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/** @file
* @brief Unit tests for Affine
* Uses the Google Testing Framework
*//*
* Authors:
* Krzysztof Kosiński <tweenk.pl@gmail.com>
*
* Copyright 2010 Authors
*
* This library is free software; you can redistribute it and/or
* modify it either under the terms of the GNU Lesser General Public
* License version 2.1 as published by the Free Software Foundation
* (the "LGPL") or, at your option, under the terms of the Mozilla
* Public License Version 1.1 (the "MPL"). If you do not alter this
* notice, a recipient may use your version of this file under either
* the MPL or the LGPL.
*
* You should have received a copy of the LGPL along with this library
* in the file COPYING-LGPL-2.1; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
* You should have received a copy of the MPL along with this library
* in the file COPYING-MPL-1.1
*
* The contents of this file are subject to the Mozilla Public License
* Version 1.1 (the "License"); you may not use this file except in
* compliance with the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
* OF ANY KIND, either express or implied. See the LGPL or the MPL for
* the specific language governing rights and limitations.
*/
#include <gtest/gtest.h>
#include <2geom/affine.h>
#include <2geom/transforms.h>
namespace Geom {
TEST(AffineTest, Equality) {
Affine e; // identity
Affine a(1, 2, 3, 4, 5, 6);
EXPECT_EQ(e, e);
EXPECT_EQ(e, Geom::identity());
EXPECT_EQ(e, Geom::Affine::identity());
EXPECT_NE(e, a);
}
TEST(AffineTest, Classification) {
{
Affine a; // identity
EXPECT_TRUE(a.isIdentity());
EXPECT_TRUE(a.isTranslation());
EXPECT_TRUE(a.isScale());
EXPECT_TRUE(a.isUniformScale());
EXPECT_TRUE(a.isRotation());
EXPECT_TRUE(a.isHShear());
EXPECT_TRUE(a.isVShear());
EXPECT_TRUE(a.isZoom());
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_FALSE(a.isNonzeroScale());
EXPECT_FALSE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_FALSE(a.isNonzeroNonpureRotation());
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_TRUE(a.preservesArea());
EXPECT_TRUE(a.preservesAngles());
EXPECT_TRUE(a.preservesDistances());
EXPECT_FALSE(a.flips());
EXPECT_FALSE(a.isSingular());
}
{
Affine a = Translate(10, 15); // pure translation
EXPECT_FALSE(a.isIdentity());
EXPECT_TRUE(a.isTranslation());
EXPECT_FALSE(a.isScale());
EXPECT_FALSE(a.isUniformScale());
EXPECT_FALSE(a.isRotation());
EXPECT_FALSE(a.isHShear());
EXPECT_FALSE(a.isVShear());
EXPECT_TRUE(a.isZoom());
EXPECT_TRUE(a.isNonzeroTranslation());
EXPECT_FALSE(a.isNonzeroScale());
EXPECT_FALSE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_FALSE(a.isNonzeroNonpureRotation());
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_TRUE(a.preservesArea());
EXPECT_TRUE(a.preservesAngles());
EXPECT_TRUE(a.preservesDistances());
EXPECT_FALSE(a.flips());
EXPECT_FALSE(a.isSingular());
}
{
Affine a = Scale(-1.0, 1.0); // flip on the X axis
EXPECT_FALSE(a.isIdentity());
EXPECT_FALSE(a.isTranslation());
EXPECT_TRUE(a.isScale());
EXPECT_TRUE(a.isUniformScale());
EXPECT_FALSE(a.isRotation());
EXPECT_FALSE(a.isHShear());
EXPECT_FALSE(a.isVShear());
