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// SPDX-License-Identifier: GPL-2.0-or-later
/*
* 3x4 transformation matrix to map points from projective 3-space into the projective plane
*
* Authors:
* Maximilian Albert <Anhalter42@gmx.de>
*
* Copyright (C) 2007 Authors
*
* Released under GNU GPL v2+, read the file 'COPYING' for more information.
*/
#include "transf_mat_3x4.h"
#include <2geom/affine.h>
#include "svg/stringstream.h"
#include "syseq.h"
namespace Proj {
TransfMat3x4::TransfMat3x4 () {
for (unsigned int i = 0; i < 3; ++i) {
for (unsigned int j = 0; j < 4; ++j) {
tmat[i][j] = (i == j ? 1 : 0); // or should we initialize all values with 0? does it matter at all?
}
}
}
TransfMat3x4::TransfMat3x4 (Proj::Pt2 vp_x, Proj::Pt2 vp_y, Proj::Pt2 vp_z, Proj::Pt2 origin) {
for (unsigned int i = 0; i < 3; ++i) {
tmat[i][0] = vp_x[i];
tmat[i][1] = vp_y[i];
tmat[i][2] = vp_z[i];
tmat[i][3] = origin[i];
}
}
TransfMat3x4::TransfMat3x4(TransfMat3x4 const &rhs) {
for (unsigned int i = 0; i < 3; ++i) {
for (unsigned int j = 0; j < 4; ++j) {
tmat[i][j] = rhs.tmat[i][j];
}
}
}
Pt2
TransfMat3x4::column (Proj::Axis axis) const {
return Proj::Pt2 (tmat[0][axis], tmat[1][axis], tmat[2][axis]);
}
Pt2
TransfMat3x4::image (Pt3 const &point) {
double x = tmat[0][0] * point[0] + tmat[0][1] * point[1] + tmat[0][2] * point[2] + tmat[0][3] * point[3];
double y = tmat[1][0] * point[0] + tmat[1][1] * point[1] + tmat[1][2] * point[2] + tmat[1][3] * point[3];
double w = tmat[2][0] * point[0] + tmat[2][1] * point[1] + tmat[2][2] * point[2] + tmat[2][3] * point[3];
return Pt2 (x, y, w);
}
Pt3
TransfMat3x4::preimage (Geom::Point const &pt, double coord, Proj::Axis axis) {
const double init_val = std::numeric_limits<double>::quiet_NaN();
double x[4] = { init_val, init_val, init_val, init_val };
double v[3] = { pt[Geom::X], pt[Geom::Y], 1.0 };
int index = (int) axis;
SysEq::SolutionKind sol = SysEq::gaussjord_solve<3,4>(tmat, x, v, index, coord, true);
if (sol != SysEq::unique) {
if (sol == SysEq::no_solution) {
g_print ("No solution. Please investigate.\n");
} else {
g_print ("Infinitely many solutions. Please investigate.\n");
}
}
return Pt3(x[0], x[1], x[2], x[3]);
}
void
TransfMat3x4::set_image_pt (Proj::Axis axis, Proj::Pt2 const &pt) {
// FIXME: Do we need to adapt the coordinates in any way or can we just use them as they are?
for (int i = 0; i < 3; ++i) {
tmat[i][axis] = pt[i];
}
}
void
TransfMat3x4::toggle_finite (Proj::Axis axis) {
g_return_if_fail (axis != Proj::W);
if (has_finite_image(axis)) {
Geom::Point dir (column(axis).affine());
Geom::Point origin (column(Proj::W).affine());
dir -= origin;
set_column (axis, Proj::Pt2(dir[Geom::X], dir[Geom::Y], 0));
} else {
Proj::Pt2 dir (column(axis));
Proj::Pt2 origin (column(Proj::W).affine());
dir = dir + origin;
dir[2] = 1.0;
set_column (axis, dir);
}
}
gchar *
TransfMat3x4::pt_to_str (Proj::Axis axis) {
Inkscape::SVGOStringStream os;
os << tmat[0][axis] << " : "
<< tmat[1][axis] << " : "
<< tmat[2][axis];
return g_strdup(os.str().c_str());
}
/* Check for equality (with a small tolerance epsilon) */
bool
TransfMat3x4::operator==(const TransfMat3x4 &rhs) const
{
// Should we allow a certain tolerance or "normalize" the matrices first?
for (int i = 0; i < 3; ++i) {
Proj::Pt2 pt1 = column(Proj::axes[i]);
Proj::Pt2 pt2 = rhs.column(Proj::axes[i]);
if (pt1 != pt2) {
return false;
}
}
return true;
}
/* Multiply a projective matrix by an affine matrix (by only multiplying the 'affine part' of the
* projective matrix) */
TransfMat3x4
TransfMat3x4::operator*(Geom::Affine const &A) const {
TransfMat3x4 ret;
for (int j = 0; j < 4; ++j) {
ret.tmat[0][j] = A[0]*tmat[0][j] + A[2]*tmat[1][j] + A[4]*tmat[2][j];
ret.tmat[1][j] = A[1]*tmat[0][j] + A[3]*tmat[1][j] + A[5]*tmat[2][j];
ret.tmat[2][j] = tmat[2][j];
}
return ret;
}
// FIXME: Shouldn't rather operator* call operator*= for efficiency? (Because in operator*=
// there is in principle no need to create a temporary object, which happens in the assignment)
TransfMat3x4 &
TransfMat3x4::operator*=(Geom::Affine const &A) {
*this = *this * A;
return *this;
}
void
TransfMat3x4::copy_tmat(double rhs[3][4]) {
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 4; ++j) {
rhs[i][j] = tmat[i][j];
}
}
}
void
TransfMat3x4::print () const {
g_print ("Transformation matrix:\n");
for (const auto & i : tmat) {
g_print (" ");
for (double j : i) {
g_print ("%8.2f ", j);
}
g_print ("\n");
}
}
void
TransfMat3x4::normalize_column (Proj::Axis axis) {
Proj::Pt2 new_col(column(axis));
new_col.normalize();
set_image_pt(axis, new_col);
}
} // namespace Proj
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
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