vec3.h
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3 ** Copyright (c) 1997-2016 The ClanLib Team
4 **
5 ** This software is provided 'as-is', without any express or implied
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11 ** freely, subject to the following restrictions:
12 **
13 ** 1. The origin of this software must not be misrepresented; you must not
14 ** claim that you wrote the original software. If you use this software
15 ** in a product, an acknowledgment in the product documentation would be
16 ** appreciated but is not required.
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24 ** File Author(s):
25 **
26 ** Magnus Norddahl
27 ** Mark Page
28 ** Harry Storbacka
29 */
30 
31 #pragma once
32 
33 #include <cmath>
34 #include "vec2.h"
35 #include "vec4.h"
36 
37 namespace clan
38 {
41 
42  template<typename Type>
43  class Vec2;
44 
45  template<typename Type>
46  class Vec3;
47 
48  template<typename Type>
49  class Vec4;
50 
51  template<typename Type>
52  class Mat2;
53 
54  template<typename Type>
55  class Mat3;
56 
57  template<typename Type>
58  class Mat4;
59 
60  template<typename Type>
61  class Sizex;
62 
63  template<typename Type>
64  class Pointx;
65 
66  class Angle;
67 
73  template<typename Type>
74  class Vec3
75  {
76  public:
77  typedef Type datatype;
78 
79  union { Type x; Type s; Type r; };
80  union { Type y; Type t; Type g; };
81  union { Type z; Type u; Type b; };
82 
83  Vec3() : x(0), y(0), z(0) { }
84  explicit Vec3(const Type &scalar) : x(scalar), y(scalar), z(scalar) { }
85  explicit Vec3(const Vec2<Type> &copy, const Type &p3) { x = copy.x; y = copy.y; z = p3; }
86  explicit Vec3(const Vec4<Type> &copy) { x = copy.x; y = copy.y; z = copy.z; }
87 
88  Vec3(const Vec3<double> &copy);
89  Vec3(const Vec3<float> &copy);
90  Vec3(const Vec3<int> &copy);
91 
92  explicit Vec3(const Type &p1, const Type &p2, const Type &p3) : x(p1), y(p2), z(p3) { }
93  explicit Vec3(const Type *array_xyz) : x(array_xyz[0]), y(array_xyz[1]), z(array_xyz[2]) { }
94 
100  static Vec3<Type> normalize(const Vec3<Type>& vector);
101 
105  static Type dot(const Vec3<Type>& vector1, const Vec3<Type>& vector2) { return vector1.x*vector2.x + vector1.y*vector2.y + vector1.z*vector2.z; }
106 
112  static Vec3<Type> cross(const Vec3<Type>& vector1, const Vec3<Type>& vector2);
113 
120  static Vec3<Type> rotate(const Vec3<Type>& vector, const Angle &angle, const Vec3<Type>& axis);
121 
127  static Vec3<Type> round(const Vec3<Type>& vector);
128 
132  static Vec3<Type> reflect(const Vec3<Type>& incident, const Vec3<Type>& normal);
133 
139  static bool is_equal(const Vec3<Type> &first, const Vec3<Type> &second, Type epsilon)
140  {
141  Type diff_x = second.x - first.x; Type diff_y = second.y - first.y; Type diff_z = second.z - first.z;
142  return (diff_x >= -epsilon && diff_x <= epsilon && diff_y >= -epsilon && diff_y <= epsilon && diff_z >= -epsilon && diff_z <= epsilon);
143  }
144 
149  Type length() const;
150 
156 
163  Type dot(const Vec3<Type>& vector) const { return x*vector.x + y*vector.y + z*vector.z; }
164 
170  Angle angle(const Vec3<Type>& vector) const;
171 
177  Angle angle_normed(const Vec3<Type>& vector) const;
