-
Notifications
You must be signed in to change notification settings - Fork 63
/
im3d_math.h
306 lines (270 loc) · 14.1 KB
/
im3d_math.h
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
#pragma once
// im3d_math.h is optional - include only if you want to use the Im3d math types directly
#include "im3d.h"
#include <cmath>
namespace Im3d {
// Vec2
inline Vec2 operator+(const Vec2& _lhs, const Vec2& _rhs) { return Vec2(_lhs.x + _rhs.x, _lhs.y + _rhs.y); }
inline Vec2 operator-(const Vec2& _lhs, const Vec2& _rhs) { return Vec2(_lhs.x - _rhs.x, _lhs.y - _rhs.y); }
inline Vec2 operator*(const Vec2& _lhs, const Vec2& _rhs) { return Vec2(_lhs.x * _rhs.x, _lhs.y * _rhs.y); }
inline Vec2 operator/(const Vec2& _lhs, const Vec2& _rhs) { return Vec2(_lhs.x / _rhs.x, _lhs.y / _rhs.y); }
inline Vec2 operator*(const Vec2& _lhs, float _rhs) { return Vec2(_lhs.x * _rhs, _lhs.y * _rhs); }
inline Vec2 operator/(const Vec2& _lhs, float _rhs) { return Vec2(_lhs.x / _rhs, _lhs.y / _rhs); }
inline Vec2 operator-(const Vec2& _v) { return Vec2(-_v.x, -_v.y); }
inline float Dot(const Vec2& _lhs, const Vec2& _rhs) { return _lhs.x * _rhs.x + _lhs.y * _rhs.y; }
inline float Length(const Vec2& _v) { return sqrtf(Dot(_v, _v)); }
inline float Length2(const Vec2& _v) { return Dot(_v, _v); }
inline Vec2 Abs(const Vec2& _v) { return Vec2(fabs(_v.x), fabs(_v.y)); }
inline Vec2 Normalize(const Vec2& _v) { return _v / Length(_v); }
// Vec3
inline Vec3 operator+(const Vec3& _lhs, const Vec3& _rhs) { return Vec3(_lhs.x + _rhs.x, _lhs.y + _rhs.y, _lhs.z + _rhs.z); }
inline Vec3 operator-(const Vec3& _lhs, const Vec3& _rhs) { return Vec3(_lhs.x - _rhs.x, _lhs.y - _rhs.y, _lhs.z - _rhs.z); }
inline Vec3 operator*(const Vec3& _lhs, const Vec3& _rhs) { return Vec3(_lhs.x * _rhs.x, _lhs.y * _rhs.y, _lhs.z * _rhs.z); }
inline Vec3 operator/(const Vec3& _lhs, const Vec3& _rhs) { return Vec3(_lhs.x / _rhs.x, _lhs.y / _rhs.y, _lhs.z / _rhs.z); }
inline Vec3 operator*(const Vec3& _lhs, float _rhs) { return Vec3(_lhs.x * _rhs, _lhs.y * _rhs, _lhs.z * _rhs); }
inline Vec3 operator/(const Vec3& _lhs, float _rhs) { return Vec3(_lhs.x / _rhs, _lhs.y / _rhs, _lhs.z / _rhs); }
inline Vec3 operator-(const Vec3& _v) { return Vec3(-_v.x, -_v.y, -_v.z); }
inline float Dot(const Vec3& _lhs, const Vec3& _rhs) { return _lhs.x * _rhs.x + _lhs.y * _rhs.y + _lhs.z * _rhs.z; }
inline float Length(const Vec3& _v) { return sqrtf(Dot(_v, _v)); }
inline float Length2(const Vec3& _v) { return Dot(_v, _v); }
inline Vec3 Abs(const Vec3& _v) { return Vec3(fabs(_v.x), fabs(_v.y), fabs(_v.z)); }
