Class: Cosmos::Quaternion

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

Overview

A quaternion where q is the scalar component

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



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# File 'lib/cosmos/utilities/quaternion.rb', line 26

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

Class Method Details

.arc(f, t) ⇒ Object 



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# File 'lib/cosmos/utilities/quaternion.rb', line 162

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



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# File 'lib/cosmos/utilities/quaternion.rb', line 215

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



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# File 'lib/cosmos/utilities/quaternion.rb', line 202

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



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# File 'lib/cosmos/utilities/quaternion.rb', line 118

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



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# File 'lib/cosmos/utilities/quaternion.rb', line 50

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

#[]=(index, value) ⇒ Object

Parameters:

  • index (Integer) —

    The component to set

  • value (Float) —

    The quaternion component



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# File 'lib/cosmos/utilities/quaternion.rb', line 56

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

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

the last element is the scalar

Returns:

  • (Array<Float, Float, Float, Float>) —

    The entire quaternion where the



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# File 'lib/cosmos/utilities/quaternion.rb', line 62

def data
  return @data
end

#data=(array) ⇒ Object

where the the last element is the scalar

Parameters:

  • array (Array<Float, Float, Float, Float>) —

    The entire quaternion



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# File 'lib/cosmos/utilities/quaternion.rb', line 68

def data=(array)
  @data = array
end

#inverse ⇒ Quaternion Also known as: inv

Returns The inverse of the current quaternion.

Returns:

  • (Quaternion) —

    The inverse of the current quaternion



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

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



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# File 'lib/cosmos/utilities/quaternion.rb', line 141

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



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

def q0
  return @data[0]
end

#q0=(value) ⇒ Object

Parameters:

  • value (Float) —

    Set the first element



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

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

#q1 ⇒ Float Also known as: y

Returns The second element.

Returns:

  • (Float) —

    The second element



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

def q1
  return @data[1]
end

#q1=(value) ⇒ Object

Parameters:

  • value (Float) —

    Set the second element



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

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

#q2 ⇒ Float Also known as: z

Returns The third element.

Returns:

  • (Float) —

    The third element



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

def q2
  return @data[2]
end

#q2=(value) ⇒ Object

Parameters:

  • value (Float) —

    Set the third element



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

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

#q3 ⇒ Float Also known as: w

Returns The scalar element.

Returns:

  • (Float) —

    The scalar element



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

def q3
  return @data[3]
end

#q3=(value) ⇒ Object

Parameters:

  • value (Float) —

    Set the scalar element



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

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



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# File 'lib/cosmos/utilities/quaternion.rb', line 44

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:

  • vector (Array<Float, Float Float>) —

    Vector to rotate

Returns:

  • (Array<Float, Float, Float>) —

    New rotated vector



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

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