178 
184  Type distance(const Vec3<Type>& vector) const;
185 
191  Vec3<Type> &cross(const Vec3<Type>& vector);
192 
198  Vec3<Type> &rotate(const Angle &angle, const Vec3<Type>& axis);
199 
204  Vec3<Type> &round();
205 
210  bool is_equal(const Vec3<Type> &other, Type epsilon) const { return Vec3<Type>::is_equal(*this, other, epsilon); }
211 
213  void operator += (const Vec3<Type>& vector) { x += vector.x; y += vector.y; z += vector.z; }
214 
216  void operator += (Type value) { x += value; y += value; z += value; }
217 
219  void operator -= (const Vec3<Type>& vector) { x -= vector.x; y -= vector.y; z -= vector.z; }
220 
222  void operator -= (Type value) { x -= value; y -= value; z -= value; }
223 
225  Vec3<Type> operator - () const { return Vec3<Type>(-x, -y, -z); }
226 
228  void operator *= (const Vec3<Type>& vector) { x *= vector.x; y *= vector.y; z *= vector.z; }
229 
231  void operator *= (Type value) { x *= value; y *= value; z *= value; }
232 
234  void operator /= (const Vec3<Type>& vector) { x /= vector.x; y /= vector.y; z /= vector.z; }
235 
237  void operator /= (Type value) { x /= value; y /= value; z /= value; }
238 
240  Vec3<Type> &operator = (const Vec3<Type>& vector) { x = vector.x; y = vector.y; z = vector.z; return *this; }
241 
243  bool operator == (const Vec3<Type>& vector) const { return ((x == vector.x) && (y == vector.y) && (z == vector.z)); }
244 
246  bool operator != (const Vec3<Type>& vector) const { return ((x != vector.x) || (y != vector.y) || (z != vector.z)); }
247 
249  bool operator < (const Vec3<Type>& vector) const { return z < vector.z || (z == vector.z && (y < vector.y || (y == vector.y && x < vector.x))); }
250  };
251 
253  template<typename Type>
254  Vec3<Type> operator + (const Vec3<Type>& v1, const Vec3<Type>& v2) { return Vec3<Type>(v1.x + v2.x, v1.y + v2.y, v1.z + v2.z); }
255 
257  template<typename Type>
258  Vec3<Type> operator + (Type s, const Vec3<Type>& v) { return Vec3<Type>(s + v.x, s + v.y, s + v.z); }
259 
261  template<typename Type>
262  Vec3<Type> operator + (const Vec3<Type>& v, Type s) { return Vec3<Type>(v.x + s, v.y + s, v.z + s); }
263 
265  template<typename Type>
266  Vec3<Type> operator - (const Vec3<Type>& v1, const Vec3<Type>& v2) { return Vec3<Type>(v1.x - v2.x, v1.y - v2.y, v1.z - v2.z); }
267 
269  template<typename Type>
270  Vec3<Type> operator - (Type s, const Vec3<Type>& v) { return Vec3<Type>(s - v.x, s - v.y, s - v.z); }
271 
273  template<typename Type>
274  Vec3<Type> operator - (const Vec3<Type>& v, Type s) { return Vec3<Type>(v.x - s, v.y - s, v.z - s); }
275 
277  template<typename Type>
278  Vec3<Type> operator * (const Vec3<Type>& v1, const Vec3<Type>& v2) { return Vec3<Type>(v1.x * v2.x, v1.y * v2.y, v1.z * v2.z); }
279 
281  template<typename Type>
282  Vec3<Type> operator * (Type s, const Vec3<Type>& v) { return Vec3<Type>(s * v.x, s * v.y, s * v.z); }
283 
285  template<typename Type>
286  Vec3<Type> operator * (const Vec3<Type>& v, Type s) { return Vec3<Type>(v.x * s, v.y * s, v.z * s); }
287 
289  template<typename Type>
290  Vec3<Type> operator / (const Vec3<Type>& v1, const Vec3<Type>& v2) { return Vec3<Type>(v1.x / v2.x, v1.y / v2.y, v1.z / v2.z); }