EXPECT_FALSE(a.isZoom()); // zoom must be non-flipping
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_TRUE(a.isNonzeroScale());
EXPECT_TRUE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_FALSE(a.isNonzeroNonpureRotation());
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_TRUE(a.preservesArea());
EXPECT_TRUE(a.preservesAngles());
EXPECT_TRUE(a.preservesDistances());
EXPECT_TRUE(a.flips());
EXPECT_FALSE(a.isSingular());
}
{
Affine a = Scale(0.5, 0.5); // pure uniform scale
EXPECT_FALSE(a.isIdentity());
EXPECT_FALSE(a.isTranslation());
EXPECT_TRUE(a.isScale());
EXPECT_TRUE(a.isUniformScale());
EXPECT_FALSE(a.isRotation());
EXPECT_FALSE(a.isHShear());
EXPECT_FALSE(a.isVShear());
EXPECT_TRUE(a.isZoom());
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_TRUE(a.isNonzeroScale());
EXPECT_TRUE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_FALSE(a.isNonzeroNonpureRotation());
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_FALSE(a.preservesArea());
EXPECT_TRUE(a.preservesAngles());
EXPECT_FALSE(a.preservesDistances());
EXPECT_FALSE(a.flips());
EXPECT_FALSE(a.isSingular());
}
{
Affine a = Scale(0.5, -0.5); // pure uniform flipping scale
EXPECT_FALSE(a.isIdentity());
EXPECT_FALSE(a.isTranslation());
EXPECT_TRUE(a.isScale());
EXPECT_TRUE(a.isUniformScale());
EXPECT_FALSE(a.isRotation());
EXPECT_FALSE(a.isHShear());
EXPECT_FALSE(a.isVShear());
EXPECT_FALSE(a.isZoom()); // zoom must be non-flipping
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_TRUE(a.isNonzeroScale());
EXPECT_TRUE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_FALSE(a.isNonzeroNonpureRotation());
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_FALSE(a.preservesArea());
EXPECT_TRUE(a.preservesAngles());
EXPECT_FALSE(a.preservesDistances());
EXPECT_TRUE(a.flips());
EXPECT_FALSE(a.isSingular());
}
{
Affine a = Scale(0.5, 0.7); // pure non-uniform scale
EXPECT_FALSE(a.isIdentity());
EXPECT_FALSE(a.isTranslation());
EXPECT_TRUE(a.isScale());
EXPECT_FALSE(a.isUniformScale());
EXPECT_FALSE(a.isRotation());
EXPECT_FALSE(a.isHShear());
EXPECT_FALSE(a.isVShear());
EXPECT_FALSE(a.isZoom());
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_TRUE(a.isNonzeroScale());
EXPECT_FALSE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_FALSE(a.isNonzeroNonpureRotation());
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_FALSE(a.preservesArea());
EXPECT_FALSE(a.preservesAngles());
EXPECT_FALSE(a.preservesDistances());
EXPECT_FALSE(a.flips());
EXPECT_FALSE(a.isSingular());
}
{
Affine a = Scale(0.5, 2.0); // "squeeze" transform (non-uniform scale with det=1)
EXPECT_FALSE(a.isIdentity());
EXPECT_FALSE(a.isTranslation());
EXPECT_TRUE(a.isScale());
EXPECT_FALSE(a.isUniformScale());
EXPECT_FALSE(a.isRotation());
EXPECT_FALSE(a.isHShear());
EXPECT_FALSE(a.isVShear());
EXPECT_FALSE(a.isZoom());
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_TRUE(a.isNonzeroScale());
EXPECT_FALSE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_FALSE(a.isNonzeroNonpureRotation());
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_TRUE(a.preservesArea());
EXPECT_FALSE(a.preservesAngles());
EXPECT_FALSE(a.preservesDistances());
