.values[3][2] << ", " << m.values[3][3] << "} }";

    return os;
}