lolengine
/
lolengine
의 미러 https://github.com/lolengine/lolengine
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Update lol-core submodule and get rid of numerous headers.

wip/submodule
Sam Hocevar 5 년 전
부모
9d4b7ff456
커밋
b631cbe292
14개의 변경된 파일과 6개의 추가작업 그리고 3469개의 파일을 삭제
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Show Stats Download Patch File Download Diff File
  1. +1
    -1
      lol-core
  2. +3
    -4
      src/Makefile.am
  3. +1
    -1
      src/application/egl-app.h
  4. +1
    -1
      src/camera.h
  5. +0
    -7
      src/lol-core.vcxproj
  6. +0
    -21
      src/lol-core.vcxproj.filters
  7. +0
    -2
      src/lol/math/all.h
  8. +0
    -638
      src/lol/math/matrix.h
  9. +0
    -362
      src/lol/math/ops.h
  10. +0
    -499
      src/lol/math/transform.h
  11. +0
    -1349
      src/lol/math/vector.h
  12. +0
    -226
      src/math/matrix.cpp
  13. +0
    -262
      src/math/transform.cpp
  14. +0
    -96
      src/math/vector.cpp

+ 1
- 1
lol-core

@@ -1 +1 @@
Subproject commit f30c17f180002170d3d25bcc133b6792175c8bb7
Subproject commit ca3fb5a4ba22c012ed6349aba52186a961a39341

+ 3
- 4
src/Makefile.am 파일 보기

@@ -36,10 +36,9 @@ liblol_core_headers = \
lol/base/log.h \
\
lol/math/all.h \
lol/math/functions.h lol/math/vector.h lol/math/half.h \
lol/math/functions.h lol/math/half.h \
lol/math/geometry.h lol/math/interp.h lol/math/arraynd.h \
lol/math/constants.h lol/math/matrix.h lol/math/ops.h \
lol/math/transform.h lol/math/bigint.h \
lol/math/constants.h lol/math/bigint.h \
lol/math/noise/gradient.h lol/math/noise/perlin.h \
lol/math/noise/simplex.h \
\
@@ -92,7 +91,7 @@ liblol_core_sources = \
\
base/assert.cpp base/features.cpp base/log.cpp base/string.cpp \
\
math/vector.cpp math/matrix.cpp math/transform.cpp math/half.cpp \
math/half.cpp \
math/geometry.cpp \
\
gpu/shader.cpp gpu/indexbuffer.cpp gpu/vertexbuffer.cpp \


+ 1
- 1
src/application/egl-app.h 파일 보기

@@ -15,7 +15,7 @@
// ----------------
//

#include "lol/math/vector.h"
#include <lol/math/vector.h>

namespace lol
{


+ 1
- 1
src/camera.h 파일 보기

@@ -17,7 +17,7 @@
// ----------------
//

#include <lol/math/matrix.h>
#include <lol/math/transform.h>

#include "engine/worldentity.h"



+ 0
- 7
src/lol-core.vcxproj 파일 보기

@@ -177,9 +177,6 @@
<ClCompile Include="lolua\baselua.cpp" />
<ClCompile Include="math\geometry.cpp" />
<ClCompile Include="math\half.cpp" />
<ClCompile Include="math\matrix.cpp" />
<ClCompile Include="math\transform.cpp" />
<ClCompile Include="math\vector.cpp" />
<ClCompile Include="mesh\mesh.cpp" />
<ClCompile Include="mesh\primitivemesh.cpp" />
<ClCompile Include="messageservice.cpp" />
@@ -291,13 +288,9 @@
<ClInclude Include="lol\math\geometry.h" />
<ClInclude Include="lol\math\half.h" />
<ClInclude Include="lol\math\interp.h" />
<ClInclude Include="lol\math\matrix.h" />
<ClInclude Include="lol\math\noise\gradient.h" />
<ClInclude Include="lol\math\noise\perlin.h" />
<ClInclude Include="lol\math\noise\simplex.h" />
<ClInclude Include="lol\math\ops.h" />
<ClInclude Include="lol\math\transform.h" />
<ClInclude Include="lol\math\vector.h" />
<ClInclude Include="lol\net\all.h" />
<ClInclude Include="lol\net\http.h" />
<ClInclude Include="lol\public.h" />


+ 0
- 21
src/lol-core.vcxproj.filters 파일 보기

@@ -207,15 +207,6 @@
<ClCompile Include="math\half.cpp">
<Filter>math</Filter>
</ClCompile>
<ClCompile Include="math\matrix.cpp">
<Filter>math</Filter>
</ClCompile>
<ClCompile Include="math\transform.cpp">
<Filter>math</Filter>
</ClCompile>
<ClCompile Include="math\vector.cpp">
<Filter>math</Filter>
</ClCompile>
<ClCompile Include="mesh\mesh.cpp">
<Filter>mesh</Filter>
</ClCompile>
@@ -458,9 +449,6 @@
<ClInclude Include="lol\math\interp.h">
<Filter>lol\math</Filter>
</ClInclude>
<ClInclude Include="lol\math\matrix.h">
<Filter>lol\math</Filter>
</ClInclude>
<ClInclude Include="lol\math\noise\gradient.h">
<Filter>lol\math\noise</Filter>
</ClInclude>
@@ -470,15 +458,6 @@
<ClInclude Include="lol\math\noise\simplex.h">
<Filter>lol\math\noise</Filter>
</ClInclude>
<ClInclude Include="lol\math\ops.h">
<Filter>lol\math</Filter>
</ClInclude>
<ClInclude Include="lol\math\transform.h">
<Filter>lol\math</Filter>
</ClInclude>
<ClInclude Include="lol\math\vector.h">
<Filter>lol\math</Filter>
</ClInclude>
<ClInclude Include="lol\net\all.h">
<Filter>lol\net</Filter>
</ClInclude>


+ 0
- 2
src/lol/math/all.h 파일 보기

@@ -15,9 +15,7 @@
#include <lol/math/half.h>
#include <lol/math/bigint.h>
#include <lol/math/real.h>
#include <lol/math/ops.h>
#include <lol/math/vector.h>
#include <lol/math/matrix.h>
#include <lol/math/transform.h>
#include <lol/math/arraynd.h>
#include <lol/math/geometry.h>


+ 0
- 638
src/lol/math/matrix.h 파일 보기

@@ -1,638 +0,0 @@
//
// Lol Engine
//
// Copyright © 2010—2019 Sam Hocevar <sam@hocevar.net>
//
// Lol Engine is free software. It comes without any warranty, to
// the extent permitted by applicable law. You can redistribute it
// and/or modify it under the terms of the Do What the Fuck You Want
// to Public License, Version 2, as published by the WTFPL Task Force.
// See http://www.wtfpl.net/ for more details.
//

#pragma once

//
// The matrix classes
// ------------------
//

#include <ostream>

#include <lol/math/vector.h>
#include <lol/math/transform.h>

#if _WIN32
# pragma push_macro("near")
# pragma push_macro("far")
# undef near
# undef far
#endif

namespace lol
{

/*
* The generic “mat_t” type, which is fixed-size
*/

template<typename T, int COLS, int ROWS>
struct LOL_ATTR_NODISCARD mat_t
: public linear_ops::base<vec_t<T,ROWS>>
{
static int const count = COLS;
typedef T scalar_element;
typedef vec_t<T,ROWS> element;
typedef mat_t<T,COLS,ROWS> type;

inline mat_t() {}

explicit inline mat_t(T const &val)
{
T const zero = T(0);
for (int i = 0; i < COLS; ++i)
for (int j = 0; j < ROWS; ++j)
m_data[i][j] = i == j ? val : zero;
}

/* Explicit constructor for type conversion */
template<typename U>
explicit inline mat_t(mat_t<U, COLS, ROWS> const &m)
{
for (int i = 0; i < COLS; ++i)
m_data[i] = (vec_t<T,ROWS>)m[i];
}

inline vec_t<T,ROWS>& operator[](size_t n) { return m_data[n]; }
inline vec_t<T,ROWS> const& operator[](size_t n) const { return m_data[n]; }

private:
vec_t<T,ROWS> m_data[COLS];
};

/*
* 2×2-element matrices
*/

template <typename T>
struct LOL_ATTR_NODISCARD mat_t<T, 2, 2>
: public linear_ops::base<vec_t<T,2>>
{
static int const count = 2;
typedef T scalar_element;
typedef vec_t<T,2> element;
typedef mat_t<T,2,2> type;

inline mat_t() {}
inline mat_t(vec_t<T,2> v0, vec_t<T,2> v1)
: m_data{ v0, v1 } {}

explicit inline mat_t(T const &val)
: m_data{ vec_t<T,2>(val, T(0)),
vec_t<T,2>(T(0), val) } {}

explicit inline mat_t(mat_t<T,4,4> const &m)
: m_data{ m[0].xy, m[1].xy } {}

/* Explicit constructor for type conversion */
template<typename U>
explicit inline mat_t(mat_t<U,2,2> const &m)
: m_data{ (element)m[0], (element)m[1] } {}

inline vec_t<T,2>& operator[](size_t n) { return m_data[n]; }
inline vec_t<T,2> const& operator[](size_t n) const { return m_data[n]; }