inline Vec3 Normalize(const Vec3& _v) { return _v / Length(_v); }
inline Vec3 Cross(const Vec3& _a, const Vec3& _b)
{
return Vec3(
_a.y * _b.z - _b.y * _a.z,
_a.z * _b.x - _b.z * _a.x,
_a.x * _b.y - _b.x * _a.y
);
}
// Vec4
inline Vec4 operator+(const Vec4& _lhs, const Vec4& _rhs) { return Vec4(_lhs.x + _rhs.x, _lhs.y + _rhs.y, _lhs.z + _rhs.z, _lhs.w + _rhs.w); }
inline Vec4 operator-(const Vec4& _lhs, const Vec4& _rhs) { return Vec4(_lhs.x - _rhs.x, _lhs.y - _rhs.y, _lhs.z - _rhs.z, _lhs.w - _rhs.w); }
inline Vec4 operator*(const Vec4& _lhs, const Vec4& _rhs) { return Vec4(_lhs.x * _rhs.x, _lhs.y * _rhs.y, _lhs.z * _rhs.z, _lhs.w * _rhs.w); }
inline Vec4 operator/(const Vec4& _lhs, const Vec4& _rhs) { return Vec4(_lhs.x / _rhs.x, _lhs.y / _rhs.y, _lhs.z / _rhs.z, _lhs.w / _rhs.w); }
inline Vec4 operator*(const Vec4& _lhs, float _rhs) { return Vec4(_lhs.x * _rhs, _lhs.y * _rhs, _lhs.z * _rhs, _lhs.w * _rhs); }
inline Vec4 operator/(const Vec4& _lhs, float _rhs) { return Vec4(_lhs.x / _rhs, _lhs.y / _rhs, _lhs.z / _rhs, _lhs.w / _rhs); }
inline Vec4 operator-(const Vec4& _v) { return Vec4(-_v.x, -_v.y, -_v.z, -_v.w); }
inline float Dot(const Vec4& _lhs, const Vec4& _rhs) { return _lhs.x * _rhs.x + _lhs.y * _rhs.y + _lhs.z * _rhs.z + _lhs.w * _rhs.w; }
inline float Length(const Vec4& _v) { return sqrtf(Dot(_v, _v)); }
inline float Length2(const Vec4& _v) { return Dot(_v, _v); }
inline Vec4 Abs(const Vec4& _v) { return Vec4(fabs(_v.x), fabs(_v.y), fabs(_v.z), fabs(_v.w)); }
inline Vec4 Normalize(const Vec4& _v) { return _v / Length(_v); }
// Mat3
inline Mat3 operator*(const Mat3& _lhs, const Mat3& _rhs)
{
Mat3 ret;
ret(0, 0) = _lhs(0, 0) * _rhs(0, 0) + _lhs(0, 1) * _rhs(1, 0) + _lhs(0, 2) * _rhs(2, 0);
ret(0, 1) = _lhs(0, 0) * _rhs(0, 1) + _lhs(0, 1) * _rhs(1, 1) + _lhs(0, 2) * _rhs(2, 1);
ret(0, 2) = _lhs(0, 0) * _rhs(0, 2) + _lhs(0, 1) * _rhs(1, 2) + _lhs(0, 2) * _rhs(2, 2);
ret(1, 0) = _lhs(1, 0) * _rhs(0, 0) + _lhs(1, 1) * _rhs(1, 0) + _lhs(1, 2) * _rhs(2, 0);
ret(1, 1) = _lhs(1, 0) * _rhs(0, 1) + _lhs(1, 1) * _rhs(1, 1) + _lhs(1, 2) * _rhs(2, 1);
ret(1, 2) = _lhs(1, 0) * _rhs(0, 2) + _lhs(1, 1) * _rhs(1, 2) + _lhs(1, 2) * _rhs(2, 2);
ret(2, 0) = _lhs(2, 0) * _rhs(0, 0) + _lhs(2, 1) * _rhs(1, 0) + _lhs(2, 2) * _rhs(2, 0);
ret(2, 1) = _lhs(2, 0) * _rhs(0, 1) + _lhs(2, 1) * _rhs(1, 1) + _lhs(2, 2) * _rhs(2, 1);
ret(2, 2) = _lhs(2, 0) * _rhs(0, 2) + _lhs(2, 1) * _rhs(1, 2) + _lhs(2, 2) * _rhs(2, 2);
return ret;
}
inline Vec3 operator*(const Mat3& _m, const Vec3& _v)
{
return Vec3(
_m(0, 0) * _v.x + _m(0, 1) * _v.y + _m(0, 2) * _v.z,
