Class: Cosmos::Quaternion

Inherits:
Object show all
Defined in:
lib/cosmos/utilities/quaternion.rb

Overview

A quaternion where q is the scalar component

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(array = [0.0, 0.0, 0.0, 0.0], angle = nil) ⇒ Quaternion

Create a Quaternion given the initial components

the forth value is the scalar or [Array<Float, Float, Float>] which as an axis of rotation

Parameters:

  • array (Array<Float, Float, Float, Float>) (defaults to: [0.0, 0.0, 0.0, 0.0]) —

    Initial values where

  • angle (Float) (defaults to: nil) —

    if axis given for array parameter



33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
 
# File 'lib/cosmos/utilities/quaternion.rb', line 33

def initialize(array = [0.0, 0.0, 0.0, 0.0], angle = nil)
  if array.length == 4
    @data = array.clone
  elsif array.length == 3 and angle
    a = 0.5 * angle
    s = sin(a) / sqrt(array[0] * array[0] + array[1] * array[1] + array[2] * array[2])
    @data = []
    @data[0] = array[0] * s
    @data[1] = array[1] * s
    @data[2] = array[2] * s
    @data[3] = cos(a)
  else
    raise "Invalid arguments given to Quaternion.new"
  end
end

Instance Attribute Details

#data ⇒ Array<Float, Float, Float, Float>

the last element is the scalar

Returns:



69
70
71
 
# File 'lib/cosmos/utilities/quaternion.rb', line 69

def data
  @data
end

Class Method Details

.arc(f, t) ⇒ Object 



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
 
# File 'lib/cosmos/utilities/quaternion.rb', line 161

def self.arc(f, t)
  dot = f[0] * t[0] + f[1] * t[1] + f[2] * t[2]
  if dot > 0.999999
    x = 0.0
    y = 0.0
    z = 0.0
    w = 1.0
  elsif dot < -0.999999
    if (f.z.abs < f.x.abs) && (f.z.abs < f.y.abs)
      x = f[0] * f[2] - f[2] * f[1]
      y = f[2] * f[0] + f[1] * f[2]
      z = -f[1] * f[1] - f[0] * f[0]
    elsif f.y.abs < f.x.abs
      x = f[1] * f[2] - f[0] * f[1]
      y = f[0] * f[0] + f[2] * f[2]
      z = -f[2] * f[1] - f[1] * f[0]
    else
      x = -f[2] * f[2] - f[1] * f[1]
      y = f[1] * f[0] - f[0] * f[2]
      z = f[0] * f[1] + f[2] * f[0]
    end

    dot = x * x + y * y + z * z
    div = sqrt(dot)
    x /= div
    y /= div
    z /= div
    w = 0.0
  else
    div = sqrt((dot + 1.0) * 2.0)
    x = (f[1] * t[2] - f[2] * t[1]) / div
    y = (f[2] * t[0] - f[0] * t[2]) / div
    z = (f[0] * t[1] - f[1] * t[0]) / div
    w = div * 0.5
  end
  return Quaternion.new([x, y, z, w])
end

.qfromc(rotation_matrix) ⇒ Quaternion

Create a quaternion from a direction-cosine matrix (rotation matrix). Reference Article: J. Spacecraft Vol.13, No.12 Dec.1976 p754

Parameters:

  • rotation_matrix (Matrix) —

    The rotation matrix

Returns:

  • (Quaternion) —

    New quaternion resulting from the matrix



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
 
# File 'lib/cosmos/utilities/quaternion.rb', line 214

def self.qfromc(rotation_matrix)
  tracec = rotation_matrix.trace()
  p = 1.0 + tracec
  if p < 0.0
    p = 0.0
  end
  q = Quaternion.new([0.0, 0.0, 0.0, sqrt(p) / 2.0])
  if q[3] >= 0.1
    factor = 1.0 / (4.0 * q[3])
    q[0] = (rotation_matrix[1][2] - rotation_matrix[2][1]) * factor
    q[1] = (rotation_matrix[2][0] - rotation_matrix[0][2]) * factor
    q[2] = (rotation_matrix[0][1] - rotation_matrix[1][0]) * factor
  else # For rotations near 180 degrees
    q[0] = sqrt(((2.0 * rotation_matrix[0][0]) + 1.0 - tracec) / 4.0)
    q[1] = sqrt(((2.0 * rotation_matrix[1][1]) + 1.0 - tracec) / 4.0)
    q[2] = sqrt(((2.0 * rotation_matrix[2][2]) + 1.0 - tracec) / 4.0)

    i = 0
    if q[1] >= q[i]
      i = 1
    end
    if q[2] >= q[i]
      i = 2
    end
    case i
    when 0
      q[0] = q[0].abs * Quaternion.signnz(rotation_matrix[1][2] - rotation_matrix[2][1])
      q[1] = q[1].abs * Quaternion.signnz((rotation_matrix[1][0] + rotation_matrix[0][1]) * q[0])
      q[2] = q[2].abs * Quaternion.signnz((rotation_matrix[2][0] + rotation_matrix[0][2]) * q[0])
    when 1
      q[1] = q[1].abs * Quaternion.signnz(rotation_matrix[2][0] - rotation_matrix[0][2])
      q[0] = q[0].abs * Quaternion.signnz((rotation_matrix[1][0] + rotation_matrix[0][1]) * q[1])
      q[2] = q[2].abs * Quaternion.signnz((rotation_matrix[2][1] + rotation_matrix[1][2]) * q[1])
    else
      q[2] = q[2].abs * Quaternion.signnz(rotation_matrix[0][1] - rotation_matrix[1][0])
      q[0] = q[0].abs * Quaternion.signnz((rotation_matrix[0][2] + rotation_matrix[2][0]) * q[2])
      q[1] = q[1].abs * Quaternion.signnz((rotation_matrix[1][2] + rotation_matrix[2][1]) * q[2])
    end
  end

  return q
end

.signnz(value) ⇒ Float

Returns The sign of a number as 1.0 = positive, -1.0 = negative.

Parameters:

Returns:

  • (Float) —

    The sign of a number as 1.0 = positive, -1.0 = negative



201
202
203
204
205
206
207
 
# File 'lib/cosmos/utilities/quaternion.rb', line 201

def self.signnz(value)
  if value >= 0.0
    return 1.0
  else
    return -1.0
  end
end

Instance Method Details

#*(other) ⇒ Quaternion Also known as: qmult

Returns New quaternion resulting from the muliplication.

Parameters:

  • other (Quaternion) —

    Quaternion to multiply with

Returns:

  • (Quaternion) —

    New quaternion resulting from the muliplication



117
118
119
120
121
122
123
124
125
126
127
128
129
130
 
# File 'lib/cosmos/utilities/quaternion.rb', line 117

def *(other)
  q = Quaternion.new()

  q[0] =  (@data[3] * other[0]) - (@data[2] * other[1]) +
          (@data[1] * other[2]) + (@data[0] * other[3])
  q[1] = (@data[2] * other[0]) + (@data[3] * other[1]) -
         (@data[0] * other[2]) + (@data[1] * other[3])
  q[2] = -(@data[1] * other[0]) + (@data[0] * other[1]) +
         (@data[3] * other[2]) + (@data[2] * other[3])
  q[3] = -(@data[0] * other[0]) - (@data[1] * other[1]) -
         (@data[2] * other[2]) + (@data[3] * other[3])

  return q
end

#[](index) ⇒ Float

Returns The quaternion component.