/* Helpers for transformation matrices */
static mat_t<T,2,2> rotate(T radians);
static inline mat_t<T,2,2> rotate(mat_t<T,2,2> m, T radians)
{
return rotate(radians) * m;
}

void printf() const;
std::string tostring() const;

static const mat_t<T,2,2> identity;

private:
vec_t<T,2> m_data[2];
};

static_assert(sizeof(imat2) == 16, "sizeof(imat2) == 16");
static_assert(sizeof(f16mat2) == 8, "sizeof(f16mat2) == 8");
static_assert(sizeof(mat2) == 16, "sizeof(mat2) == 16");
static_assert(sizeof(dmat2) == 32, "sizeof(dmat2) == 32");

/*
* 3×3-element matrices
*/

template <typename T>
struct LOL_ATTR_NODISCARD mat_t<T, 3, 3>
: public linear_ops::base<vec_t<T,3>>
{
static int const count = 3;
typedef T scalar_element;
typedef vec_t<T,3> element;
typedef mat_t<T,3,3> type;

inline mat_t() {}
inline mat_t(vec_t<T,3> v0, vec_t<T,3> v1, vec_t<T,3> v2)
: m_data{ v0, v1, v2 } {}

explicit inline mat_t(T const &val)
: m_data{ vec_t<T,3>(val, (T)0, (T)0),
vec_t<T,3>((T)0, val, (T)0),
vec_t<T,3>((T)0, (T)0, val) } {}

explicit inline mat_t(mat_t<T,2,2> m, T const &val = T(1))
: m_data{ vec_t<T,3>(m[0], (T)0),
vec_t<T,3>(m[1], (T)0),
vec_t<T,3>((T)0, (T)0, val) } {}

explicit inline mat_t(mat_t<T,4,4> const &m)
: m_data{ m[0].xyz, m[1].xyz, m[2].xyz } {}

/* Explicit constructor for type conversion */
template<typename U>
explicit inline mat_t(mat_t<U,3,3> const &m)
: m_data{ (element)m[0], (element)m[1], (element)m[2] } {}

explicit mat_t(quat_t<T> const &q);

inline vec_t<T,3>& operator[](size_t n) { return m_data[n]; }
inline vec_t<T,3> const& operator[](size_t n) const { return m_data[n]; }

/* Helpers for transformation matrices */
static mat_t<T,3,3> scale(T x);
static mat_t<T,3,3> scale(T x, T y, T z);
static mat_t<T,3,3> scale(vec_t<T,3> v);
static mat_t<T,3,3> rotate(T radians, T x, T y, T z);
static mat_t<T,3,3> rotate(T radians, vec_t<T,3> v);

static mat_t<T,3,3> fromeuler_xyz(vec_t<T,3> const &v);
static mat_t<T,3,3> fromeuler_xzy(vec_t<T,3> const &v);
static mat_t<T,3,3> fromeuler_yxz(vec_t<T,3> const &v);
static mat_t<T,3,3> fromeuler_yzx(vec_t<T,3> const &v);
static mat_t<T,3,3> fromeuler_zxy(vec_t<T,3> const &v);
static mat_t<T,3,3> fromeuler_zyx(vec_t<T,3> const &v);
static mat_t<T,3,3> fromeuler_xyz(T phi, T theta, T psi);
static mat_t<T,3,3> fromeuler_xzy(T phi, T theta, T psi);
static mat_t<T,3,3> fromeuler_yxz(T phi, T theta, T psi);
static mat_t<T,3,3> fromeuler_yzx(T phi, T theta, T psi);
static mat_t<T,3,3> fromeuler_zxy(T phi, T theta, T psi);
static mat_t<T,3,3> fromeuler_zyx(T phi, T theta, T psi);

static mat_t<T,3,3> fromeuler_xyx(vec_t<T,3> const &v);
static mat_t<T,3,3> fromeuler_xzx(vec_t<T,3> const &v);
static mat_t<T,3,3> fromeuler_yxy(vec_t<T,3> const &v);
static mat_t<T,3,3> fromeuler_yzy(vec_t<T,3> const &v);
static mat_t<T,3,3> fromeuler_zxz(vec_t<T,3> const &v);
static mat_t<T,3,3> fromeuler_zyz(vec_t<T,3> const &v);
static mat_t<T,3,3> fromeuler_xyx(T phi, T theta, T psi);
static mat_t<T,3,3> fromeuler_xzx(T phi, T theta, T psi);
static mat_t<T,3,3> fromeuler_yxy(T phi, T theta, T psi);
static mat_t<T,3,3> fromeuler_yzy(T phi, T theta, T psi);
static mat_t<T,3,3> fromeuler_zxz(T phi, T theta, T psi);
static mat_t<T,3,3> fromeuler_zyz(T phi, T theta, T psi);

static inline mat_t<T,3,3> rotate(mat_t<T,3,3> m, T radians, vec_t<T,3> v)
{
return rotate(radians, v) * m;
}

void printf() const;
std::string tostring() const;

static const mat_t<T,3,3> identity;

private:
vec_t<T,3> m_data[3];
};

static_assert(sizeof(imat3) == 36, "sizeof(imat3) == 36");
static_assert(sizeof(f16mat3) == 18, "sizeof(f16mat3) == 18");
static_assert(sizeof(mat3) == 36, "sizeof(mat3) == 36");
static_assert(sizeof(dmat3) == 72, "sizeof(dmat3) == 72");

/*
* 4×4-element matrices
*/

template <typename T>
struct LOL_ATTR_NODISCARD mat_t<T, 4, 4>
: public linear_ops::base<vec_t<T,4>>
{
static int const count = 4;
typedef T scalar_element;
typedef vec_t<T,4> element;
typedef mat_t<T,4,4> type;

inline mat_t() {}
inline mat_t(vec_t<T,4> v0, vec_t<T,4> v1, vec_t<T,4> v2, vec_t<T,4> v3)
: m_data{ v0, v1, v2, v3 } {}

explicit inline mat_t(T const &val)
: m_data{ vec_t<T,4>(val, (T)0, (T)0, (T)0),
vec_t<T,4>((T)0, val, (T)0, (T)0),
vec_t<T,4>((T)0, (T)0, val, (T)0),
vec_t<T,4>((T)0, (T)0, (T)0, val) } {}

explicit inline mat_t(mat_t<T,2,2> m, T const &val = T(1))
: m_data{ vec_t<T,4>(m[0], (T)0, (T)0),
vec_t<T,4>(m[1], (T)0, (T)0),
vec_t<T,4>((T)0, (T)0, val, (T)0),
vec_t<T,4>((T)0, (T)0, (T)0, val) } {}

explicit inline mat_t(mat_t<T,3,3> m, T const &val = T(1))
: m_data{ vec_t<T,4>(m[0], (T)0),
vec_t<T,4>(m[1], (T)0),
vec_t<T,4>(m[2], (T)0),
vec_t<T,4>((T)0, (T)0, (T)0, val) } {}

/* Explicit constructor for type conversion */
template<typename U>
explicit inline mat_t(mat_t<U,4,4> const &m)
: m_data{ (element)m[0], (element)m[1],
(element)m[2], (element)m[3] } {}

explicit mat_t(quat_t<T> const &q);

inline vec_t<T,4>& operator[](size_t n) { return m_data[n]; }
inline vec_t<T,4> const& operator[](size_t n) const { return m_data[n]; }

/* Helpers for transformation matrices */
static mat_t<T,4,4> translate(T x, T y, T z);
static mat_t<T,4,4> translate(vec_t<T,3> v);

static inline mat_t<T,4,4> scale(T x)
{
return mat_t<T,4,4>(mat_t<T,3,3>::scale(x), (T)1);
}

static inline mat_t<T,4,4> scale(T x, T y, T z)
{
return mat_t<T,4,4>(mat_t<T,3,3>::scale(x, y, z), (T)1);
}

static inline mat_t<T,4,4> scale(vec_t<T,3> v)
{
return mat_t<T,4,4>(mat_t<T,3,3>::scale(v), (T)1);
}

static inline mat_t<T,4,4> translate(mat_t<T,4,4> const &m, vec_t<T,3> v)
{
return translate(v) * m;
}

static inline mat_t<T,4,4> rotate(T radians, T x, T y, T z)
{
return mat_t<T,4,4>(mat_t<T,3,3>::rotate(radians, x, y, z), (T)1);
}

static inline mat_t<T,4,4> rotate(T radians, vec_t<T,3> v)
{
return mat_t<T,4,4>(mat_t<T,3,3>::rotate(radians, v), (T)1);
}

static inline mat_t<T,4,4> rotate(mat_t<T,4,4> &m, T radians, vec_t<T,3> v)
{
return rotate(radians, v) * m;
}

static mat_t<T,4,4> fromeuler_xyz(vec_t<T,3> const &v);
static mat_t<T,4,4> fromeuler_xzy(vec_t<T,3> const &v);
static mat_t<T,4,4> fromeuler_yxz(vec_t<T,3> const &v);
static mat_t<T,4,4> fromeuler_yzx(vec_t<T,3> const &v);
static mat_t<T,4,4> fromeuler_zxy(vec_t<T,3> const &v);
static mat_t<T,4,4> fromeuler_zyx(vec_t<T,3> const &v);
static mat_t<T,4,4> fromeuler_xyz(T phi, T theta, T psi);
static mat_t<T,4,4> fromeuler_xzy(T phi, T theta, T psi);
static mat_t<T,4,4> fromeuler_yxz(T phi, T theta, T psi);
static mat_t<T,4,4> fromeuler_yzx(T phi, T theta, T psi);
static mat_t<T,4,4> fromeuler_zxy(T phi, T theta, T psi);
static mat_t<T,4,4> fromeuler_zyx(T phi, T theta, T psi);

static mat_t<T,4,4> fromeuler_xyx(vec_t<T,3> const &v);
static mat_t<T,4,4> fromeuler_xzx(vec_t<T,3> const &v);
static mat_t<T,4,4> fromeuler_yxy(vec_t<T,3> const &v);
static mat_t<T,4,4> fromeuler_yzy(vec_t<T,3> const &v);
static mat_t<T,4,4> fromeuler_zxz(vec_t<T,3> const &v);
static mat_t<T,4,4> fromeuler_zyz(vec_t<T,3> const &v);
static mat_t<T,4,4> fromeuler_xyx(T phi, T theta, T psi);
static mat_t<T,4,4> fromeuler_xzx(T phi, T theta, T psi);
static mat_t<T,4,4> fromeuler_yxy(T phi, T theta, T psi);
static mat_t<T,4,4> fromeuler_yzy(T phi, T theta, T psi);
static mat_t<T,4,4> fromeuler_zxz(T phi, T theta, T psi);
static mat_t<T,4,4> fromeuler_zyz(T phi, T theta, T psi);