_m(1, 0) * _v.x + _m(1, 1) * _v.y + _m(1, 2) * _v.z,
_m(2, 0) * _v.x + _m(2, 1) * _v.y + _m(2, 2) * _v.z
);
}
inline Vec4 operator*(const Mat3& _m, const Vec4& _v)
{
return Vec4(
_m(0, 0) * _v.x + _m(0, 1) * _v.y + _m(0, 2) * _v.z,
_m(1, 0) * _v.x + _m(1, 1) * _v.y + _m(1, 2) * _v.z,
_m(2, 0) * _v.x + _m(2, 1) * _v.y + _m(2, 2) * _v.z,
_v.w
);
}
Mat3 Transpose(const Mat3& _m);
Vec3 ToEulerXYZ(const Mat3& _m);
Mat3 FromEulerXYZ(Vec3& _xyz);
Mat3 Rotation(const Vec3& _axis, float _rads); // _axis must be unit length
Mat3 Scale(const Vec3& _s);
// Mat4
inline Mat4 operator*(const Mat4& _lhs, const Mat4& _rhs)
{
Mat4 ret;
ret(0, 0) = _lhs(0, 0) * _rhs(0, 0) + _lhs(0, 1) * _rhs(1, 0) + _lhs(0, 2) * _rhs(2, 0) + _lhs(0, 3) * _rhs(3, 0);
ret(0, 1) = _lhs(0, 0) * _rhs(0, 1) + _lhs(0, 1) * _rhs(1, 1) + _lhs(0, 2) * _rhs(2, 1) + _lhs(0, 3) * _rhs(3, 1);
ret(0, 2) = _lhs(0, 0) * _rhs(0, 2) + _lhs(0, 1) * _rhs(1, 2) + _lhs(0, 2) * _rhs(2, 2) + _lhs(0, 3) * _rhs(3, 2);
ret(0, 3) = _lhs(0, 0) * _rhs(0, 3) + _lhs(0, 1) * _rhs(1, 3) + _lhs(0, 2) * _rhs(2, 3) + _lhs(0, 3) * _rhs(3, 3);
ret(1, 0) = _lhs(1, 0) * _rhs(0, 0) + _lhs(1, 1) * _rhs(1, 0) + _lhs(1, 2) * _rhs(2, 0) + _lhs(1, 3) * _rhs(3, 0);
ret(1, 1) = _lhs(1, 0) * _rhs(0, 1) + _lhs(1, 1) * _rhs(1, 1) + _lhs(1, 2) * _rhs(2, 1) + _lhs(1, 3) * _rhs(3, 1);
ret(1, 2) = _lhs(1, 0) * _rhs(0, 2) + _lhs(1, 1) * _rhs(1, 2) + _lhs(1, 2) * _rhs(2, 2) + _lhs(1, 3) * _rhs(3, 2);
ret(1, 3) = _lhs(1, 0) * _rhs(0, 3) + _lhs(1, 1) * _rhs(1, 3) + _lhs(1, 2) * _rhs(2, 3) + _lhs(1, 3) * _rhs(3, 3);
ret(2, 0) = _lhs(2, 0) * _rhs(0, 0) + _lhs(2, 1) * _rhs(1, 0) + _lhs(2, 2) * _rhs(2, 0) + _lhs(2, 3) * _rhs(3, 0);
ret(2, 1) = _lhs(2, 0) * _rhs(0, 1) + _lhs(2, 1) * _rhs(1, 1) + _lhs(2, 2) * _rhs(2, 1) + _lhs(2, 3) * _rhs(3, 1);
ret(2, 2) = _lhs(2, 0) * _rhs(0, 2) + _lhs(2, 1) * _rhs(1, 2) + _lhs(2, 2) * _rhs(2, 2) + _lhs(2, 3) * _rhs(3, 2);
ret(2, 3) = _lhs(2, 0) * _rhs(0, 3) + _lhs(2, 1) * _rhs(1, 3) + _lhs(2, 2) * _rhs(2, 3) + _lhs(2, 3) * _rhs(3, 3);
ret(3, 0) = _lhs(3, 0) * _rhs(0, 0) + _lhs(3, 1) * _rhs(1, 0) + _lhs(3, 2) * _rhs(2, 0) + _lhs(3, 3) * _rhs(3, 0);
ret(3, 1) = _lhs(3, 0) * _rhs(0, 1) + _lhs(3, 1) * _rhs(1, 1) + _lhs(3, 2) * _rhs(2, 1) + _lhs(3, 3) * _rhs(3, 1);
ret(3, 2) = _lhs(3, 0) * _rhs(0, 2) + _lhs(3, 1) * _rhs(1, 2) + _lhs(3, 2) * _rhs(2, 2) + _lhs(3, 3) * _rhs(3, 2);
ret(3, 3) = _lhs(3, 0) * _rhs(0, 3) + _lhs(3, 1) * _rhs(1, 3) + _lhs(3, 2) * _rhs(2, 3) + _lhs(3, 3) * _rhs(3, 3);
return ret;
}
inline Vec3 operator*(const Mat4& _m, const Vec3& _pos)
{
return Vec3(
_m(0, 0) * _pos.x + _m(0, 1) * _pos.y + _m(0, 2) * _pos.z + _m(0, 3),