291 
293  template<typename Type>
294  Vec3<Type> operator / (Type s, const Vec3<Type>& v) { return Vec3<Type>(s / v.x, s / v.y, s / v.z); }
295 
297  template<typename Type>
298  Vec3<Type> operator / (const Vec3<Type>& v, Type s) { return Vec3<Type>(v.x / s, v.y / s, v.z / s); }
299 
302  template<typename Type>
303  Vec3<Type> operator * (const Vec3<Type>& v, const Mat3<Type>& matrix)
304  {
305  return Vec3<Type>(
306  matrix[0 * 3 + 0] * v.x + matrix[0 * 3 + 1] * v.y + matrix[0 * 3 + 2] * v.z,
307  matrix[1 * 3 + 0] * v.x + matrix[1 * 3 + 1] * v.y + matrix[1 * 3 + 2] * v.z,
308  matrix[2 * 3 + 0] * v.x + matrix[2 * 3 + 1] * v.y + matrix[2 * 3 + 2] * v.z);
309  }
310 
313  template<typename Type>
314  Vec3<Type> operator * (const Mat3<Type>& matrix, const Vec3<Type>& v)
315  {
316  return Vec3<Type>(
317  matrix[0 * 3 + 0] * v.x + matrix[1 * 3 + 0] * v.y + matrix[2 * 3 + 0] * v.z,
318  matrix[0 * 3 + 1] * v.x + matrix[1 * 3 + 1] * v.y + matrix[2 * 3 + 1] * v.z,
319  matrix[0 * 3 + 2] * v.x + matrix[1 * 3 + 2] * v.y + matrix[2 * 3 + 2] * v.z);
320  }
321 
322  template<>
323  inline Vec3<unsigned char>::Vec3(const Vec3<float> &copy) { x = (unsigned char)floor(copy.x + 0.5f); y = (unsigned char)floor(copy.y + 0.5f); z = (unsigned char)floor(copy.z + 0.5f); }
324 
325  template<>
326  inline Vec3<unsigned char>::Vec3(const Vec3<double> &copy) { x = (unsigned char)floor(copy.x + 0.5); y = (unsigned char)floor(copy.y + 0.5); z = (unsigned char)floor(copy.z + 0.5); }
327 
328  template<>
329  inline Vec3<unsigned char>::Vec3(const Vec3<int> &copy) { x = (unsigned char)copy.x; y = (unsigned char)copy.y; z = (unsigned char)copy.z; }
330 
331  template<>
332  inline Vec3<char>::Vec3(const Vec3<float> &copy) { x = (char)floor(copy.x + 0.5f); y = (char)floor(copy.y + 0.5f); z = (char)floor(copy.z + 0.5f); }
333 
334  template<>
335  inline Vec3<char>::Vec3(const Vec3<double> &copy) { x = (char)floor(copy.x + 0.5); y = (char)floor(copy.y + 0.5); z = (char)floor(copy.z + 0.5); }
336 
337  template<>
338  inline Vec3<char>::Vec3(const Vec3<int> &copy) { x = (char)copy.x; y = (char)copy.y; z = (char)copy.z; }
339 
340  template<>
341  inline Vec3<unsigned short>::Vec3(const Vec3<float> &copy) { x = (unsigned short)floor(copy.x + 0.5f); y = (unsigned short)floor(copy.y + 0.5f); z = (unsigned short)floor(copy.z + 0.5f); }
342 
343  template<>
344  inline Vec3<unsigned short>::Vec3(const Vec3<double> &copy) { x = (unsigned short)floor(copy.x + 0.5); y = (unsigned short)floor(copy.y + 0.5); z = (unsigned short)floor(copy.z + 0.5); }
345 
346  template<>
347  inline Vec3<unsigned short>::Vec3(const Vec3<int> &copy) { x = (unsigned short)copy.x; y = (unsigned short)copy.y; z = (unsigned short)copy.z; }
348 
349  template<>
350  inline Vec3<short>::Vec3(const Vec3<float> &copy) { x = (short)floor(copy.x + 0.5f); y = (short)floor(copy.y + 0.5f); z = (short)floor(copy.z + 0.5f); }
351 
352  template<>
353  inline Vec3<short>::Vec3(const Vec3<double> &copy) { x = (short)floor(copy.x + 0.5); y = (short)floor(copy.y + 0.5); z = (short)floor(copy.z + 0.5); }
354 
355  template<>
356  inline Vec3<short>::Vec3(const Vec3<int> &copy) { x = (short)copy.x; y = (short)copy.y; z = (short)copy.z; }