Parameters:

  • index (Integer) —

    Which component to access

Returns:

  • (Float) —

    The quaternion component



57
58
59
 
# File 'lib/cosmos/utilities/quaternion.rb', line 57

def [](index)
  return data[index]
end

#[]=(index, value) ⇒ Object

Parameters:

  • index (Integer) —

    The component to set

  • value (Float) —

    The quaternion component



63
64
65
 
# File 'lib/cosmos/utilities/quaternion.rb', line 63

def []=(index, value)
  @data[index] = value
end

#inverse ⇒ Quaternion Also known as: inv

Returns The inverse of the current quaternion.

Returns:

  • (Quaternion) —

    The inverse of the current quaternion



134
135
136
 
# File 'lib/cosmos/utilities/quaternion.rb', line 134

def inverse
  Quaternion.new([-@data[0], -@data[1], -@data[2], @data[3]])
end

#normalize ⇒ Quaternion

Returns The normalized version of the current quaternion.

Returns:

  • (Quaternion) —

    The normalized version of the current quaternion



140
141
142
143
144
145
146
147
148
149
150
 
# File 'lib/cosmos/utilities/quaternion.rb', line 140

def normalize
  t = @data[0] * @data[0] + @data[1] * @data[1] + @data[2] * @data[2] + @data[3] * @data[3]
  if t > 0.0
    f = 1.0 / sqrt(t)
    @data[0] *= f
    @data[1] *= f
    @data[2] *= f
    @data[3] *= f
  end
  return self
end

#q0 ⇒ Float Also known as: x

Returns The first element.

Returns:

  • (Float) —

    The first element



72
73
74
 
# File 'lib/cosmos/utilities/quaternion.rb', line 72

def q0
  return @data[0]
end

#q0=(value) ⇒ Object

Parameters:

  • value (Float) —

    Set the first element



96
97
98
 
# File 'lib/cosmos/utilities/quaternion.rb', line 96

def q0=(value)
  @data[0] = value
end

#q1 ⇒ Float Also known as: y

Returns The second element.

Returns:

  • (Float) —

    The second element



78
79
80
 
# File 'lib/cosmos/utilities/quaternion.rb', line 78

def q1
  return @data[1]
end

#q1=(value) ⇒ Object

Parameters:

  • value (Float) —

    Set the second element



101
102
103
 
# File 'lib/cosmos/utilities/quaternion.rb', line 101

def q1=(value)
  @data[1] = value
end

#q2 ⇒ Float Also known as: z

Returns The third element.

Returns:

  • (Float) —

    The third element



84
85
86
 
# File 'lib/cosmos/utilities/quaternion.rb', line 84

def q2
  return @data[2]
end

#q2=(value) ⇒ Object

Parameters:

  • value (Float) —

    Set the third element



106
107
108
 
# File 'lib/cosmos/utilities/quaternion.rb', line 106

def q2=(value)
  @data[2] = value
end

#q3 ⇒ Float Also known as: w

Returns The scalar element.

Returns:

  • (Float) —

    The scalar element



90
91
92
 
# File 'lib/cosmos/utilities/quaternion.rb', line 90

def q3
  return @data[3]
end

#q3=(value) ⇒ Object

Parameters:

  • value (Float) —

    Set the scalar element



111
112
113
 
# File 'lib/cosmos/utilities/quaternion.rb', line 111

def q3=(value)
  @data[3] = value
end

#to_s ⇒ String

Returns The name of the class and the object_id followed by the data.

Returns:

  • (String) —

    The name of the class and the object_id followed by the data



51
52
53
 
# File 'lib/cosmos/utilities/quaternion.rb', line 51

def to_s
  "#<Cosmos::Quaternion:0x#{self.object_id.to_s(16)}> #{@data}"
end

#vecrot(vector) ⇒ Array<Float, Float, Float>

Rotate a vector using this quaternion

Parameters:

Returns:



156
157
158
159
 
# File 'lib/cosmos/utilities/quaternion.rb', line 156

def vecrot(vector)
  temp_q = self.inverse * (Quaternion.new([vector[0], vector[1], vector[2], 0]) * self)
  return [temp_q[0], temp_q[1], temp_q[2]]
end