Class: Engine::Quaternion

Inherits:
Object
  • Object
show all
Defined in:
lib/engine/quaternion.rb

Constant Summary collapse

EULER_ORDER = 
"XYZ"

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(w, x, y, z) ⇒ Quaternion

Returns a new instance of Quaternion.



8
9
10
11
12
13
 
# File 'lib/engine/quaternion.rb', line 8

def initialize(w, x, y, z)
  @w = w
  @x = x
  @y = y
  @z = z
end

Instance Attribute Details

#euler_order ⇒ Object

Returns the value of attribute euler_order.



6
7
8
 
# File 'lib/engine/quaternion.rb', line 6

def euler_order
  @euler_order
end

#w ⇒ Object

Returns the value of attribute w.



6
7
8
 
# File 'lib/engine/quaternion.rb', line 6

def w
  @w
end

#x ⇒ Object

Returns the value of attribute x.



6
7
8
 
# File 'lib/engine/quaternion.rb', line 6

def x
  @x
end

#y ⇒ Object

Returns the value of attribute y.



6
7
8
 
# File 'lib/engine/quaternion.rb', line 6

def y
  @y
end

#z ⇒ Object

Returns the value of attribute z.



6
7
8
 
# File 'lib/engine/quaternion.rb', line 6

def z
  @z
end

Class Method Details

.from_angle_axis(angle, axis) ⇒ Object 



210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
 
# File 'lib/engine/quaternion.rb', line 210

def self.from_angle_axis(angle, axis)
  axis = axis.normalize
  angle = angle * Math::PI / 180

  half_angle = angle / 2
  sin_half_angle = Math.sin(half_angle)
  cos_half_angle = Math.cos(half_angle)

  Quaternion.new(
    cos_half_angle,
    axis[0] * sin_half_angle,
    axis[1] * sin_half_angle,
    axis[2] * sin_half_angle
  )
end

.from_euler(euler) ⇒ Object

taken from github.com/mrdoob/three.js/blob/134ff886792734a75c0a9b30aa816d19270f8526/src/math/Quaternion.js#L229



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
 
# File 'lib/engine/quaternion.rb', line 35

def self.from_euler(euler)
  e_1 = euler[0] * Math::PI / 180
  e_2 = euler[1] * Math::PI / 180
  e_3 = euler[2] * Math::PI / 180

  c_1 = Math.cos(e_1 / 2)
  c_2 = Math.cos(e_2 / 2)
  c_3 = Math.cos(e_3 / 2)

  s_1 = Math.sin(e_1 / 2)
  s_2 = Math.sin(e_2 / 2)
  s_3 = Math.sin(e_3 / 2)

  case EULER_ORDER
  when "XYZ"
    Quaternion.new(
      c_1 * c_2 * c_3 - s_1 * s_2 * s_3,
      s_1 * c_2 * c_3 + c_1 * s_2 * s_3,
      c_1 * s_2 * c_3 - s_1 * c_2 * s_3,
      c_1 * c_2 * s_3 + s_1 * s_2 * c_3
    )
  when "YXZ"
    Quaternion.new(
      c_1 * c_2 * c_3 + s_1 * s_2 * s_3,
      s_1 * c_2 * c_3 + c_1 * s_2 * s_3,
      c_1 * s_2 * c_3 - s_1 * c_2 * s_3,
      c_1 * c_2 * s_3 - s_1 * s_2 * c_3
    )
  when "ZXY"
    Quaternion.new(
      c_1 * c_2 * c_3 - s_1 * s_2 * s_3,
      s_1 * c_2 * c_3 - c_1 * s_2 * s_3,
      c_1 * s_2 * c_3 + s_1 * c_2 * s_3,
      c_1 * c_2 * s_3 + s_1 * s_2 * c_3
    )
  when "ZYX"
    Quaternion.new(
      c_1 * c_2 * c_3 + s_1 * s_2 * s_3,
      s_1 * c_2 * c_3 - c_1 * s_2 * s_3,
      c_1 * s_2 * c_3 + s_1 * c_2 * s_3,
      c_1 * c_2 * s_3 - s_1 * s_2 * c_3
    )
  when "YZX"
    Quaternion.new(
      s_1 * c_2 * c_3 + c_1 * s_2 * s_3,
      c_1 * s_2 * c_3 + s_1 * c_2 * s_3,
      c_1 * c_2 * s_3 - s_1 * s_2 * c_3,
      c_1 * c_2 * c_3 - s_1 * s_2 * s_3
    )
  when "XZY"
    Quaternion.new(
      c_1 * c_2 * c_3 + s_1 * s_2 * s_3,
      s_1 * c_2 * c_3 - c_1 * s_2 * s_3,
      c_1 * s_2 * c_3 - s_1 * c_2 * s_3,
      c_1 * c_2 * s_3 + s_1 * s_2 * c_3
    )
  end
end

