174 lines
6.1 KiB
C++
174 lines
6.1 KiB
C++
#include "../src/engine/math/matrix3d.hpp"
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#include "../src/engine/math/point3d.hpp"
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#include "../src/engine/math/vector3d.hpp"
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#include <iostream>
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using namespace engine::math;
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using namespace std;
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#define is_true(n) ((n == true) ? "yes" : "no")
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int main() {
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vector3d v1 = vector3d(1, 2, 3);
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vector3d v2 = vector3d(3, 2, 1);
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vector3d v3 = vector3d(1, 1, 1);
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cout << v1 << endl;
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cout << v2 << endl;
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cout << (v1 - v2) + v3 << endl;
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cout << -v1 << endl;
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cout << vector3d::norm(v1) << endl;
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cout << vector3d::normalize(v1) << endl;
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cout << vector3d::norm(v3) << endl;
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cout << vector3d::normalize(v3) << endl;
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engine::math::matrix3d m = engine::math::matrix3d();
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engine::math::matrix3d id = matrix3d::id();
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cout << m << endl;
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cout << m[0][0] << endl;
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cout << id << endl;
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cout << id[0][0] << id[1][1] << id[2][2] << endl;
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cout << id(0, 0) << id(0, 1) << id(0, 2) << endl;
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matrix3d m1 = matrix3d(v1, v2, v3);
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matrix3d m2 = matrix3d(v3, v2, v1);
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cout << matrix3d::id() + matrix3d::id() << endl;
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cout << m1 * id << endl;
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cout << id * m1 << endl;
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cout << id * id << endl;
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cout << m1 * m2 << endl;
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cout << (id * 3.0f) * v1 << endl;
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cout << v1 * (id * 3.0f) << endl;
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matrix3d m3(1, 2, 3, 4, 5, 5, 7, 8, 9);
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cout << endl << m3 << endl;
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cout << endl << matrix3d::trans(m3) << endl;
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cout << "Are " << m1 << " and " << m2 << " equals? "
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<< is_true(matrix3d::equals(m1, m2)) << endl;
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cout << "Are " << m2 << " and " << m2 << " equals? "
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<< is_true(matrix3d::equals(m2, m2)) << endl;
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// Validate matrix properties
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cout << "Associative law for matrix add holds: "
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<< is_true(matrix3d::equals((m1 + m2) + id, m1 + (m2 + id))) << endl;
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cout << "Comutative law for add holds: "
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<< is_true(matrix3d::equals(m1 + m2, m2 + m1)) << endl;
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cout << "Associative for scalar multiplication: "
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<< is_true(matrix3d::equals((2.0f * 2.0f) * m1, 2.0f * (2.0f * m1)))
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<< endl;
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cout << "Comutative law for scalar multiplication: "
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<< is_true(matrix3d::equals(2 * m1, m1 * 2)) << endl;
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cout << "Distributive law for scalar multiplication: "
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<< is_true(matrix3d::equals((2 + 2) * m1, 2 * m1 + 2 * m1)) << endl;
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cout << "Associative for matrix multiplication: "
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<< is_true(matrix3d::equals((m1 * m2) * m3, m1 * (m2 * m3))) << endl;
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cout << "Distributive laws for matrix: "
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<< is_true(matrix3d::equals(m1 * (m2 + m3), m1 * m2 + m1 * m3))
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<< " and "
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<< is_true(matrix3d::equals((m1 + m2) * m3, m1 * m3 + m2 * m3)) << endl;
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cout << "Scalar factorization for matrices: "
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<< is_true(matrix3d::equals((3 * m1) * m2, m1 * (3 * m2))) << " and "
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<< is_true(matrix3d::equals((3 * m1) * m2, 3 * (m1 * m2))) << endl;
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cout << "Product rule for matrix trans: "
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<< is_true(matrix3d::equals(matrix3d::trans(m1 * m2),
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matrix3d::trans(m2) * matrix3d::trans(m1)))
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<< endl;
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cout << "Dot product comutative law: "
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<< is_true(vector3d::dot(v1, v2) == vector3d::dot(v2, v1)) << endl;
