raytracer_challenge/tests/04_transformations.cpp

/*!
 * 04_transformations.cpp
 *
 * Copyright (c) 2015-2024, NADAL Jean-Baptiste. All rights reserved.
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
 * MA 02110-1301 USA
 *
 * @Author:  NADAL Jean-Baptiste
 * @Date: 05/02/2024
 *
 */

/*---------------------------------------------------------------------------*/

#include <catch.hpp>

#include "raytracing.h"

using namespace Raytracer;

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] Multiplying by a translation matrix", "[Matrix]")
{
    Matrix transform = Matrix::translation(5, -3, 2);
    Tuple p = Tuple::Point(-3, 4, 5);

    REQUIRE(transform * p == Tuple::Point(2, 1, 7));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] Multiplying by the inverse of a translation matrix", "[Matrix]")
{
    Matrix transform = Matrix::translation(5, -3, 2);
    Matrix inv = transform.inverse();
    Tuple p = Tuple::Point(-3, 4, 5);

    REQUIRE(inv * p == Tuple::Point(-8, 7, 3));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] Translation does not affect vectors", "[Matrix]")
{
    Matrix transform = Matrix::translation(5, -3, 2);
    Tuple v = Tuple::Vector(-3, 4, 5);

    REQUIRE(transform * v == v);
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] A scaling matrix applied to a point", "[Matrix]")
{
    Matrix transform = Matrix::scaling(2, 3, 4);
    Tuple p = Tuple::Point(-4, 6, 8);

    REQUIRE(transform * p == Tuple::Point(-8, 18, 32));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] A scaling matrix applied to a vector", "[Matrix]")
{
    Matrix transform = Matrix::scaling(2, 3, 4);
    Tuple v = Tuple::Vector(-4, 6, 8);

    REQUIRE(transform * v == Tuple::Vector(-8, 18, 32));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] Multiplying by the inverse of a scaling matrix", "[Matrix]")
{
    Matrix transform = Matrix::scaling(2, 3, 4);
    Matrix inv = transform.inverse();
    Tuple v = Tuple::Vector(-4, 6, 8);

    REQUIRE(inv * v == Tuple::Vector(-2, 2, 2));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] Reflection is scaling by a negative value", "[Matrix]")
{
    Matrix transform = Matrix::scaling(-1, 1, 1);
    Tuple p = Tuple::Point(2, 3, 4);

    REQUIRE(transform * p == Tuple::Point(-2, 3, 4));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] Rotating a point around the x axis", "[Matrix]")
{
    Tuple p = Tuple::Point(0, 1, 0);
    Matrix half_quarter = Matrix::rotation_x(std::numbers::pi / 4);
    Matrix full_quarter = Matrix::rotation_x(std::numbers::pi / 2);

    REQUIRE(half_quarter * p == Tuple::Point(0, sqrt(2) / 2, sqrt(2) / 2));
    REQUIRE(full_quarter * p == Tuple::Point(0, 0, 1));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] The inverse of an x-rotation rotates in the opposite direction", "[Matrix]")
{
    Tuple p = Tuple::Point(0, 1, 0);
    Matrix half_quarter = Matrix::rotation_x(std::numbers::pi / 4);
    Matrix inv = half_quarter.inverse();

    REQUIRE(inv * p == Tuple::Point(0, sqrt(2) / 2, -sqrt(2) / 2));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] Rotating a point around the y axis", "[Matrix]")
{
    Tuple p = Tuple::Point(0, 0, 1);
    Matrix half_quarter = Matrix::rotation_y(std::numbers::pi / 4);
    Matrix full_quarter = Matrix::rotation_y(std::numbers::pi / 2);

    REQUIRE(half_quarter * p == Tuple::Point(sqrt(2) / 2, 0, sqrt(2) / 2));
    REQUIRE(full_quarter * p == Tuple::Point(1, 0, 0));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] Rotating a point around the z axis", "[Matrix]")
{
    Tuple p = Tuple::Point(0, 1, 0);
    Matrix half_quarter = Matrix::rotation_z(std::numbers::pi / 4);
    Matrix full_quarter = Matrix::rotation_z(std::numbers::pi / 2);

    Tuple z = half_quarter * p;

    REQUIRE(half_quarter * p == Tuple::Point(-sqrt(2) / 2, sqrt(2) / 2, 0));
    REQUIRE(full_quarter * p == Tuple::Point(-1, 0, 0));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] A shearing transformation moves x in proportion to y", "[Matrix]")
{
    Matrix transform = Matrix::shearing(1, 0, 0, 0, 0, 0);
    Tuple p = Tuple::Point(2, 3, 4);

    REQUIRE(transform * p == Tuple::Point(5, 3, 4));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] A shearing transformation moves y in proportion to x", "[Matrix]")
{
    Matrix transform = Matrix::shearing(0, 0, 1, 0, 0, 0);
    Tuple p = Tuple::Point(2, 3, 4);

    REQUIRE(transform * p == Tuple::Point(2, 5, 4));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] A shearing transformation moves y in proportion to z", "[Matrix]")
{
    Matrix transform = Matrix::shearing(0, 0, 0, 1, 0, 0);
    Tuple p = Tuple::Point(2, 3, 4);

    REQUIRE(transform * p == Tuple::Point(2, 7, 4));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] A shearing transformation moves z in proportion to x", "[Matrix]")
{
    Matrix transform = Matrix::shearing(0, 0, 0, 0, 1, 0);
    Tuple p = Tuple::Point(2, 3, 4);

    REQUIRE(transform * p == Tuple::Point(2, 3, 6));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] A shearing transformation moves z in proportion to y", "[Matrix]")
{
    Matrix transform = Matrix::shearing(0, 0, 0, 0, 0, 1);
    Tuple p = Tuple::Point(2, 3, 4);

    REQUIRE(transform * p == Tuple::Point(2, 3, 7));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] Individual transformations are applied in sequence", "[Matrix]")
{
    Tuple p = Tuple::Point(1, 0, 1);
    Matrix a = Matrix::rotation_x(std::numbers::pi / 2);
    Matrix b = Matrix::scaling(5, 5, 5);
    Matrix c = Matrix::translation(10, 5, 7);

    // Appply rotation first.
    Tuple p2 = a * p;
    REQUIRE(p2 == Tuple::Point(1, -1, 0));
    // Then Apply scaling
    Tuple p3 = b * p2;
    REQUIRE(p3 == Tuple::Point(5, -5, 0));
    // Then Apply translation
    Tuple p4 = c * p3;
    REQUIRE(p4 == Tuple::Point(15, 0, 7));
}

/* ------------------------------------------------------------------------- */

TEST_CASE("[04][Trans] Chained transformation must be applied in rever order", "[Matrix]")
{
    Tuple p = Tuple::Point(1, 0, 1);
    Matrix a = Matrix::rotation_x(std::numbers::pi / 2);
    Matrix b = Matrix::scaling(5, 5, 5);
    Matrix c = Matrix::translation(10, 5, 7);
    Matrix t = c * b * a;

    REQUIRE(t * p == Tuple::Point(15, 0, 7));
}