EXPECT_FALSE(a.flips());
EXPECT_FALSE(a.isSingular());
}
{
Affine a = Rotate(0.7); // pure rotation
EXPECT_FALSE(a.isIdentity());
EXPECT_FALSE(a.isTranslation());
EXPECT_FALSE(a.isScale());
EXPECT_FALSE(a.isUniformScale());
EXPECT_TRUE(a.isRotation());
EXPECT_FALSE(a.isHShear());
EXPECT_FALSE(a.isVShear());
EXPECT_FALSE(a.isZoom());
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_FALSE(a.isNonzeroScale());
EXPECT_FALSE(a.isNonzeroUniformScale());
EXPECT_TRUE(a.isNonzeroRotation());
EXPECT_TRUE(a.isNonzeroNonpureRotation());
EXPECT_EQ(a.rotationCenter(), Point(0.0,0.0));
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_TRUE(a.preservesArea());
EXPECT_TRUE(a.preservesAngles());
EXPECT_TRUE(a.preservesDistances());
EXPECT_FALSE(a.flips());
EXPECT_FALSE(a.isSingular());
}
{
Point rotation_center(1.23,4.56);
Affine a = Translate(-rotation_center) * Rotate(0.7) * Translate(rotation_center); // rotation around (1.23,4.56)
EXPECT_FALSE(a.isIdentity());
EXPECT_FALSE(a.isTranslation());
EXPECT_FALSE(a.isScale());
EXPECT_FALSE(a.isUniformScale());
EXPECT_FALSE(a.isRotation());
EXPECT_FALSE(a.isHShear());
EXPECT_FALSE(a.isVShear());
EXPECT_FALSE(a.isZoom());
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_FALSE(a.isNonzeroScale());
EXPECT_FALSE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_TRUE(a.isNonzeroNonpureRotation());
EXPECT_TRUE(are_near(a.rotationCenter(), rotation_center, 1e-7));
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_TRUE(a.preservesArea());
EXPECT_TRUE(a.preservesAngles());
EXPECT_TRUE(a.preservesDistances());
EXPECT_FALSE(a.flips());
EXPECT_FALSE(a.isSingular());
}
{
Affine a = HShear(0.5); // pure horizontal shear
EXPECT_FALSE(a.isIdentity());
EXPECT_FALSE(a.isTranslation());
EXPECT_FALSE(a.isScale());
EXPECT_FALSE(a.isUniformScale());
EXPECT_FALSE(a.isRotation());
EXPECT_TRUE(a.isHShear());
EXPECT_FALSE(a.isVShear());
EXPECT_FALSE(a.isZoom());
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_FALSE(a.isNonzeroScale());
EXPECT_FALSE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_FALSE(a.isNonzeroNonpureRotation());
EXPECT_TRUE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_TRUE(a.preservesArea());
EXPECT_FALSE(a.preservesAngles());
EXPECT_FALSE(a.preservesDistances());
EXPECT_FALSE(a.flips());
EXPECT_FALSE(a.isSingular());
}
{
Affine a = VShear(0.5); // pure vertical shear
EXPECT_FALSE(a.isIdentity());
EXPECT_FALSE(a.isTranslation());
EXPECT_FALSE(a.isScale());
EXPECT_FALSE(a.isUniformScale());
EXPECT_FALSE(a.isRotation());
EXPECT_FALSE(a.isHShear());
EXPECT_TRUE(a.isVShear());
EXPECT_FALSE(a.isZoom());
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_FALSE(a.isNonzeroScale());
EXPECT_FALSE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_FALSE(a.isNonzeroNonpureRotation());
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_TRUE(a.isNonzeroVShear());
EXPECT_TRUE(a.preservesArea());
EXPECT_FALSE(a.preservesAngles());
EXPECT_FALSE(a.preservesDistances());
EXPECT_FALSE(a.flips());
EXPECT_FALSE(a.isSingular());
}
{
Affine a = Zoom(3.0, Translate(10, 15)); // zoom
EXPECT_FALSE(a.isIdentity());
EXPECT_FALSE(a.isTranslation());