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cout << "Dot product distributive law: "
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<< is_true(vector3d::dot(v1, (v2 + v3)) ==
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(vector3d::dot(v1, v2) + vector3d::dot(v1, v3)))
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<< endl;
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cout << "Dot scalar factorization: "
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<< is_true(vector3d::dot(2.0 * v1, v2) == vector3d::dot(v1, 2 * v2))
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<< " and "
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<< is_true(vector3d::dot(v1, 2 * v2) == 2 * vector3d::dot(v1, v2))
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<< endl;
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cout << "Cross anticomutativity: "
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<< is_true(vector3d::equals(vector3d::cross(v1, v2),
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-vector3d::cross(v2, v1)))
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<< endl;
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cout << "Cross distributive law: "
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<< is_true(vector3d::equals(vector3d::cross(v1, v2 + v3),
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vector3d::cross(v1, v2) +
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vector3d::cross(v1, v3)))
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<< endl;
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cout << "Scalar factorization in cross: "
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<< is_true(vector3d::equals(vector3d::cross(2 * v1, v2),
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vector3d::cross(v1, 2 * v2)))
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<< " and "
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<< is_true(vector3d::equals(vector3d::cross(v1, 2 * v2),
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2 * vector3d::cross(v1, v2)))
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<< endl;
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cout << "Vector triple product: "
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<< is_true(vector3d::equals(vector3d::cross(v1, vector3d::cross(v2, v3)),
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v2 * vector3d::dot(v1, v3) -
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v3 * vector3d::dot(v1, v2)))
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<< endl;
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// Check lagrande id:
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// This means:
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// dot(cross(v1,v2),cross(v1,v2)) = dot(v1,v1)*dot(v2,v2) -
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// dot(v1,v2)*dot(v1,v2)
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cout << "Lagrange id: "
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<< is_true(
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vector3d::dot(vector3d::cross(v1, v2), vector3d::cross(v1, v2)) ==
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(vector3d::dot(v1, v1) * vector3d::dot(v2, v2) -
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(vector3d::dot(v1, v2) * vector3d::dot(v1, v2))))
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<< endl;
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// Projections
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cout << "Project [1,1,0] in [1,0,0]: "
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<< vector3d::project(vector3d(1, 1, 0), vector3d(1, 0, 0)) << endl;
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cout << "Reject [1,1,0] over [1,0,0]: "
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<< vector3d::reject(vector3d(1, 1, 0), vector3d(1, 0, 0)) << endl;
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// Checking determinant properties
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cout << "Det of identity matrix should be 1: "
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<< is_true(matrix3d::det(id) == 1) << endl;
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cout << "Det(m^T) should be the same as Det(m): "
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<< is_true(matrix3d::det(m3) == matrix3d::det(matrix3d::trans(m3)))
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<< endl;
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matrix3d m4 = matrix3d(4, -1, 1, 4, 5, 3, -2, 0, 0);
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matrix3d m4_inv = matrix3d::inv(m4);
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float32 dm4 = matrix3d::det(m4);
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float32 dm4_inv = matrix3d::det(m4_inv);
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float inv_dm4 = 1.0f / dm4;
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float32 pdet = dm4 * dm4_inv;
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cout << "Determinant of inverse should be the inverse of the determinant: "
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<< is_true(dm4_inv == inv_dm4) << endl;
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cout << "Determinant of product should be the product of determinants: "
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<< is_true(matrix3d::det(m4 * m4_inv) ==
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matrix3d::det(m4) * matrix3d::det(m4_inv))
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<< endl;
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cout << id.to_string() << endl;
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point3d p1 = point3d(0, 1, 0);
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point3d p2 = point3d(1, 0, 0);
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point3d p3 = point3d(0, 0, 1);
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point3d p4 = p1 + v1;
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cout << v1 << endl;
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cout << point3d() - p4 << endl;
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}
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