/* Helpers for view matrices */
static mat_t<T,4,4> lookat(vec_t<T,3> eye, vec_t<T,3> center, vec_t<T,3> up);

/* Helpers for projection matrices; FOV values are in radians */
static mat_t<T,4,4> ortho(T left, T right, T bottom, T top, T near, T far);
static mat_t<T,4,4> ortho(T width, T height, T near, T far);
static mat_t<T,4,4> frustum(T left, T right, T bottom, T top, T near, T far);
static mat_t<T,4,4> perspective(T fov_y, T width, T height, T near, T far);
static mat_t<T,4,4> shifted_perspective(T fov_y, T screen_size, T screen_ratio_yx, T near, T far);

void printf() const;
std::string tostring() const;

static const mat_t<T,4,4> identity;

private:
vec_t<T,4> m_data[4];
};

static_assert(sizeof(imat4) == 64, "sizeof(imat4) == 64");
static_assert(sizeof(f16mat4) == 32, "sizeof(f16mat4) == 32");
static_assert(sizeof(mat4) == 64, "sizeof(mat4) == 64");
static_assert(sizeof(dmat4) == 128, "sizeof(dmat4) == 128");

/*
* stdstream method implementations
*/

template<class U, int COLS, int ROWS>
static std::ostream &operator<<(std::ostream &stream,
mat_t<U,COLS,ROWS> const &m)
{
for (int y = 0; y < ROWS; ++y)
{
stream << (y == 0 ? "(" : ", ");
for (int x = 0; x < COLS; ++x)
stream << (x == 0 ? "(" : ", ") << m[x][y];
stream << ")";
}
return stream << ")";
}

/*
* Transpose any matrix
*/

template<typename T, int COLS, int ROWS>
static inline mat_t<T, ROWS, COLS> transpose(mat_t<T, COLS, ROWS> const &m)
{
mat_t<T, ROWS, COLS> ret;
for (int i = 0; i < COLS; ++i)
for (int j = 0; j < ROWS; ++j)
ret[j][i] = m[i][j];
return ret;
}

/*
* Compute a square submatrix, useful for minors and cofactor matrices
*/

template<typename T, int N>
mat_t<T, N - 1, N - 1> submatrix(mat_t<T, N, N> const &m, int i, int j)
{
ASSERT(i >= 0); ASSERT(j >= 0); ASSERT(i < N); ASSERT(j < N);

mat_t<T, N - 1, N - 1> ret;
for (int i2 = 0; i2 < N - 1; ++i2)
for (int j2 = 0; j2 < N - 1; ++j2)
ret[i2][j2] = m[i2 + (i2 >= i)][j2 + (j2 >= j)];

return ret;
}

/*
* Compute square matrix cofactor
*/

template<typename T, int N> LOL_ATTR_NODISCARD
T cofactor(mat_t<T, N, N> const &m, int i, int j)
{
ASSERT(i >= 0); ASSERT(j >= 0); ASSERT(i < N); ASSERT(j < N);
T tmp = determinant(submatrix(m, i, j));
return ((i + j) & 1) ? -tmp : tmp;
}

template<typename T> LOL_ATTR_NODISCARD
T cofactor(mat_t<T, 2, 2> const &m, int i, int j)
{
/* This specialisation shouldn't be needed, but Visual Studio. */
ASSERT(i >= 0); ASSERT(j >= 0); ASSERT(i < 2); ASSERT(j < 2);
T tmp = m[1 - i][1 - j];
return (i ^ j) ? -tmp : tmp;
}

// Lu decomposition with partial pivoting
template<typename T, int N> LOL_ATTR_NODISCARD
std::tuple<mat_t<T, N, N>, vec_t<int, N>, int> lu_decomposition(mat_t<T, N, N> const &m)
{
mat_t<T, N, N> lu = m;
vec_t<int, N> perm;
int sign = 1;

for (int i = 0; i < N; ++i)
perm[i] = i;

for (int k = 0; k < N; ++k)
{
// Find row with the largest absolute value
int best_j = k;
for (int j = k + 1; j < N; ++j)
if (abs(lu[k][j]) > lol::abs(lu[k][best_j]))
best_j = j;

// Swap rows in result
if (best_j != k)
{
std::swap(perm[k], perm[best_j]);
sign = -sign;
for (int i = 0; i < N; ++i)
std::swap(lu[i][k], lu[i][best_j]);
}

// Compute the Schur complement in the lower triangular part
for (int j = k + 1; j < N; ++j)
{
lu[k][j] /= lu[k][k];
for (int i = k + 1; i < N; ++i)
lu[i][j] -= lu[i][k] * lu[k][j];
}
}

return std::make_tuple(lu, perm, sign);
}

/*
* Compute square matrix determinant, with a specialisation for 1×1 matrices
*/

template<typename T, int N> LOL_ATTR_NODISCARD
T determinant(mat_t<T, N, N> const &m)
{
auto lup = lu_decomposition(m);

T det(T(std::get<2>(lup)));
for (int i = 0; i < N; ++i)
det *= std::get<0>(lup)[i][i];

return det;
}

template<typename T> LOL_ATTR_NODISCARD
T const & determinant(mat_t<T, 1, 1> const &m)
{
return m[0][0];
}

// Compute inverse of the L matrix of an LU decomposition
template<typename T, int N>
mat_t<T, N, N> l_inverse(mat_t<T, N, N> const & lu)
{
mat_t<T, N, N> ret { 0 };

for (int j = 0; j < N; ++j)
{
for (int i = j; i >= 0; --i)
{
T sum = 0;
for (int k = i + 1; k <= j; ++k)
sum += ret[k][j] * lu[i][k];
ret[i][j] = T(j == i ? 1 : 0) - sum;
}
}

return ret;
}

// Compute inverse of the U matrix of an LU decomposition
template<typename T, int N>
mat_t<T, N, N> u_inverse(mat_t<T, N, N> const & lu)
{
mat_t<T, N, N> ret { 0 };

for (int i = 0; i < N; ++i)
{
for (int j = i; j < N; ++j)
{
T sum = 0;
for (int k = i; k < j; ++k)
sum += ret[k][i] * lu[j][k];
ret[j][i] = ((i == j ? 1 : 0) - sum) / lu[j][j];
}
}

return ret;
}

/*
* Compute square matrix inverse
*/

template<typename T, int N>
mat_t<T, N, N> inverse(mat_t<T, N, N> const &m)
{
auto lup = lu_decomposition(m);
auto lu = std::get<0>(lup);
auto p = std::get<1>(lup);
auto invlu = u_inverse(lu) * l_inverse(lu);

// Rearrange columns according to the original permutation vector
mat_t<T, N, N> ret;
for (int i = 0; i < N; ++i)
ret[p[i]] = invlu[i];
return ret;
}

/*
* Matrix-vector and vector-matrix multiplication
*/

template<typename T, int COLS, int ROWS, int SWIZZLE>
static inline vec_t<T, ROWS> operator *(mat_t<T, COLS, ROWS> const &m,
vec_t<T, COLS, SWIZZLE> const &v)
{
vec_t<T, ROWS> ret(T(0));
for (int i = 0; i < COLS; ++i)
ret += m[i] * v[i];
return ret;
}

template<typename T, int COLS, int ROWS, int SWIZZLE>
static inline vec_t<T, COLS> operator *(vec_t<T, ROWS, SWIZZLE> const &v,
mat_t<T, COLS, ROWS> const &m)
{
vec_t<T, COLS> ret(T(0));
for (int i = 0; i < COLS; ++i)
ret[i] = dot(v, m[i]);
return ret;
}

/*
* Matrix-matrix multiplication
*/

template<typename T, int COLS, int N, int ROWS>
static inline mat_t<T, COLS, ROWS> operator *(mat_t<T, N, ROWS> const &a,
mat_t<T, COLS, N> const &b)
{
mat_t<T, COLS, ROWS> ret;
for (int i = 0; i < COLS; ++i)
ret[i] = a * b[i];
return ret;
}

template<typename T, int N>
static inline mat_t<T, N, N> &operator *=(mat_t<T, N, N> &a,
mat_t<T, N, N> const &b)
{
return a = a * b;
}

/*
* Vector-vector outer product
*/

template<typename T, int COLS, int ROWS>
static inline mat_t<T, COLS, ROWS> outer(vec_t<T, ROWS> const &a,
vec_t<T, COLS> const &b)
{
/* Valid cast because mat_t and vec_t have similar layouts */
return *reinterpret_cast<mat_t<T, 1, ROWS> const *>(&a)
* *reinterpret_cast<mat_t<T, COLS, 1> const *>(&b);
}