EXPECT_FALSE(a.isScale());
EXPECT_FALSE(a.isUniformScale());
EXPECT_FALSE(a.isRotation());
EXPECT_FALSE(a.isHShear());
EXPECT_FALSE(a.isVShear());
EXPECT_TRUE(a.isZoom());
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_FALSE(a.isNonzeroScale());
EXPECT_FALSE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_FALSE(a.isNonzeroNonpureRotation());
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_FALSE(a.preservesArea());
EXPECT_TRUE(a.preservesAngles());
EXPECT_FALSE(a.preservesDistances());
EXPECT_FALSE(a.flips());
EXPECT_FALSE(a.isSingular());
EXPECT_TRUE(a.withoutTranslation().isUniformScale());
EXPECT_TRUE(a.withoutTranslation().isNonzeroUniformScale());
}
{
Affine a(0, 0, 0, 0, 0, 0); // zero matrix (singular)
EXPECT_FALSE(a.isIdentity());
EXPECT_FALSE(a.isTranslation());
EXPECT_FALSE(a.isScale());
EXPECT_FALSE(a.isUniformScale());
EXPECT_FALSE(a.isRotation());
EXPECT_FALSE(a.isHShear());
EXPECT_FALSE(a.isVShear());
EXPECT_FALSE(a.isZoom());
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_FALSE(a.isNonzeroScale());
EXPECT_FALSE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_FALSE(a.isNonzeroNonpureRotation());
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_FALSE(a.preservesArea());
EXPECT_FALSE(a.preservesAngles());
EXPECT_FALSE(a.preservesDistances());
EXPECT_FALSE(a.flips());
EXPECT_TRUE(a.isSingular());
}
{
Affine a(0, 1, 0, 1, 10, 10); // another singular matrix
EXPECT_FALSE(a.isIdentity());
EXPECT_FALSE(a.isTranslation());
EXPECT_FALSE(a.isScale());
EXPECT_FALSE(a.isUniformScale());
EXPECT_FALSE(a.isRotation());
EXPECT_FALSE(a.isHShear());
EXPECT_FALSE(a.isVShear());
EXPECT_FALSE(a.isZoom());
EXPECT_FALSE(a.isNonzeroTranslation());
EXPECT_FALSE(a.isNonzeroScale());
EXPECT_FALSE(a.isNonzeroUniformScale());
EXPECT_FALSE(a.isNonzeroRotation());
EXPECT_FALSE(a.isNonzeroNonpureRotation());
EXPECT_FALSE(a.isNonzeroHShear());
EXPECT_FALSE(a.isNonzeroVShear());
EXPECT_FALSE(a.preservesArea());
EXPECT_FALSE(a.preservesAngles());
EXPECT_FALSE(a.preservesDistances());
EXPECT_FALSE(a.flips());
EXPECT_TRUE(a.isSingular());
}
}
TEST(AffineTest, Inversion) {
Affine i(1, 2, 1, -2, 10, 15); // invertible
Affine n(1, 2, 1, 2, 15, 30); // non-invertible
Affine e; // identity
EXPECT_EQ(i * i.inverse(), e);
EXPECT_EQ(i.inverse().inverse(), i);
EXPECT_EQ(n.inverse(), e);
EXPECT_EQ(e.inverse(), e);
}
TEST(AffineTest, CoordinateAccess) {
Affine a(0, 1, 2, 3, 4, 5);
for (int i=0; i<6; ++i) {
EXPECT_EQ(a[i], i);
}
for (int i=0; i<6; ++i) {
a[i] = 5*i;
}
for (int i=0; i<6; ++i) {
EXPECT_EQ(a[i], 5*i);
}
}
TEST(AffineTest, Nearness) {
Affine a1(1, 0, 1, 2, 1e-8, 1e-8);
Affine a2(1+1e-8, 0, 1, 2-1e-8, -1e-8, -1e-8);
EXPECT_TRUE(are_near(a1, a2, 1e-7));
EXPECT_FALSE(are_near(a1, a2, 1e-9));
}
TEST(AffineTest, Multiplication) {
// test whether noncommutative multiplications work correctly
Affine a1 = Scale(0.1), a2 = Translate(10, 10), a3 = Scale(10.0);
Affine t1 = Translate(1, 1), t100 = Translate(100, 100);
EXPECT_EQ(a1 * a2 * a3, t100);
EXPECT_EQ(a3 * a2 * a1, t1);
}
} // end namespace Geom
/*
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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