357 
358  template<>
359  inline Vec3<int>::Vec3(const Vec3<float> &copy) { x = (int)floor(copy.x + 0.5f); y = (int)floor(copy.y + 0.5f); z = (int)floor(copy.z + 0.5f); }
360 
361  template<>
362  inline Vec3<int>::Vec3(const Vec3<double> &copy) { x = (int)floor(copy.x + 0.5); y = (int)floor(copy.y + 0.5); z = (int)floor(copy.z + 0.5); }
363 
364  template<>
365  inline Vec3<int>::Vec3(const Vec3<int> &copy) { x = (int)copy.x; y = (int)copy.y; z = (int)copy.z; }
366 
367  template<>
368  inline Vec3<unsigned int>::Vec3(const Vec3<float> &copy) { x = (unsigned int)floor(copy.x + 0.5f); y = (unsigned int)floor(copy.y + 0.5f); z = (unsigned int)floor(copy.z + 0.5f); }
369 
370  template<>
371  inline Vec3<unsigned int>::Vec3(const Vec3<double> &copy) { x = (unsigned int)floor(copy.x + 0.5); y = (unsigned int)floor(copy.y + 0.5); z = (unsigned int)floor(copy.z + 0.5); }
372 
373  template<>
374  inline Vec3<unsigned int>::Vec3(const Vec3<int> &copy) { x = (unsigned int)copy.x; y = (unsigned int)copy.y; z = (unsigned int)copy.z; }
375 
376  template<>
377  inline Vec3<float>::Vec3(const Vec3<float> &copy) { x = (float)copy.x; y = (float)copy.y; z = (float)copy.z; }
378 
379  template<>
380  inline Vec3<float>::Vec3(const Vec3<double> &copy) { x = (float)copy.x; y = (float)copy.y; z = (float)copy.z; }
381 
382  template<>
383  inline Vec3<float>::Vec3(const Vec3<int> &copy) { x = (float)copy.x; y = (float)copy.y; z = (float)copy.z; }
384 
385  template<>
386  inline Vec3<double>::Vec3(const Vec3<float> &copy) { x = (double)copy.x; y = (double)copy.y; z = (double)copy.z; }
387 
388  template<>
389  inline Vec3<double>::Vec3(const Vec3<double> &copy) { x = (double)copy.x; y = (double)copy.y; z = (double)copy.z; }
390 
391  template<>
392  inline Vec3<double>::Vec3(const Vec3<int> &copy) { x = (double)copy.x; y = (double)copy.y; z = (double)copy.z; }
393 
394  template<typename Type>
395  inline Type Vec3<Type>::length() const { return (Type)floor(sqrt(float(x*x + y*y + z*z)) + 0.5f); }
396 
397  template<>
398  inline double Vec3<double>::length() const { return sqrt(x*x + y*y + z*z); }
399 
400  template<>
401  inline float Vec3<float>::length() const { return sqrt(x*x + y*y + z*z); }
402 
403  template<typename Type>
404  inline Vec3<Type> &Vec3<Type>::normalize() { Type f = length(); if (f != 0) { x /= f; y /= f; z /= f; } return *this; }
405 
406  template<typename Type>
407  inline Vec3<Type> Vec3<Type>::normalize(const Vec3<Type>& vector) { Vec3<Type> dest(vector); dest.normalize(); return dest; }
408 
410  typedef Vec3<char> Vec3b;
414  typedef Vec3<int> Vec3i;
417 
419 }
Type distance(const Vec3< Type > &vector) const
Calculate the distance between this vector and an other vector.
void operator*=(const Vec3< Type > &vector)
*= operator.
Definition: vec3.h:228
Angle angle(const Vec3< Type > &vector) const
Calculate the angle between this vector and an other vector.
Definition: clanapp.h:35
Vec3< float > Vec3f
Definition: vec3.h:415
Angle class.
Definition: angle.h:59
4D vector
Definition: size.h:47
static bool is_equal(const Vec3< Type > &first, const Vec3< Type > &second, Type epsilon)
Returns true if equal within the bounds of an epsilon.