/*
* Matrix-matrix outer product (Kronecker product)
*/

template<typename T, int COLS1, int COLS2, int ROWS1, int ROWS2>
static inline mat_t<T, COLS1 * COLS2, ROWS1 * ROWS2>
outer(mat_t<T, COLS1, ROWS1> const &a, mat_t<T, COLS2, ROWS2> const &b)
{
mat_t<T, COLS1 * COLS2, ROWS1 * ROWS2> ret;
for (int i1 = 0; i1 < COLS1; ++i1)
for (int i2 = 0; i2 < COLS2; ++i2)
{
/* Valid cast because mat_t and vec_t have similar layouts */
*reinterpret_cast<mat_t<T, ROWS1, ROWS2> *>(&ret[i1 * COLS2 + i2])
= outer(b[i2], a[i1]);
}
return ret;
}

/*
* Constants
*/

template<typename T>
mat_t<T,2,2> const mat_t<T,2,2>::identity = mat_t<T,2,2>((T)1);
template<typename T>
mat_t<T,3,3> const mat_t<T,3,3>::identity = mat_t<T,3,3>((T)1);
template<typename T>
mat_t<T,4,4> const mat_t<T,4,4>::identity = mat_t<T,4,4>((T)1);

} /* namespace lol */

#if _WIN32
# pragma pop_macro("near")
# pragma pop_macro("far")
#endif


+ 0
- 362
src/lol/math/ops.h 파일 보기

@@ -1,362 +0,0 @@
//
// Lol Engine
//
// Copyright: (c) 2010-2014 Sam Hocevar <sam@hocevar.net>
// This program is free software; you can redistribute it and/or
// modify it under the terms of the Do What The Fuck You Want To
// Public License, Version 2, as published by Sam Hocevar. See
// http://www.wtfpl.net/ for more details.
//

#pragma once

//
// Operations for vector classes
// -----------------------------
//

#include <ostream>
#include <type_traits>

#include <lol/math/half.h>
#include <lol/math/real.h>

namespace lol
{

/*
* Utility namespaces for traits -- this file uses a combination of
* ADL black magic and enable_if to ensure that only the expected type
* conversions are done.
*
* vec_t (swizzle) needs swizzle_ops
* vec_t (generic) needs linear_ops + componentwise_ops
* vec_t (specialisation) needs swizzle_ops + linear_ops + componentwise_ops
* mat_t (all) needs linear_ops
* cmplx_t quat_t need linear_ops
*
* We can only inherit from one class, because Visual Studio will not
* perform EBCO (empty base class optimisation) when there is multiple
* inheritance.
*/

namespace linear_ops
{
template<typename T>
struct base {};
}

namespace componentwise_ops
{
template<typename T>
struct base : public linear_ops::base<T> {};
}

namespace swizzle_ops
{
template<typename T, int SWIZZLE = FULL_SWIZZLE>
struct base {};

template<typename T>
struct base<T, FULL_SWIZZLE> : public componentwise_ops::base<T> {};
}

/*
* Operators for swizzled vectors. Since template deduction cannot be
* done for two arbitrary vec_t<> values, we help the compiler understand
* the expected type.
*/

namespace swizzle_ops
{

template<typename T, int N, int SWIZZLE1, int SWIZZLE2> LOL_ATTR_NODISCARD
static inline typename std::enable_if<SWIZZLE1 != FULL_SWIZZLE || SWIZZLE2 != FULL_SWIZZLE, bool>::type
operator ==(vec_t<T,N,SWIZZLE1> const &a, vec_t<T,N,SWIZZLE2> const &b)
{
return vec_t<T,N>(a) == vec_t<T,N>(b);
}

template<typename T, int N, int SWIZZLE1, int SWIZZLE2> LOL_ATTR_NODISCARD
static inline typename std::enable_if<SWIZZLE1 != FULL_SWIZZLE || SWIZZLE2 != FULL_SWIZZLE, bool>::type
operator !=(vec_t<T,N,SWIZZLE1> const &a, vec_t<T,N,SWIZZLE2> const &b)
{
return vec_t<T,N>(a) != vec_t<T,N>(b);
}

#define LOL_SWIZZLE_V_VV_OP(op) \
template<typename T, int N, int SWIZZLE1, int SWIZZLE2> \
inline typename std::enable_if<SWIZZLE1 != FULL_SWIZZLE \
|| SWIZZLE2 != FULL_SWIZZLE,vec_t<T,N>>::type \
operator op(vec_t<T,N,SWIZZLE1> const &a, \
vec_t<T,N,SWIZZLE2> const &b) \
{ \
return vec_t<T,N>(a) op vec_t<T,N>(b); \
} \
\
template<typename T, int N, int SWIZZLE> \
inline typename std::enable_if<SWIZZLE != FULL_SWIZZLE,vec_t<T,N>>::type & \
operator op##=(vec_t<T,N> &a, \
vec_t<T,N,SWIZZLE> const &b) \
{ \
return a op##= vec_t<T,N>(b); \
} \
\
template<typename T, int N, int SWIZZLE> \
inline typename std::enable_if<SWIZZLE != FULL_SWIZZLE,vec_t<T,N>>::type \
operator op(vec_t<T,N,SWIZZLE> const &a, T const &b) \
{ \
return vec_t<T,N>(a) op b; \
}

LOL_SWIZZLE_V_VV_OP(+)
LOL_SWIZZLE_V_VV_OP(-)
LOL_SWIZZLE_V_VV_OP(*)
LOL_SWIZZLE_V_VV_OP(/)

#undef LOL_SWIZZLE_V_VV_OP

} /* namespace swizzle_ops */


/*
* Linear operations: operators and functions that work on all types
* (vectors, matrices, quaternions...) such as addition or equality test.
*
* Others, e.g. multiplication, cannot be implemented here, since it should
* be implemented as per-component multiplication for vectors, and matrix
* product for matrices.
*/

namespace linear_ops
{

/*
* Comparisons
*/

template<typename V> LOL_ATTR_NODISCARD
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, bool>::type
operator ==(V const &a, V const &b)
{
for (int i = 0; i < V::count; ++i)
if (!(a[i] == b[i]))
return false;
return true;
}

template<typename V> LOL_ATTR_NODISCARD
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, bool>::type
operator !=(V const &a, V const &b)
{
for (int i = 0; i < V::count; ++i)
if (a[i] != b[i])
return true;
return false;
}

/*
* Unary plus and minus
*/

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, typename V::type>::type
operator +(V const &v)
{
return v;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, typename V::type>::type
operator -(V const &v)
{
typename V::type ret;
for (int i = 0; i < V::count; ++i)
ret[i] = -v[i];
return ret;
}

/*
* Addition and subtraction
*/

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, typename V::type>::type
operator +(V const &a, V const &b)
{
typename V::type ret;
for (int i = 0; i < V::count; ++i)
ret[i] = a[i] + b[i];
return ret;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, typename V::type>::type
&operator +=(V &a, V const &b)
{
return a = a + b;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, typename V::type>::type
operator -(V const &a, V const &b)
{
typename V::type ret;
for (int i = 0; i < V::count; ++i)
ret[i] = a[i] - b[i];
return ret;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, typename V::type>::type
&operator -=(V &a, V const &b)
{
return a = a - b;
}

/*
* Multiplication by scalar (left)
*/

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::scalar_element>, V>::value, typename V::type>::type
operator *(typename V::scalar_element const &val, V const &a)
{
typename V::type ret;
for (int i = 0; i < V::count; ++i)
ret[i] = val * a[i];
return ret;
}

/*
* Multiplication/division by scalar (right)
*/

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::scalar_element>, V>::value, typename V::type>::type
operator *(V const &a, typename V::scalar_element const &val)
{
typename V::type ret;
for (int i = 0; i < V::count; ++i)
ret[i] = a[i] * val;
return ret;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::scalar_element>, V>::value, typename V::type>::type &
operator *=(V &a, typename V::scalar_element const &val)
{
return a = a * val;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::scalar_element>, V>::value, typename V::type>::type
operator /(V const &a, typename V::scalar_element const &val)
{
typename V::type ret;
for (int i = 0; i < V::count; ++i)
ret[i] = a[i] / val;
return ret;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::scalar_element>, V>::value, typename V::type>::type &
operator /=(V &a, typename V::scalar_element const &val)
{
return a = a / val;
}

} /* namespace linear_ops */


/*
* Operations that work component-wise, such as comparisons or multiplication.
* This is only for vector types, as the other types (matrices, quaternions,
* complexes) have different meanings.
*/

namespace componentwise_ops
{

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, typename V::type>::type
operator *(V const &a, V const &b)
{
typename V::type ret;
for (int i = 0; i < V::count; ++i)
ret[i] = a[i] * b[i];
return ret;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, typename V::type>::type
&operator *=(V &a, V const &b)
{
return a = a * b;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, typename V::type>::type
operator /(V const &a, V const &b)
{
typename V::type ret;
for (int i = 0; i < V::count; ++i)
ret[i] = a[i] / b[i];
return ret;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, typename V::type>::type
&operator /=(V &a, V const &b)
{
return a = a / b;
}

