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////////////////////////////////////////////////////////////
//
// SFML - Simple and Fast Multimedia Library
// Copyright (C) 2007-2025 Laurent Gomila (laurent@sfml-dev.org)
//
// This software is provided 'as-is', without any express or implied warranty.
// In no event will the authors be held liable for any damages arising from the use of this software.
//
// Permission is granted to anyone to use this software for any purpose,
// including commercial applications, and to alter it and redistribute it freely,
// subject to the following restrictions:
//
// 1. The origin of this software must not be misrepresented;
// you must not claim that you wrote the original software.
// If you use this software in a product, an acknowledgment
// in the product documentation would be appreciated but is not required.
//
// 2. Altered source versions must be plainly marked as such,
// and must not be misrepresented as being the original software.
//
// 3. This notice may not be removed or altered from any source distribution.
//
////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////
// Headers
////////////////////////////////////////////////////////////
#include <SFML/Graphics/Transform.hpp> // NOLINT(misc-header-include-cycle)
#include <array>
#include <cstddef>
namespace sf
{
////////////////////////////////////////////////////////////
// clang-format off
constexpr Transform::Transform(float a00, float a01, float a02,
float a10, float a11, float a12,
float a20, float a21, float a22)
: m_matrix{a00, a10, 0.f, a20,
a01, a11, 0.f, a21,
0.f, 0.f, 1.f, 0.f,
a02, a12, 0.f, a22}
{
}
// clang-format on
////////////////////////////////////////////////////////////
constexpr const float* Transform::getMatrix() const
{
return m_matrix.data();
}
////////////////////////////////////////////////////////////
constexpr Transform Transform::getInverse() const
{
// clang-format off
// Compute the determinant
const float det = m_matrix[0] * (m_matrix[15] * m_matrix[5] - m_matrix[7] * m_matrix[13]) -
m_matrix[1] * (m_matrix[15] * m_matrix[4] - m_matrix[7] * m_matrix[12]) +
m_matrix[3] * (m_matrix[13] * m_matrix[4] - m_matrix[5] * m_matrix[12]);
// clang-format on
// Compute the inverse if the determinant is not zero
// (don't use an epsilon because the determinant may *really* be tiny)
if (det != 0.f)
{
// clang-format off
return {(m_matrix[15] * m_matrix[5] - m_matrix[7] * m_matrix[13]) / det,
-(m_matrix[15] * m_matrix[4] - m_matrix[7] * m_matrix[12]) / det,
(m_matrix[13] * m_matrix[4] - m_matrix[5] * m_matrix[12]) / det,
-(m_matrix[15] * m_matrix[1] - m_matrix[3] * m_matrix[13]) / det,
(m_matrix[15] * m_matrix[0] - m_matrix[3] * m_matrix[12]) / det,
-(m_matrix[13] * m_matrix[0] - m_matrix[1] * m_matrix[12]) / det,
(m_matrix[7] * m_matrix[1] - m_matrix[3] * m_matrix[5]) / det,
-(m_matrix[7] * m_matrix[0] - m_matrix[3] * m_matrix[4]) / det,
(m_matrix[5] * m_matrix[0] - m_matrix[1] * m_matrix[4]) / det};
// clang-format on
}
return Identity;
}
////////////////////////////////////////////////////////////
constexpr Vector2f Transform::transformPoint(Vector2f point) const
{
return {m_matrix[0] * point.x + m_matrix[4] * point.y + m_matrix[12],
m_matrix[1] * point.x + m_matrix[5] * point.y + m_matrix[13]};
}
////////////////////////////////////////////////////////////
constexpr FloatRect Transform::transformRect(const FloatRect& rectangle) const
{
// Transform the 4 corners of the rectangle
const std::array points = {transformPoint(rectangle.position),
transformPoint(rectangle.position + Vector2f(0.f, rectangle.size.y)),
transformPoint(rectangle.position + Vector2f(rectangle.size.x, 0.f)),
transformPoint(rectangle.position + rectangle.size)};
// Compute the bounding rectangle of the transformed points
Vector2f pmin = points[0];
Vector2f pmax = points[0];
for (std::size_t i = 1; i < points.size(); ++i)
{
// clang-format off
if (points[i].x < pmin.x) pmin.x = points[i].x;
else if (points[i].x > pmax.x) pmax.x = points[i].x;
if (points[i].y < pmin.y) pmin.y = points[i].y;
else if (points[i].y > pmax.y) pmax.y = points[i].y;
// clang-format on
}
return {pmin, pmax - pmin};
}
////////////////////////////////////////////////////////////
constexpr Transform& Transform::combine(const Transform& transform)
{
const auto& a = m_matrix;
const auto& b = transform.m_matrix;
// clang-format off
*this = Transform(a[0] * b[0] + a[4] * b[1] + a[12] * b[3],
a[0] * b[4] + a[4] * b[5] + a[12] * b[7],
a[0] * b[12] + a[4] * b[13] + a[12] * b[15],
a[1] * b[0] + a[5] * b[1] + a[13] * b[3],
a[1] * b[4] + a[5] * b[5] + a[13] * b[7],
a[1] * b[12] + a[5] * b[13] + a[13] * b[15],
a[3] * b[0] + a[7] * b[1] + a[15] * b[3],
a[3] * b[4] + a[7] * b[5] + a[15] * b[7],
a[3] * b[12] + a[7] * b[13] + a[15] * b[15]);
// clang-format on
return *this;
}
////////////////////////////////////////////////////////////
constexpr Transform& Transform::translate(Vector2f offset)
{
// clang-format off
const Transform translation(1, 0, offset.x,
0, 1, offset.y,
0, 0, 1);
// clang-format on
return combine(translation);
}
////////////////////////////////////////////////////////////
constexpr Transform& Transform::scale(Vector2f factors)
{
// clang-format off
const Transform scaling(factors.x, 0, 0,
0, factors.y, 0,
0, 0, 1);
// clang-format on
return combine(scaling);
}
////////////////////////////////////////////////////////////
constexpr Transform& Transform::scale(Vector2f factors, Vector2f center)
{
// clang-format off
const Transform scaling(factors.x, 0, center.x * (1 - factors.x),
0, factors.y, center.y * (1 - factors.y),
0, 0, 1);
// clang-format on
return combine(scaling);
}
////////////////////////////////////////////////////////////
constexpr Transform operator*(const Transform& left, const Transform& right)
{
return Transform(left).combine(right);
}
////////////////////////////////////////////////////////////
constexpr Transform& operator*=(Transform& left, const Transform& right)
{
return left.combine(right);
}
////////////////////////////////////////////////////////////
constexpr Vector2f operator*(const Transform& left, Vector2f right)
{
return left.transformPoint(right);
}
////////////////////////////////////////////////////////////
constexpr bool operator==(const Transform& left, const Transform& right)
{
const float* a = left.getMatrix();
const float* b = right.getMatrix();
// clang-format off
return ((a[0] == b[0]) && (a[1] == b[1]) && (a[3] == b[3]) &&
(a[4] == b[4]) && (a[5] == b[5]) && (a[7] == b[7]) &&
(a[12] == b[12]) && (a[13] == b[13]) && (a[15] == b[15]));
// clang-format on
}
////////////////////////////////////////////////////////////
constexpr bool operator!=(const Transform& left, const Transform& right)
{
return !(left == right);
}
////////////////////////////////////////////////////////////
// Static member data
////////////////////////////////////////////////////////////
// Note: the 'inline' keyword here is technically not required, but VS2019 fails
// to compile with a bogus "multiple definition" error if not explicitly used.
inline constexpr Transform Transform::Identity;
} // namespace sf
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