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/*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#pragma once
#include "BLI_assert.h"
#include "BLI_float2.hh"
#include "BLI_math_matrix.h"
#include <cmath>
#include <tuple>
namespace blender {
/**
* A 2x2 column major matrix.
*
* float2x2::values[i] is the ith column of the matrix.
*
* |m00 m10|
* |m01 m11|
*
*/
struct float2x2 {
float values[2][2];
float2x2() = default;
float2x2(const float *matrix)
{
memcpy(values, matrix, sizeof(float) * 4);
}
float2x2(const float matrix[2][2]) : float2x2(static_cast<const float *>(matrix[0]))
{
}
static float2x2 identity()
{
float2x2 mat;
unit_m2(mat.values);
return mat;
}
operator float *()
{
return &values[0][0];
}
operator const float *() const
{
return &values[0][0];
}
using c_style_float2x2 = float[2][2];
c_style_float2x2 &ptr()
{
return values;
}
const c_style_float2x2 &ptr() const
{
return values;
}
friend float2x2 operator*(const float2x2 &a, const float2x2 &b)
{
float2x2 result;
mul_m2_m2m2(result.values, a.values, b.values);
return result;
}
friend float2 operator*(const float2x2 &m, const float2 &v)
{
float2 result;
mul_v2_m2v2(result, m.values, v);
return result;
}
friend float2 operator*(const float2x2 &m, const float (*v)[2])
{
return m * float2(v);
}
/**
* Multiplies all the elements of `m` with `val`
*/
friend float2x2 operator*(const float2x2 &m, const float val)
{
float2x2 res;
res.ptr()[0][0] = m.ptr()[0][0] * val;
res.ptr()[0][1] = m.ptr()[0][1] * val;
res.ptr()[1][0] = m.ptr()[1][0] * val;
res.ptr()[1][1] = m.ptr()[1][1] * val;
return res;
}
friend float2x2 operator+(const float2x2 &m1, const float2x2 &m2)
{
float2x2 res;
res.ptr()[0][0] = m1.ptr()[0][0] + m2.ptr()[0][0];
res.ptr()[0][1] = m1.ptr()[0][1] + m2.ptr()[0][1];
res.ptr()[1][0] = m1.ptr()[1][0] + m2.ptr()[1][0];
res.ptr()[1][1] = m1.ptr()[1][1] + m2.ptr()[1][1];
return float2x2(res);
}
float2x2 linear_blend(const float2x2 &other, float factor) const
{
BLI_assert(factor >= 0.0 && factor <= 1.0);
const float inv_factor = 1.0 - factor;
float2x2 res;
res.ptr()[0][0] = this->ptr()[0][0] * factor + other.ptr()[0][0] * inv_factor;
res.ptr()[0][1] = this->ptr()[0][1] * factor + other.ptr()[0][1] * inv_factor;
res.ptr()[1][0] = this->ptr()[1][0] * factor + other.ptr()[1][0] * inv_factor;
res.ptr()[1][1] = this->ptr()[1][1] * factor + other.ptr()[1][1] * inv_factor;
return float2x2(res);
}
/**
* Computes the eigen decomposition of the 2x2 matrix and returns Q
* and Lambda
*
* A = Q * Lambda * Q.inverse()
*
* A is this matrix.
*
* Q is a 2x2 matrix whose ith column is the eigen vector q_i of the
* matrix A.
*
* Lambda is the diagonal matrix whose diagonal elements are the
* corresponding eigenvalues.
*
* Reference https://en.wikipedia.org/wiki/Eigenvalue_algorithm
* http://www.math.harvard.edu/archive/21b_fall_04/exhibits/2dmatrices/index.html
*/
std::tuple<float2x2, float2> eigen_decomposition() const
{
const auto a = this->ptr()[0][0];
const auto b = this->ptr()[1][0];
const auto c = this->ptr()[0][1];
const auto d = this->ptr()[1][1];
const auto trace = a + d;
const auto det = a * d - b * c;
const auto l1 = (trace + std::sqrt(trace * trace - 4.0 * det)) / 2.0;
const auto l2 = (trace - std::sqrt(trace * trace - 4.0 * det)) / 2.0;
const auto lambda = float2(l1, l2);
if (c != 0.0) {
float2x2 q;
q.ptr()[0][0] = l1 - d;
q.ptr()[1][0] = l2 - d;
q.ptr()[0][1] = c;
q.ptr()[1][1] = c;
return {q, lambda};
}
if (b != 0.0) {
float2x2 q;
q.ptr()[0][0] = b;
q.ptr()[1][0] = b;
q.ptr()[0][1] = l1 - a;
q.ptr()[1][1] = l2 - a;
return {q, lambda};
}
float2x2 q;
q.ptr()[0][0] = 1;
q.ptr()[1][0] = 0;
q.ptr()[0][1] = 0;
q.ptr()[1][1] = 1;
return {q, lambda};
}
uint64_t hash() const
{
uint64_t h = 435109;
for (int i = 0; i < 4; i++) {
float value = (static_cast<const float *>(values[0]))[i];
h = h * 33 + *reinterpret_cast<const uint32_t *>(&value);
}
return h;
}
};
} /* namespace blender */
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