/*
* Comparisons
*/

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, bool>::type
operator <(V const &a, V const &b)
{
for (int i = 0; i < V::count; ++i)
if (!(a[i] < b[i]))
return false;
return true;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, bool>::type
operator >(V const &a, V const &b)
{
for (int i = 0; i < V::count; ++i)
if (!(a[i] > b[i]))
return false;
return true;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, bool>::type
operator <=(V const &a, V const &b)
{
for (int i = 0; i < V::count; ++i)
if (!(a[i] <= b[i]))
return false;
return true;
}

template<typename V>
static inline typename std::enable_if<std::is_base_of<base<typename V::element>, V>::value, bool>::type
operator >=(V const &a, V const &b)
{
for (int i = 0; i < V::count; ++i)
if (!(a[i] >= b[i]))
return false;
return true;
}

} /* namespace componentwise_ops */

} /* namespace lol */


+ 0
- 499
src/lol/math/transform.h 파일 보기

@@ -1,499 +0,0 @@
//
// Lol Engine
//
// Copyright © 2010—2019 Sam Hocevar <sam@hocevar.net>
//
// Lol Engine is free software. It comes without any warranty, to
// the extent permitted by applicable law. You can redistribute it
// and/or modify it under the terms of the Do What the Fuck You Want
// to Public License, Version 2, as published by the WTFPL Task Force.
// See http://www.wtfpl.net/ for more details.
//

#pragma once

//
// The complex, quaternion and dual quaternion classes
// ---------------------------------------------------
//

#include <lol/math/vector.h>

#include <ostream>

namespace lol
{

/*
* 2-element transforms: complex numbers
*/

template<typename T>
struct LOL_ATTR_NODISCARD cmplx_t : public linear_ops::base<T>
{
static int const count = 2;
typedef T scalar_element;
typedef T element;
typedef cmplx_t<T> type;

inline constexpr cmplx_t() = default;
inline constexpr cmplx_t(cmplx_t<T> const &) = default;
inline constexpr cmplx_t(T X) : x(X), y(T(0)) {}
inline constexpr cmplx_t(T X, T Y) : x(X), y(Y) {}

template<typename U>
explicit inline constexpr cmplx_t(cmplx_t<U> const &z)
: x(z.x), y(z.y) {}

LOL_COMMON_MEMBER_OPS(x)

inline cmplx_t<T> operator *(cmplx_t<T> const &val) const
{
return cmplx_t<T>(x * val.x - y * val.y, x * val.y + y * val.x);
}

inline cmplx_t<T> operator *=(cmplx_t<T> const &val)
{
return *this = (*this) * val;
}

inline cmplx_t<T> operator ~() const
{
return cmplx_t<T>(x, -y);
}

template<typename U>
friend std::ostream &operator<<(std::ostream &stream, cmplx_t<U> const &v);

T x, y;
};

static_assert(sizeof(f16cmplx) == 4, "sizeof(f16cmplx) == 4");
static_assert(sizeof(cmplx) == 8, "sizeof(cmplx) == 8");
static_assert(sizeof(dcmplx) == 16, "sizeof(dcmplx) == 16");

/*
* 4-element transforms: quaternions
*/

template<typename T>
struct LOL_ATTR_NODISCARD quat_t : public linear_ops::base<T>
{
static int const count = 4;
typedef T scalar_element;
typedef T element;
typedef quat_t<T> type;

/* Default constructor and copy constructor */
inline constexpr quat_t() = default;
inline constexpr quat_t(quat_t<T> const &) = default;

/* Explicit constructor for type conversion */
template<typename U>
explicit inline constexpr quat_t(quat_t<U> const &q)
: w(q.w), x(q.x), y(q.y), z(q.z) {}

/* Various explicit constructors */
explicit inline constexpr quat_t(T W, T X, T Y, T Z)
: w(W), x(X), y(Y), z(Z) {}
explicit inline constexpr quat_t(T W)
: w(W), x(0), y(0), z(0) {}

/* Construct a unit quaternion from a pure rotation matrix */
explicit quat_t(mat_t<T,3,3> const &m)
{
T tr = m[0][0] + m[1][1] + m[2][2];

if (tr > T(0))
{
T const p = T(0.5) * std::sqrt(T(1) + tr);
T const q = T(0.25) / p;

w = p;
x = q * (m[1][2] - m[2][1]);
y = q * (m[2][0] - m[0][2]);
z = q * (m[0][1] - m[1][0]);
}
else
{
int i = (m[0][0] > m[1][1] && m[0][0] > m[2][2]) ? 0
: (m[1][1] > m[2][2]) ? 1
: 2;
int j = (i + 1) % 3, k = (i + 2) % 3;

T const p = T(0.5) * lol::sqrt(T(1) - tr + m[i][i] + m[i][i]);
T const q = T(0.25) / p;

w = q * (m[j][k] - m[k][j]);
(*this)[1 + i] = p;
(*this)[1 + j] = q * (m[i][j] + m[j][i]);
(*this)[1 + k] = q * (m[k][i] + m[i][k]);
}
}

LOL_COMMON_MEMBER_OPS(w)

inline quat_t operator *(quat_t const &val) const
{
vec_t<T,3> v1(x, y, z);
vec_t<T,3> v2(val.x, val.y, val.z);
vec_t<T,3> v3 = cross(v1, v2) + w * v2 + val.w * v1;
return quat_t(w * val.w - dot(v1, v2), v3.x, v3.y, v3.z);
}

inline quat_t operator *=(quat_t const &val)
{
return *this = (*this * val);
}

/* Create a unit quaternion representing a rotation around an axis. */
static quat_t rotate(T radians, T x, T y, T z);
static quat_t rotate(T radians, vec_t<T,3> const &v);

/* Create a unit quaternion representing a rotation between two vectors.
* Input vectors need not be normalised. */
static quat_t rotate(vec_t<T,3> const &src, vec_t<T,3> const &dst);

/* Convert from Euler angles. The axes in fromeuler_xyx are
* x, then y', then x", ie. the axes are attached to the model.
* If you want to rotate around static axes, just reverse the order
* of the arguments. Angle values are in radians. */
static quat_t fromeuler_xyx(vec_t<T,3> const &v);
static quat_t fromeuler_xzx(vec_t<T,3> const &v);
static quat_t fromeuler_yxy(vec_t<T,3> const &v);
static quat_t fromeuler_yzy(vec_t<T,3> const &v);
static quat_t fromeuler_zxz(vec_t<T,3> const &v);
static quat_t fromeuler_zyz(vec_t<T,3> const &v);
static quat_t fromeuler_xyx(T phi, T theta, T psi);
static quat_t fromeuler_xzx(T phi, T theta, T psi);
static quat_t fromeuler_yxy(T phi, T theta, T psi);
static quat_t fromeuler_yzy(T phi, T theta, T psi);
static quat_t fromeuler_zxz(T phi, T theta, T psi);
static quat_t fromeuler_zyz(T phi, T theta, T psi);

/* Convert from Tait-Bryan angles (incorrectly called Euler angles,
* but since everyone does it…). The axes in fromeuler_xyz are
* x, then y', then z", ie. the axes are attached to the model.
* If you want to apply yaw around x, pitch around y, and roll
* around z, use fromeuler_xyz. Angle values are in radians.
* If you want to rotate around static axes, reverse the order in
* the function name (_zyx instead of _xyz) AND reverse the order
* of the arguments. */
static quat_t fromeuler_xyz(vec_t<T,3> const &v);
static quat_t fromeuler_xzy(vec_t<T,3> const &v);
static quat_t fromeuler_yxz(vec_t<T,3> const &v);
static quat_t fromeuler_yzx(vec_t<T,3> const &v);
static quat_t fromeuler_zxy(vec_t<T,3> const &v);
static quat_t fromeuler_zyx(vec_t<T,3> const &v);
static quat_t fromeuler_xyz(T phi, T theta, T psi);
static quat_t fromeuler_xzy(T phi, T theta, T psi);
static quat_t fromeuler_yxz(T phi, T theta, T psi);
static quat_t fromeuler_yzx(T phi, T theta, T psi);
static quat_t fromeuler_zxy(T phi, T theta, T psi);
static quat_t fromeuler_zyx(T phi, T theta, T psi);

inline quat_t operator ~() const
{
return quat_t(w, -x, -y, -z);
}

/* Transform vectors or points */
inline vec_t<T,3> transform(vec_t<T,3> const &v) const
{
quat_t p = quat_t(0, v.x, v.y, v.z);
quat_t q = *this * p / *this;
return vec_t<T,3>(q.x, q.y, q.z);
}

inline vec_t<T,4> transform(vec_t<T,4> const &v) const
{
quat_t p = quat_t(0, v.x, v.y, v.z);
quat_t q = *this * p / *this;
return vec_t<T,4>(q.x, q.y, q.z, v.w);
}

inline vec_t<T,3> operator *(vec_t<T,3> const &v) const
{
return transform(v);
}

inline vec_t<T,4> operator *(vec_t<T,4> const &v) const
{
return transform(v);
}

inline vec_t<T,3> axis()
{
vec_t<T,3> v(x, y, z);
T n2 = sqlength(v);
if (n2 <= (T)1e-6)
return vec_t<T,3>::axis_x;
return normalize(v);
}

LOL_ATTR_NODISCARD inline T angle()
{
vec_t<T,3> v(x, y, z);
T n2 = sqlength(v);
if (n2 <= (T)1e-6)
return (T)0;
return (T)2 * lol::atan2(lol::sqrt(n2), w);
}

template<typename U>
friend std::ostream &operator<<(std::ostream &stream, quat_t<U> const &v);

/* XXX: storage order is wxyz, unlike vectors! */
T w, x, y, z;
};

static_assert(sizeof(f16quat) == 8, "sizeof(f16quat) == 8");
static_assert(sizeof(quat) == 16, "sizeof(quat) == 16");
static_assert(sizeof(dquat) == 32, "sizeof(dquat) == 32");