Definition: vec3.h:139
2D vector
Definition: line.h:46
Vec3< unsigned int > Vec3ui
Definition: vec3.h:413
Vec3< Type > & normalize()
Normalizes this vector.
Definition: vec3.h:404
Type z
Definition: vec4.h:81
Type r
Definition: vec3.h:79
bool is_equal(const Vec3< Type > &other, Type epsilon) const
Returns true if equal within the bounds of an epsilon.
Definition: vec3.h:210
Type b
Definition: vec3.h:81
static Vec3< Type > cross(const Vec3< Type > &vector1, const Vec3< Type > &vector2)
Calculate the cross product between two vectors.
void operator+=(const Vec3< Type > &vector)
+= operator.
Definition: vec3.h:213
Type g
Definition: vec3.h:80
3D matrix
Definition: mat2.h:47
Vec3(const Type *array_xyz)
Definition: vec3.h:93
Vec2< Type > operator/(const Vec2< Type > &v1, const Vec2< Type > &v2)
/ operator.
Definition: vec2.h:302
void operator-=(const Vec3< Type > &vector)
-= operator.
Definition: vec3.h:219
Vec3< unsigned char > Vec3ub
Definition: vec3.h:409
Type y
Definition: vec4.h:80
Type length() const
Returns the length (magnitude) of this vector.
Definition: vec3.h:395
Type y
Definition: vec3.h:80
bool operator==(const Vec3< Type > &vector) const
== operator.
Definition: vec3.h:243
Type dot(const Vec3< Type > &vector) const
Dot products this vector with an other vector.
Definition: vec3.h:163
static Vec3< Type > rotate(const Vec3< Type > &vector, const Angle &angle, const Vec3< Type > &axis)
Rotate a vector around an axis. Same as glRotate[f|d](angle, a);.
Vec3< short > Vec3s
Definition: vec3.h:412
Vec3(const Type &p1, const Type &p2, const Type &p3)
Definition: vec3.h:92
Vec3< int > Vec3i
Definition: vec3.h:414
Vec3(const Type &scalar)
Definition: vec3.h:84
Vec3< Type > & round()
Rounds all components on this vector.
Type datatype
Definition: vec3.h:77
Vec2< Type > operator+(const Vec2< Type > &v1, const Vec2< Type > &v2)
operator.
Definition: vec2.h:266
Vec3< Type > & operator=(const Vec3< Type > &vector)
= operator.
Definition: vec3.h:240
Type y
Definition: vec2.h:81
Type z
Definition: vec3.h:81
Vec3< unsigned short > Vec3us
Definition: vec3.h:411
Vec3< char > Vec3b
Definition: vec3.h:410
Angle angle_normed(const Vec3< Type > &vector) const
Calculate the angle between this vector and an other vector, where the vectors are unit vectors...
Vec3< Type > operator-() const
operator.
Definition: vec3.h:225
Vec3(const Vec4< Type > &copy)
Definition: vec3.h:86
value is a keyword
Vec2< Type > operator*(const Vec2< Type > &v1, const Vec2< Type > &v2)
operator.
Definition: vec2.h:290
Type u
Definition: vec3.h:81
bool operator!=(const Vec3< Type > &vector) const
!= operator.
Definition: vec3.h:246
Vec3(const Vec2< Type > &copy, const Type &p3)
Definition: vec3.h:85
void operator/=(const Vec3< Type > &vector)
/= operator.
Definition: vec3.h:234
Type x
Definition: vec3.h:79
Type t
Definition: vec3.h:80
Type x
Definition: vec4.h:79
Vec3< double > Vec3d
Definition: vec3.h:416
Type x
Definition: vec2.h:80
static Type dot(const Vec3< Type > &vector1, const Vec3< Type > &vector2)
Dot products between two vectors.
Definition: vec3.h:105
Vec3()
Definition: vec3.h:83
Vec2< Type > operator-(const Vec2< Type > &v1, const Vec2< Type > &v2)
operator.
Definition: vec2.h:278
Type s
Definition: vec3.h:79
static Vec3< Type > reflect(const Vec3< Type > &incident, const Vec3< Type > &normal)
Calculate the reflection direction for an incident vector.