_m(1, 0) * _pos.x + _m(1, 1) * _pos.y + _m(1, 2) * _pos.z + _m(1, 3),
_m(2, 0) * _pos.x + _m(2, 1) * _pos.y + _m(2, 2) * _pos.z + _m(2, 3)
);
}
inline Vec4 operator*(const Mat4& _m, const Vec4& _v)
{
return Vec4(
_m(0, 0) * _v.x + _m(0, 1) * _v.y + _m(0, 2) * _v.z + _m(0, 3) * _v.w,
_m(1, 0) * _v.x + _m(1, 1) * _v.y + _m(1, 2) * _v.z + _m(1, 3) * _v.w,
_m(2, 0) * _v.x + _m(2, 1) * _v.y + _m(2, 2) * _v.z + _m(2, 3) * _v.w,
_m(3, 0) * _v.x + _m(3, 1) * _v.y + _m(3, 2) * _v.z + _m(3, 3) * _v.w
);
}
Mat4 Inverse(const Mat4& _m);
Mat4 Transpose(const Mat4& _m);
Mat4 Translation(const Vec3& _t);
Mat4 AlignZ(const Vec3& _axis, const Vec3& _up = Vec3(0.0f, 1.0f, 0.0f)); // generate an orthonormal bases with +z as _axis, which must be unit length
Mat4 LookAt(const Vec3& _from, const Vec3& _to, const Vec3& _up = Vec3(0.0f, 1.0f, 0.0f)); // align _z with (_to - _from), set _from as translation
struct Line
{
Vec3 m_origin;
Vec3 m_direction; // unit length
Line() {}
Line(const Vec3& _origin, const Vec3& _direction);
};
struct Ray
{
Vec3 m_origin;
Vec3 m_direction; // unit length
Ray() {}
Ray(const Vec3& _origin, const Vec3& _direction);
};
struct LineSegment
{
Vec3 m_start;
Vec3 m_end;
LineSegment() {}
LineSegment(const Vec3& _start, const Vec3& _end);
};
struct Sphere
{
Vec3 m_origin;
float m_radius;
Sphere() {}
Sphere(const Vec3& _origin, float _radius);
};
struct Plane
{
Vec3 m_normal;
float m_offset;
Plane() {}
Plane(const Vec3& _normal, float _offset);
Plane(const Vec3& _normal, const Vec3& _origin);
};
struct Capsule
{
Vec3 m_start;
Vec3 m_end;
float m_radius;
Capsule() {}
Capsule(const Vec3& _start, const Vec3& _end, float _radius);
};
// Ray-primitive intersections. Use Intersects() when you don't need t.
bool Intersects(const Ray& _ray, const Plane& _plane );
bool Intersect (const Ray& _ray, const Plane& _plane, float& t0_ );
bool Intersects(const Ray& _ray, const Sphere& _sphere );
bool Intersect (const Ray& _ray, const Sphere& _sphere, float& t0_, float& t1_);
bool Intersects(const Ray& _ray, const Capsule& _capsule );
bool Intersect (const Ray& _ray, const Capsule& _capsule, float& t0_, float& t1_);
// Find point t0_ along _line0 nearest to _line1 and t1_ along _line1 nearest to _line0.
void Nearest(const Line& _line0, const Line& _line1, float& t0_, float& t1_);
// Find point tr_ along _ray nearest to _line and tl_ along _line nearest to _ray.
void Nearest(const Ray& _ray, const Line& _line, float& tr_, float& tl_);
// Find point tr_ along _ray nearest to _segment, return point on segment nearest to _ray.