/*
* SQT transforms: scale / rotation / translation
*/

template<typename T>
struct LOL_ATTR_NODISCARD sqt_t
{
/* Default constructor and copy constructor */
inline constexpr sqt_t() = default;
inline constexpr sqt_t(sqt_t<T> const &) = default;
inline constexpr sqt_t<T>& operator =(const sqt_t<T>&) = default;

/* Explicit constructor for type conversion */
template<typename U>
explicit inline constexpr sqt_t(sqt_t<U> const &other)
: q(other.q), t(other.t), s(other.s) {}

/* Various explicit constructors */
explicit inline constexpr sqt_t(T const &s_,
quat_t<T> const &q_,
vec_t<T,3> const &t_)
: q(q_), t(t_), s(s_) {}

explicit inline constexpr sqt_t(T const &s_)
: q(1.f), t(0.f), s(s_) {}

explicit inline constexpr sqt_t(quat_t<T> const &q_)
: q(q_), t(0.f), s(1.f) {}

explicit inline constexpr sqt_t(vec_t<T,3> const &t_)
: q(1.f), t(t_), s(1.f) {}

/* Transform vectors or points */
inline vec_t<T,3> transform(vec_t<T,3> const &v) const
{
return t + q.transform(s * v);
}

inline vec_t<T,4> transform(vec_t<T,4> const &v) const
{
// XXX: needs serious testing for w != 1
vec_t<T,4> tmp = q.transform(vec_t<T,4>(s * v.xyz, v.w));
return vec_t<T,4>(tmp.xyz, 0.f) + vec_t<T,4>(t, 1.f) * tmp.w;
}

inline vec_t<T,3> operator *(vec_t<T,3> const &v) const
{
return transform(v);
}

inline vec_t<T,4> operator *(vec_t<T,4> const &v) const
{
return transform(v);
}

/* Compose two SQTs together */
inline sqt_t<T> operator *(sqt_t<T> const &other) const
{
return sqt_t<T>(s * other.s,
q * other.q,
transform(other.t));
}

quat_t<T> q;
vec_t<T,3> t;
T s;
};

/*
* stdstream method implementations
*/

template<typename U>
std::ostream &operator<<(std::ostream &stream, cmplx_t<U> const &c)
{
return stream << "(" << c.x << ", " << c.y << ")";
}

template<typename U>
std::ostream &operator<<(std::ostream &stream, quat_t<U> const &q)
{
return stream << "(" << q.w << ", " << q.x << ", "
<< q.y << ", " << q.z << ")";
}

/*
* Common operations on transforms
*/

template<typename T> LOL_ATTR_NODISCARD
static inline T dot(cmplx_t<T> const &t1, cmplx_t<T> const &t2)
{
T ret(0);
for (size_t i = 0; i < sizeof(t1) / sizeof(T); ++i)
ret += t1[i] * t2[i];
return ret;
}

template<typename T> LOL_ATTR_NODISCARD
static inline T sqlength(cmplx_t<T> const &t)
{
return dot(t, t);
}

template<typename T> LOL_ATTR_NODISCARD
static inline T length(cmplx_t<T> const &t)
{
/* FIXME: this is not very nice */
return (T)sqrt((double)sqlength(t));
}

template<typename T> LOL_ATTR_NODISCARD
static inline T norm(cmplx_t<T> const &t)
{
return length(t);
}

template<typename T>
static inline cmplx_t<T> normalize(cmplx_t<T> const &z)
{
T norm = (T)length(z);
return norm ? z / norm : cmplx_t<T>(T(0));
}

/* XXX: duplicate */

template<typename T> LOL_ATTR_NODISCARD
static inline T dot(quat_t<T> const &t1, quat_t<T> const &t2)
{
T ret(0);
for (size_t i = 0; i < sizeof(t1) / sizeof(T); ++i)
ret += t1[i] * t2[i];
return ret;
}

template<typename T> LOL_ATTR_NODISCARD
static inline T sqlength(quat_t<T> const &t)
{
return dot(t, t);
}

template<typename T> LOL_ATTR_NODISCARD
static inline T length(quat_t<T> const &t)
{
/* FIXME: this is not very nice */
return (T)sqrt((double)sqlength(t));
}

template<typename T> LOL_ATTR_NODISCARD
static inline T norm(quat_t<T> const &t)
{
return length(t);
}

template<typename T>
static inline quat_t<T> normalize(quat_t<T> const &z)
{
T norm = (T)length(z);
return norm ? z / norm : quat_t<T>(T(0));
}

/*
* Complex numbers only
*/

template<typename T>
static inline cmplx_t<T> inverse(cmplx_t<T> const &z)
{
return ~z / sqlength(z);
}

template<typename T>
static inline cmplx_t<T> operator /(T a, cmplx_t<T> const &b)
{
return a * inverse(b);
}

template<typename T>
static inline cmplx_t<T> operator /(cmplx_t<T> a, cmplx_t<T> const &b)
{
return a * inverse(b);
}

template<typename T> LOL_ATTR_NODISCARD
static inline bool operator ==(cmplx_t<T> const &a, T b)
{
return (a.x == b) && !a.y;
}

template<typename T> LOL_ATTR_NODISCARD
static inline bool operator !=(cmplx_t<T> const &a, T b)
{
return (a.x != b) || a.y;
}

template<typename T> LOL_ATTR_NODISCARD
static inline bool operator ==(T a, cmplx_t<T> const &b) { return b == a; }

template<typename T> LOL_ATTR_NODISCARD
static inline bool operator !=(T a, cmplx_t<T> const &b) { return b != a; }

/*
* Quaternions only
*/

template<typename T>
static inline quat_t<T> inverse(quat_t<T> const &q)
{
return ~q / sqlength(q);
}

template<typename T>
static inline quat_t<T> operator /(T x, quat_t<T> const &y)
{
return x * inverse(y);
}

template<typename T>
static inline quat_t<T> operator /(quat_t<T> const &x, quat_t<T> const &y)
{
return x * inverse(y);
}

template<typename T>
extern quat_t<T> slerp(quat_t<T> const &qa, quat_t<T> const &qb, T f);

/*
* SQTs only
*/

template<typename T>
static inline sqt_t<T> inverse(sqt_t<T> const &tr)
{
auto inv_s = T(1) / tr.s;
auto inv_q = inverse(tr.q);
return sqt_t<T>(inv_s, inv_q, inv_q * tr.t * -inv_s);
}

template<typename T>
static inline sqt_t<T> operator /(sqt_t<T> const &x, sqt_t<T> const &y)
{
return x * inverse(y);
}

} /* namespace lol */


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src/lol/math/vector.h
파일 크기가 너무 크기때문에 변경 상태를 표시하지 않습니다.
파일 보기


+ 0
- 226
src/math/matrix.cpp 파일 보기

@@ -1,226 +0,0 @@
//
// Lol Engine
//
// Copyright © 2010—2015 Sam Hocevar <sam@hocevar.net>
//
// Lol Engine is free software. It comes without any warranty, to
// the extent permitted by applicable law. You can redistribute it
// and/or modify it under the terms of the Do What the Fuck You Want
// to Public License, Version 2, as published by the WTFPL Task Force.
// See http://www.wtfpl.net/ for more details.
//

#include <lol/engine-internal.h>

namespace lol
{

template<> mat3 mat3::scale(float x, float y, float z)
{
mat3 ret(1.0f);

ret[0][0] = x;
ret[1][1] = y;
ret[2][2] = z;

return ret;
}

template<> mat3 mat3::scale(float x)
{
return scale(x, x, x);
}

template<> mat3 mat3::scale(vec3 v)
{
return scale(v.x, v.y, v.z);
}

template<> mat4 mat4::translate(float x, float y, float z)
{
mat4 ret(1.0f);
ret[3][0] = x;
ret[3][1] = y;
ret[3][2] = z;
return ret;
}

template<> mat4 mat4::translate(vec3 v)
{
return translate(v.x, v.y, v.z);
}

template<> mat2 mat2::rotate(float radians)
{
float st = sin(radians);
float ct = cos(radians);

mat2 ret;

ret[0][0] = ct;
ret[0][1] = st;

ret[1][0] = -st;
ret[1][1] = ct;

return ret;
}

template<> mat3 mat3::rotate(float radians, float x, float y, float z)
{
float st = sin(radians);
float ct = cos(radians);

float len = std::sqrt(x * x + y * y + z * z);
float invlen = len ? 1.0f / len : 0.0f;
x *= invlen;
y *= invlen;
z *= invlen;

float mtx = (1.0f - ct) * x;
float mty = (1.0f - ct) * y;
float mtz = (1.0f - ct) * z;

mat3 ret;

ret[0][0] = x * mtx + ct;
ret[0][1] = x * mty + st * z;
ret[0][2] = x * mtz - st * y;

ret[1][0] = y * mtx - st * z;
ret[1][1] = y * mty + ct;
ret[1][2] = y * mtz + st * x;

ret[2][0] = z * mtx + st * y;
ret[2][1] = z * mty - st * x;
ret[2][2] = z * mtz + ct;

return ret;
}

template<> mat3 mat3::rotate(float radians, vec3 v)
{
return rotate(radians, v.x, v.y, v.z);
}

template<> mat3::mat_t(quat const &q)
{
float n = norm(q);

if (!n)
{
for (int j = 0; j < 3; j++)
for (int i = 0; i < 3; i++)
(*this)[i][j] = (i == j) ? 1.f : 0.f;
return;
}

float s = 2.0f / n;

