Class: Quaternion

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

Direct Known Subclasses

UnitQuaternion

Instance Method Summary collapse

Constructor Details

#initialize(*args) ⇒ Quaternion

Create new quaternion from 4 values. If no arguments are provided, creates the zero quaternion.



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# File 'lib/quaternion.rb', line 15

def initialize(*args)
  if args.length() == 4
    set(*args)
  elsif args.length() == 0
    set(0, 0, 0, 0)
  else
    raise(ArgumentError, "wrong number of arguments (must be 0 or 4)")
  end
end

Instance Method Details

#*(q) ⇒ Object

Returns the result of multiplying the quaternion by a scalar or another quaternion.



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# File 'lib/quaternion.rb', line 87

def *(q)
  if q.is_a?(Numeric)
    return Quaternion.new(@beta0 * q, *(@beta_s * q))
  elsif q.is_a?(Quaternion)
    q_beta0, q_beta_s = q.get()
    beta0 = @beta0 * q_beta0 - @beta_s.inner_product(q_beta_s)
    beta_s =  @beta0 * q_beta_s + q_beta0 * @beta_s +
      cross_product(@beta_s, q_beta_s)
    result = self.class.new(beta0, *beta_s)
    return result
  end
end

#+(q) ⇒ Object

Returns the sum of two quaternions.



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# File 'lib/quaternion.rb', line 64

def +(q)
  beta0, beta_s = q.get()
  return Quaternion.new(@beta0 + beta0, *(@beta_s + beta_s))
end

#-(q) ⇒ Object

Returns the difference of two quaternions.



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# File 'lib/quaternion.rb', line 70

def -(q)
  beta0, beta_s = q.get()
  return Quaternion.new(@beta0 - beta0, *(@beta_s - beta_s))
end

#-@ ⇒ Object

Returns the additive inverse of the quaternion.



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# File 'lib/quaternion.rb', line 76

def -@
  Quaternion.new(-@beta0, -@beta_s[0], -@beta_s[1], -@beta_s[2])
end

#/(s) ⇒ Object

Returns the result of dividing the quaternion by a scalar.



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# File 'lib/quaternion.rb', line 81

def /(s)
  return Quaternion.new(@beta0 / s, *(@beta_s / s))
end

#==(q) ⇒ Object

Returns true if two quaternions are equal (meaning that their corresponding entries are equal to each other) and false otherwise.



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

def ==(q)
  if get() == q.get()
    return true
  else
    return false
  end
end

#coerce(other) ⇒ Object 



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# File 'lib/quaternion.rb', line 115

def coerce(other)
  return self, other
end

#conjugate ⇒ Object

Returns the conjugate of the quaternion.



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# File 'lib/quaternion.rb', line 48

def conjugate
  return Quaternion.new(@beta0, *(-1*@beta_s))
end

#get ⇒ Object

Returns the quaternion’s values as a scalar and a vector.



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# File 'lib/quaternion.rb', line 38

def get
  return @beta0, @beta_s
end

#inverse ⇒ Object

Returns the multiplicative inverse of the quaterion.



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# File 'lib/quaternion.rb', line 53

def inverse
  return self.conjugate() / self.norm() ** 2
end

#norm ⇒ Object

Returns the magnitude of the quaternion.



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# File 'lib/quaternion.rb', line 43

def norm
  return Math.sqrt(@beta0**2 + @beta_s.norm()**2)
end

#normalized ⇒ Object

Returns a normalized quaternion. q.normalized() is equivalent to q/q.norm().



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# File 'lib/quaternion.rb', line 59

def normalized
  return self / norm()
end

#set(w, x, y, z) ⇒ Object

Set the quaternion’s values.

Params:

w

the real part of the quaterion

x

the i-component

y

the j-component

z

the k-component



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# File 'lib/quaternion.rb', line 32

def set(w, x, y, z)
  @beta0 = w
  @beta_s = Vector[x,y,z]
end

#to_s ⇒ Object

Returns the string representation of the quaternion.



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# File 'lib/quaternion.rb', line 111

def to_s
  return "(" + @beta0.to_s + ", " + @beta_s.to_s + ")"
end