Vec3 Nearest(const Ray& _ray, const LineSegment& _segment, float& tr_);
float Distance2(const Ray& _ray, const LineSegment& _segment);
inline float Distance(const Vec4& _plane, const Vec3& _point){ return _plane.x * _point.x + _plane.y * _point.y + _plane.z * _point.z - _plane.w; }
constexpr float Pi = 3.14159265359f;
constexpr float TwoPi = 2.0f * Pi;
constexpr float HalfPi = 0.5f * Pi;
inline float Radians(float _degrees) { return _degrees * (Pi / 180.0f); }
inline float Degrees(float _radians) { return _radians * (180.0f / Pi); }
namespace internal {
struct ScalarT {};
struct FloatT: public ScalarT {};
struct IntT: public ScalarT {};
struct CompositeT {};
struct VecT: public CompositeT {};
struct MatT: public CompositeT {};
template <typename T>
struct TypeTraits { typedef typename T::Type Type; enum { kSize = T::kSize }; };
template<> struct TypeTraits<int> { typedef IntT Type; enum { kSize = 1 }; };
template<> struct TypeTraits<float> { typedef FloatT Type; enum { kSize = 1 }; };
template<> struct TypeTraits<Vec2> { typedef VecT Type; enum { kSize = 2 }; };
template<> struct TypeTraits<Vec3> { typedef VecT Type; enum { kSize = 3 }; };
template<> struct TypeTraits<Vec4> { typedef VecT Type; enum { kSize = 4 }; };
template<> struct TypeTraits<Mat4> { typedef MatT Type; enum { kSize = 16 }; };
template <typename T>
inline bool _AllLess(const T& _a, const T& _b, ScalarT)
{
return _a < _b;
}
template <typename T>
inline bool _AllLess(const T& _a, const T& _b, CompositeT)
{
for (int i = 0, n = TypeTraits<T>::kSize; i < n; ++i)
{
if (_a[i] > _b[i])
{
return false;
}
}
return true;
}
template <typename T>
inline T _Max(const T& _a, const T& _b, ScalarT)
{
return _a < _b ? _b : _a;
}
template <typename T>
inline T _Max(const T& _a, const T& _b, CompositeT)
{
T ret;
for (int i = 0, n = TypeTraits<T>::kSize; i < n; ++i) {
ret[i] = _Max(_a[i], _b[i], ScalarT());
}
return ret;
}
template <typename T>
inline T _Min(const T& _a, const T& _b, ScalarT)
{
return _a < _b ? _a : _b;
}
template <typename T>
inline T _Min(const T& _a, const T& _b, CompositeT)
{
T ret;
for (int i = 0, n = TypeTraits<T>::kSize; i < n; ++i)
{
ret[i] = _Min(_a[i], _b[i], ScalarT());
}
return ret;
}
} // namespace internal
template <typename T>
inline bool AllLess(const T& _a, const T& _b) { return internal::_AllLess(_a, _b, typename internal::TypeTraits<T>::Type()); }
template <typename T>
inline T Max(T _a, T _b) { return internal::_Max(_a, _b, typename internal::TypeTraits<T>::Type()); }
template <typename T>
inline T Min(T _a, T _b) { return internal::_Min(_a, _b, typename internal::TypeTraits<T>::Type()); }
template <typename T>
inline T Clamp(T _a, T _min, T _max) { return Max(Min(_a, _max), _min); }
// Remap _x in [_start,_end] to [0,1].
inline float Remap(float _x, float _start, float _end) { return Clamp(_x * (1.0f / (_end - _start)) + (-_start / (_end - _start)), 0.0f, 1.0f); }
} // namespace Im3d