(*this)[0][0] = 1.0f - s * (q.y * q.y + q.z * q.z);
(*this)[0][1] = s * (q.x * q.y + q.z * q.w);
(*this)[0][2] = s * (q.x * q.z - q.y * q.w);

(*this)[1][0] = s * (q.x * q.y - q.z * q.w);
(*this)[1][1] = 1.0f - s * (q.z * q.z + q.x * q.x);
(*this)[1][2] = s * (q.y * q.z + q.x * q.w);

(*this)[2][0] = s * (q.x * q.z + q.y * q.w);
(*this)[2][1] = s * (q.y * q.z - q.x * q.w);
(*this)[2][2] = 1.0f - s * (q.x * q.x + q.y * q.y);
}

template<> mat4::mat_t(quat const &q)
{
*this = mat4(mat3(q), 1.f);
}

template<> mat4 mat4::lookat(vec3 eye, vec3 center, vec3 up)
{
vec3 v3 = normalize(eye - center);
vec3 v1 = normalize(cross(up, v3));
vec3 v2 = cross(v3, v1);

return mat4(vec4(v1.x, v2.x, v3.x, 0.f),
vec4(v1.y, v2.y, v3.y, 0.f),
vec4(v1.z, v2.z, v3.z, 0.f),
vec4(-dot(eye, v1), -dot(eye, v2), -dot(eye, v3), 1.f));
}

template<> mat4 mat4::ortho(float left, float right, float bottom,
float top, float near, float far)
{
float invrl = (right != left) ? 1.0f / (right - left) : 0.0f;
float invtb = (top != bottom) ? 1.0f / (top - bottom) : 0.0f;
float invfn = (far != near) ? 1.0f / (far - near) : 0.0f;

mat4 ret(0.0f);
ret[0][0] = 2.0f * invrl;
ret[1][1] = 2.0f * invtb;
ret[2][2] = -2.0f * invfn;
ret[3][0] = - (right + left) * invrl;
ret[3][1] = - (top + bottom) * invtb;
ret[3][2] = - (far + near) * invfn;
ret[3][3] = 1.0f;
return ret;
}

template<> mat4 mat4::ortho(float width, float height,
float near, float far)
{
return mat4::ortho(-0.5f * width, 0.5f * width,
-0.5f * height, 0.5f * height, near, far);
}

template<> mat4 mat4::frustum(float left, float right, float bottom,
float top, float near, float far)
{
float invrl = (right != left) ? 1.0f / (right - left) : 0.0f;
float invtb = (top != bottom) ? 1.0f / (top - bottom) : 0.0f;
float invfn = (far != near) ? 1.0f / (far - near) : 0.0f;

mat4 ret(0.0f);
ret[0][0] = 2.0f * near * invrl;
ret[1][1] = 2.0f * near * invtb;
ret[2][0] = (right + left) * invrl;
ret[2][1] = (top + bottom) * invtb;
ret[2][2] = - (far + near) * invfn;
ret[2][3] = -1.0f;
ret[3][2] = -2.0f * far * near * invfn;
return ret;
}

/*
* Return a standard perspective matrix
*/

template<> mat4 mat4::perspective(float fov_y, float width,
float height, float near, float far)
{
float t2 = lol::tan(fov_y * 0.5f);
float t1 = t2 * width / height;

return frustum(-near * t1, near * t1, -near * t2, near * t2, near, far);
}

/*
* Return a perspective matrix with the camera location shifted to be on
* the near plane
*/

template<> mat4 mat4::shifted_perspective(float fov_y, float screen_size,
float screen_ratio_yx,
float near, float far)
{
float tan_y = tanf(fov_y * .5f);
ASSERT(tan_y > 0.000001f);
float dist_scr = (screen_size * screen_ratio_yx * .5f) / tan_y;

return mat4::perspective(fov_y, screen_size, screen_size * screen_ratio_yx,
max(.001f, dist_scr + near),
max(.001f, dist_scr + far)) *
mat4::translate(.0f, .0f, -dist_scr);
}

} /* namespace lol */


+ 0
- 262
src/math/transform.cpp 파일 보기

@@ -1,262 +0,0 @@
//
// Lol Engine
//
// Copyright © 2010—2015 Sam Hocevar <sam@hocevar.net>
//
// Lol Engine is free software. It comes without any warranty, to
// the extent permitted by applicable law. You can redistribute it
// and/or modify it under the terms of the Do What the Fuck You Want
// to Public License, Version 2, as published by the WTFPL Task Force.
// See http://www.wtfpl.net/ for more details.
//

#include <lol/engine-internal.h>

namespace lol
{

template<> quat quat::rotate(float radians, vec3 const &v)
{
float half_angle = radians * 0.5f;

vec3 tmp = normalize(v) * sin(half_angle);

return quat(cos(half_angle), tmp.x, tmp.y, tmp.z);
}

template<> quat quat::rotate(float radians, float x, float y, float z)
{
return quat::rotate(radians, vec3(x, y, z));
}

template<> quat quat::rotate(vec3 const &src, vec3 const &dst)
{
/* Algorithm directly taken from Sam Hocevar's article "Quaternion from
* two vectors: the final version".
* http://lolengine.net/blog/2014/02/24/quaternion-from-two-vectors-final */
float magnitude = lol::sqrt(sqlength(src) * sqlength(dst));
float real_part = magnitude + dot(src, dst);
vec3 w;

if (real_part < 1.e-6f * magnitude)
{
/* If src and dst are exactly opposite, rotate 180 degrees
* around an arbitrary orthogonal axis. Axis normalisation
* can happen later, when we normalise the quaternion. */
real_part = 0.0f;
w = abs(src.x) > abs(src.z) ? vec3(-src.y, src.x, 0.f)
: vec3(0.f, -src.z, src.y);
}
else
{
/* Otherwise, build quaternion the standard way. */
w = cross(src, dst);
}

return normalize(quat(real_part, w.x, w.y, w.z));
}

template<> quat slerp(quat const &qa, quat const &qb, float f)
{
float const magnitude = lol::sqrt(sqlength(qa) * sqlength(qb));
float const product = lol::dot(qa, qb) / magnitude;

/* If quaternions are equal or opposite, there is no need
* to slerp anything, just return qa. */
if (std::abs(product) >= 1.0f)
return qa;

float const sign = (product < 0.0f) ? -1.0f : 1.0f;
float const theta = lol::acos(sign * product);
float const s1 = lol::sin(sign * f * theta);
float const s0 = lol::sin((1.0f - f) * theta);

/* This is the same as 1/sin(theta) */
float const d = 1.0f / lol::sqrt(1.f - product * product);

return qa * (s0 * d) + qb * (s1 * d);
}

static inline vec3 quat_toeuler_generic(quat const &q, int i, int j, int k)
{
float n = norm(q);

if (!n)
return vec3::zero;

/* (2 + i - j) % 3 means x-y-z direct order; otherwise indirect */
float const sign = ((2 + i - j) % 3) ? 1.f : -1.f;

vec3 ret;

/* k == i means X-Y-X style Euler angles; otherwise we’re
* actually handling X-Y-Z style Tait-Bryan angles. */
if (k == i)
{
k = 3 - i - j;

ret[0] = atan2(q[1 + i] * q[1 + j] + sign * (q.w * q[1 + k]),
q.w * q[1 + j] - sign * (q[1 + i] * q[1 + k]));
ret[1] = acos(2.f * (sq(q.w) + sq(q[1 + i])) - 1.f);
ret[2] = atan2(q[1 + i] * q[1 + j] - sign * (q.w * q[1 + k]),
q.w * q[1 + j] + sign * (q[1 + i] * q[1 + k]));
}
else
{
ret[0] = atan2(2.f * (q.w * q[1 + i] - sign * (q[1 + j] * q[1 + k])),
1.f - 2.f * (sq(q[1 + i]) + sq(q[1 + j])));
ret[1] = asin(2.f * (q.w * q[1 + j] + sign * (q[1 + i] * q[1 + k])));
ret[2] = atan2(2.f * (q.w * q[1 + k] - sign * (q[1 + j] * q[1 + i])),
1.f - 2.f * (sq(q[1 + k]) + sq(q[1 + j])));
}

return ret / n;
}

static inline mat3 mat3_fromeuler_generic(vec3 const &v, int i, int j, int k)
{
mat3 ret;

float const s0 = sin(v[0]), c0 = cos(v[0]);
float const s1 = sin(v[1]), c1 = cos(v[1]);
float const s2 = sin(v[2]), c2 = cos(v[2]);

/* (2 + i - j) % 3 means x-y-z direct order; otherwise indirect */
float const sign = ((2 + i - j) % 3) ? 1.f : -1.f;