Instance Method Details

#*(other) ⇒ Object 



25
26
27
28
29
30
31
32
 
# File 'lib/engine/quaternion.rb', line 25

def *(other)
  Quaternion.new(
    @w * other.w - @x * other.x - @y * other.y - @z * other.z,
    @w * other.x + @x * other.w + @y * other.z - @z * other.y,
    @w * other.y - @x * other.z + @y * other.w + @z * other.x,
    @w * other.z + @x * other.y - @y * other.x + @z * other.w
  )
end

#==(other) ⇒ Object 



19
20
21
22
23
 
# File 'lib/engine/quaternion.rb', line 19

def ==(other)
  return false unless other.is_a?(Quaternion)

  @w == other.w && @x == other.x && @y == other.y && @z == other.z
end

#te ⇒ Object 



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
 
# File 'lib/engine/quaternion.rb', line 172

def te
  x2 = x + x
  y2 = y + y
  z2 = z + z

  xx = x * x2
  xy = x * y2
  xz = x * z2
  yy = y * y2
  yz = y * z2
  zz = z * z2
  wx = w * x2
  wy = w * y2
  wz = w * z2

  [
    1 - (yy + zz),
    xy + wz,
    xz - wy,
    0,

    xy - wz,
    1 - (xx + zz),
    yz + wx,
    0,

    xz + wy,
    yz - wx,
    1 - (xx + yy),
    0,

    0,
    0,
    0,
    1,
  ]
end

#to_angle_axis ⇒ Object 



226
227
228
229
230
231
232
 
# File 'lib/engine/quaternion.rb', line 226

def to_angle_axis
  angle = 2 * Math.acos(@w)
  s = Math.sqrt(1 - @w * @w)
  s = 1 if s < 0.0001
  axis = Vector[@x / s, @y / s, @z / s]
  [angle * 180 / Math::PI, axis]
end

#to_euler ⇒ Object

taken from github.com/mrdoob/three.js/blob/134ff886792734a75c0a9b30aa816d19270f8526/src/math/Euler.js#L134



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
 
# File 'lib/engine/quaternion.rb', line 95

def to_euler
  m11 = te[0]
  m12 = te[4]
  m13 = te[8]
  m21 = te[1]
  m22 = te[5]
  m23 = te[9]
  m31 = te[2]
  m32 = te[6]
  m33 = te[10]

  case EULER_ORDER
  when "XYZ"
    e_y = Math.asin(m13.clamp(-1, 1))

    if m13.abs < 0.9999999
      e_x = Math.atan2(-m23, m33)
      e_z = Math.atan2(-m12, m11)
    else
      e_x = Math.atan2(m32, m22)
      e_z = 0
    end
  when "YXZ"
    e_x = Math.asin(-m23.clamp(-1, 1))

    if m23.abs < 0.9999999
      e_y = Math.atan2(m13, m33)
      e_z = Math.atan2(m21, m22)
    else
      e_y = Math.atan2(-m31, m11)
      e_z = 0
    end
  when "ZXY"
    e_x = Math.asin(m32.clamp(-1, 1))

    if m32.abs < 0.9999999
      e_y = Math.atan2(-m31, m33)
      e_z = Math.atan2(-m12, m22)
    else
      e_y = 0
      e_z = Math.atan2(m21, m11)
    end
  when "ZYX"
    e_y = Math.asin(-m31.clamp(-1, 1))

    if m31.abs < 0.9999999
      e_x = Math.atan2(m32, m33)
      e_z = Math.atan2(m21, m11)
    else
      e_x = 0
      e_z = Math.atan2(-m12, m22)
    end
  when "YZX"
    e_z = Math.asin(m21.clamp(-1, 1))

    if m21.abs < 0.9999999
      e_x = Math.atan2(-m23, m22)
      e_y = Math.atan2(-m31, m11)
    else
      e_x = 0
      e_y = Math.atan2(m13, m33)
    end
  when "XZY"
    e_z = Math.asin(-m12.clamp(-1, 1))

    if m12.abs < 0.9999999
      e_x = Math.atan2(m32, m22)
      e_y = Math.atan2(m13, m11)
    else
      e_x = Math.atan2(-m23, m33)
      e_y = 0
    end
  end

  Vector[e_x, e_y, e_z] * 180 / Math::PI
end

#to_s ⇒ Object 



15
16
17
 
# File 'lib/engine/quaternion.rb', line 15

def to_s
  "Quaternion(w: #{@w}, x: #{@x}, y: #{@y}, z: #{@z})"
end