class Quaternion

Public Class Methods

new(*args) click to toggle source

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

# 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

Public Instance Methods

*(q) click to toggle source

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

# 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)
    beta0, beta_s = quatMult(q)
    result = Quaternion.new(beta0, *beta_s)
    return result
  end
end

+(q) click to toggle source

Returns the sum of two quaternions.

# File lib/quaternion.rb, line 64
def +(q)
  beta0, beta_s = q.get()
  return Quaternion.new(@beta0 + beta0, *(@beta_s + beta_s))
end

-(q) click to toggle source

Returns the difference of two quaternions.

# File lib/quaternion.rb, line 70
def -(q)
  beta0, beta_s = q.get()
  return Quaternion.new(@beta0 - beta0, *(@beta_s - beta_s))
end

-@() click to toggle source

Returns the additive inverse of the quaternion.

# File lib/quaternion.rb, line 76
def -@
  Quaternion.new(-@beta0, -@beta_s[0], -@beta_s[1], -@beta_s[2])
end

/(s) click to toggle source

Returns the result of dividing the quaternion by a scalar.

# File lib/quaternion.rb, line 81
def /(s)
  return Quaternion.new(@beta0 / s, *(@beta_s / s))
end

==(q) click to toggle source

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

# File lib/quaternion.rb, line 99
def ==(q)
  if get() == q.get()
    return true
  else
    return false
  end
end

coerce(other) click to toggle source

# File lib/quaternion.rb, line 112
def coerce(other)
  return self, other
end

conjugate() click to toggle source

Returns the conjugate of the quaternion.

# File lib/quaternion.rb, line 48
def conjugate
  return Quaternion.new(@beta0, *(-1*@beta_s))
end

get() click to toggle source

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

# File lib/quaternion.rb, line 38
def get
  return @beta0, @beta_s
end

inverse() click to toggle source

Returns the multiplicative inverse of the quaterion.

# File lib/quaternion.rb, line 53
def inverse
  return self.conjugate() / self.norm() ** 2
end

norm() click to toggle source

Returns the magnitude of the quaternion.

# File lib/quaternion.rb, line 43
def norm
  return Math.sqrt(@beta0**2 + @beta_s.norm()**2)
end

normalized() click to toggle source

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

# File lib/quaternion.rb, line 59
def normalized
  return self / norm()
end

set(w, x, y, z) click to toggle source

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

# File lib/quaternion.rb, line 32
def set(w, x, y, z)
  @beta0 = w
  @beta_s = Vector[x,y,z]
end

to_s() click to toggle source

Returns the string representation of the quaternion.

# File lib/quaternion.rb, line 108
def to_s
  return "(" + @beta0.to_s + ", " + @beta_s.to_s + ")"
end

Private Instance Methods

cross_product(v1, v2) click to toggle source

# File lib/quaternion.rb, line 117
def cross_product(v1, v2)
  # returns the cross product of vectors v1 and v2.
  return Vector[ v1[1]*v2[2] - v1[2]*v2[1],
                 v1[2]*v2[0] - v1[0]*v2[2],
                 v1[0]*v2[1] - v1[1]*v2[0] ]
end

quatMult(q) click to toggle source

Multiplies with another quaternion, and returns the resulting beta0 and beta_s values.

# File lib/quaternion.rb, line 126
def quatMult(q)
  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)
  return beta0, beta_s
end