/* k == i means X-Y-X style Euler angles; otherwise we’re
* actually handling X-Y-Z style Tait-Bryan angles. */
if (k == i)
{
k = 3 - i - j;

ret[i][i] = c1;
ret[i][j] = s0 * s1;
ret[i][k] = - sign * (c0 * s1);

ret[j][i] = s1 * s2;
ret[j][j] = c0 * c2 - s0 * c1 * s2;
ret[j][k] = sign * (s0 * c2 + c0 * c1 * s2);

ret[k][i] = sign * (s1 * c2);
ret[k][j] = - sign * (c0 * s2 + s0 * c1 * c2);
ret[k][k] = - s0 * s2 + c0 * c1 * c2;
}
else
{
ret[i][i] = c1 * c2;
ret[i][j] = sign * (c0 * s2) + s0 * s1 * c2;
ret[i][k] = s0 * s2 - sign * (c0 * s1 * c2);

ret[j][i] = - sign * (c1 * s2);
ret[j][j] = c0 * c2 - sign * (s0 * s1 * s2);
ret[j][k] = sign * (s0 * c2) + c0 * s1 * s2;

ret[k][i] = sign * s1;
ret[k][j] = - sign * (s0 * c1);
ret[k][k] = c0 * c1;
}

return ret;
}

static inline quat quat_fromeuler_generic(vec3 const &v, int i, int j, int k)
{
vec3 const half_angles = v * 0.5f;
float const s0 = sin(half_angles[0]), c0 = cos(half_angles[0]);
float const s1 = sin(half_angles[1]), c1 = cos(half_angles[1]);
float const s2 = sin(half_angles[2]), c2 = cos(half_angles[2]);

quat ret;

/* (2 + i - j) % 3 means x-y-z direct order; otherwise indirect */
float const sign = ((2 + i - j) % 3) ? 1.f : -1.f;

/* k == i means X-Y-X style Euler angles; otherwise we’re
* actually handling X-Y-Z style Tait-Bryan angles. */
if (k == i)
{
k = 3 - i - j;

ret[0] = c1 * (c0 * c2 - s0 * s2);
ret[1 + i] = c1 * (c0 * s2 + s0 * c2);
ret[1 + j] = s1 * (c0 * c2 + s0 * s2);
ret[1 + k] = sign * (s1 * (s0 * c2 - c0 * s2));
}
else
{
ret[0] = c0 * c1 * c2 - sign * (s0 * s1 * s2);
ret[1 + i] = s0 * c1 * c2 + sign * (c0 * s1 * s2);
ret[1 + j] = c0 * s1 * c2 - sign * (s0 * c1 * s2);
ret[1 + k] = c0 * c1 * s2 + sign * (s0 * s1 * c2);
}

return ret;
}

#define DEFINE_GENERIC_EULER_CONVERSIONS(a1, a2, a3) \
DEFINE_GENERIC_EULER_CONVERSIONS_INNER(a1, a2, a3, a1##a2##a3) \

#define DEFINE_GENERIC_EULER_CONVERSIONS_INNER(a1, a2, a3, name) \
/* Create quaternions from Euler angles */ \
template<> quat quat::fromeuler_##name(vec3 const &v) \
{ \
int x = 0, y = 1, z = 2; UNUSED(x, y, z); \
return quat_fromeuler_generic(v, a1, a2, a3); \
} \
\
template<> quat quat::fromeuler_##name(float phi, float theta, float psi) \
{ \
return quat::fromeuler_##name(vec3(phi, theta, psi)); \
} \
\
/* Create 3×3 matrices from Euler angles */ \
template<> mat3 mat3::fromeuler_##name(vec3 const &v) \
{ \
int x = 0, y = 1, z = 2; UNUSED(x, y, z); \
return mat3_fromeuler_generic(v, a1, a2, a3); \
} \
\
template<> mat3 mat3::fromeuler_##name(float phi, float theta, float psi) \
{ \
return mat3::fromeuler_##name(vec3(phi, theta, psi)); \
} \
\
/* Create 4×4 matrices from Euler angles */ \
template<> mat4 mat4::fromeuler_##name(vec3 const &v) \
{ \
int x = 0, y = 1, z = 2; UNUSED(x, y, z); \
return mat4(mat3_fromeuler_generic(v, a1, a2, a3), 1.f); \
} \
\
template<> mat4 mat4::fromeuler_##name(float phi, float theta, float psi) \
{ \
return mat4::fromeuler_##name(vec3(phi, theta, psi)); \
} \
\
/* Retrieve Euler angles from a quaternion */ \
template<> vec3 vec3::toeuler_##name(quat const &q) \
{ \
int x = 0, y = 1, z = 2; UNUSED(x, y, z); \
return quat_toeuler_generic(q, a1, a2, a3); \
}

DEFINE_GENERIC_EULER_CONVERSIONS(x, y, x)
DEFINE_GENERIC_EULER_CONVERSIONS(x, z, x)
DEFINE_GENERIC_EULER_CONVERSIONS(y, x, y)
DEFINE_GENERIC_EULER_CONVERSIONS(y, z, y)
DEFINE_GENERIC_EULER_CONVERSIONS(z, x, z)
DEFINE_GENERIC_EULER_CONVERSIONS(z, y, z)

DEFINE_GENERIC_EULER_CONVERSIONS(x, y, z)
DEFINE_GENERIC_EULER_CONVERSIONS(x, z, y)
DEFINE_GENERIC_EULER_CONVERSIONS(y, x, z)
DEFINE_GENERIC_EULER_CONVERSIONS(y, z, x)
DEFINE_GENERIC_EULER_CONVERSIONS(z, x, y)
DEFINE_GENERIC_EULER_CONVERSIONS(z, y, x)

#undef DEFINE_GENERIC_EULER_CONVERSIONS
#undef DEFINE_GENERIC_EULER_CONVERSIONS_INNER

} /* namespace lol */


+ 0
- 96
src/math/vector.cpp 파일 보기

@@ -1,96 +0,0 @@
//
// Lol Engine
//
// Copyright © 2010—2015 Sam Hocevar <sam@hocevar.net>
//
// Lol Engine is free software. It comes without any warranty, to
// the extent permitted by applicable law. You can redistribute it
// and/or modify it under the terms of the Do What the Fuck You Want
// to Public License, Version 2, as published by the WTFPL Task Force.
// See http://www.wtfpl.net/ for more details.
//

#include <lol/engine-internal.h>

#include <ostream> /* std::ostream */

namespace lol
{

#define LOL_PRINTF_TOSTRING(type, ...) \
template<> void type::printf() const { msg::debug(__VA_ARGS__); } \
template<> std::string type::tostring() const { return format(__VA_ARGS__); }

LOL_PRINTF_TOSTRING(vec2, "[ %6.6f %6.6f ]\n", x, y);
LOL_PRINTF_TOSTRING(ivec2, "[ %i %i ]\n", x, y);
LOL_PRINTF_TOSTRING(cmplx, "[ %6.6f %6.6f ]\n", x, y);
LOL_PRINTF_TOSTRING(vec3, "[ %6.6f %6.6f %6.6f ]\n", x, y, z);
LOL_PRINTF_TOSTRING(ivec3, "[ %i %i %i ]\n", x, y, z);
LOL_PRINTF_TOSTRING(vec4, "[ %6.6f %6.6f %6.6f %6.6f ]\n", x, y, z, w);
LOL_PRINTF_TOSTRING(ivec4, "[ %i %i %i %i ]\n", x, y, z, w);
LOL_PRINTF_TOSTRING(quat, "[ %6.6f %6.6f %6.6f %6.6f ]\n", w, x, y, z);

template<> void mat2::printf() const
{
mat2 const &p = *this;

msg::debug("[ %6.6f %6.6f\n", p[0][0], p[1][0]);
msg::debug(" %6.6f %6.6f ]\n", p[0][1], p[1][1]);
}

template<> std::string mat2::tostring() const
{
mat2 const &p = *this;

return format("[ %6.6f %6.6f\n", p[0][0], p[1][0]) +
format(" %6.6f %6.6f ]\n", p[0][1], p[1][1]);
}

template<> void mat3::printf() const
{
mat3 const &p = *this;

msg::debug("[ %6.6f %6.6f %6.6f\n", p[0][0], p[1][0], p[2][0]);
msg::debug(" %6.6f %6.6f %6.6f\n", p[0][1], p[1][1], p[2][1]);
msg::debug(" %6.6f %6.6f %6.6f ]\n", p[0][2], p[1][2], p[2][2]);
}

template<> std::string mat3::tostring() const
{
mat3 const &p = *this;

return format("[ %6.6f %6.6f %6.6f\n", p[0][0], p[1][0], p[2][0]) +
format(" %6.6f %6.6f %6.6f\n", p[0][1], p[1][1], p[2][1]) +
format(" %6.6f %6.6f %6.6f ]\n", p[0][2], p[1][2], p[2][2]);
}

template<> void mat4::printf() const
{
mat4 const &p = *this;

msg::debug("[ %6.6f %6.6f %6.6f %6.6f\n",
p[0][0], p[1][0], p[2][0], p[3][0]);
msg::debug(" %6.6f %6.6f %6.6f %6.6f\n",
p[0][1], p[1][1], p[2][1], p[3][1]);
msg::debug(" %6.6f %6.6f %6.6f %6.6f\n",
p[0][2], p[1][2], p[2][2], p[3][2]);
msg::debug(" %6.6f %6.6f %6.6f %6.6f ]\n",
p[0][3], p[1][3], p[2][3], p[3][3]);
}

template<> std::string mat4::tostring() const
{
mat4 const &p = *this;

return format("[ %6.6f %6.6f %6.6f %6.6f\n",
p[0][0], p[1][0], p[2][0], p[3][0]) +
format(" %6.6f %6.6f %6.6f %6.6f\n",
p[0][1], p[1][1], p[2][1], p[3][1]) +
format(" %6.6f %6.6f %6.6f %6.6f\n",
p[0][2], p[1][2], p[2][2], p[3][2]) +
format(" %6.6f %6.6f %6.6f %6.6f ]\n",
p[0][3], p[1][3], p[2][3], p[3][3]);
}

} /* namespace lol */


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