Class: Geo3d::Quaternion

Inherits:
Object
  • Object
show all
Defined in:
lib/geo3d/quaternion.rb

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(*args) ⇒ Quaternion

Returns a new instance of Quaternion.



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# File 'lib/geo3d/quaternion.rb', line 5

def initialize *args
  @x, @y, @z, @w = 0.0, 0.0, 0.0, 0.0
  @x = args[0].to_f if args.size > 0
  @y = args[1].to_f if args.size > 1
  @z = args[2].to_f if args.size > 2
  @w = args[3].to_f if args.size > 3
end

Instance Attribute Details

#w ⇒ Object

Returns the value of attribute w.



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# File 'lib/geo3d/quaternion.rb', line 3

def w
  @w
end

#x ⇒ Object

Returns the value of attribute x.



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# File 'lib/geo3d/quaternion.rb', line 3

def x
  @x
end

#y ⇒ Object

Returns the value of attribute y.



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# File 'lib/geo3d/quaternion.rb', line 3

def y
  @y
end

#z ⇒ Object

Returns the value of attribute z.



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# File 'lib/geo3d/quaternion.rb', line 3

def z
  @z
end

Class Method Details

.from_axis(rotation_axis, radians = 0) ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 49

def self.from_axis rotation_axis, radians = 0
  radians = Geo3d::Utils.normalize_angle radians  #todo: is this cheating?....
  normalized_rotation_axis = rotation_axis.zero_w.normalize
  q = self.new
  q.x = Math.sin(radians / 2.0) * normalized_rotation_axis.x
  q.y = Math.sin(radians / 2.0) * normalized_rotation_axis.y
  q.z = Math.sin(radians / 2.0) * normalized_rotation_axis.z
  q.w = Math.cos(radians / 2.0)
  q
end

.from_axis_degrees(rotation_axis, degrees = 0) ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 60

def self.from_axis_degrees rotation_axis, degrees = 0
  from_axis rotation_axis, Geo3d::Utils.to_radians(degrees)
end

.from_matrix(pm) ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 64

def self.from_matrix pm
  pout = self.new

  #puts "trace is #{pm.trace}"
  if false && pm.trace > 1.0
    sq_root_of_trace = Math.sqrt pm.trace
    pout.x = (pm._23 - pm._32) / (2.0 * sq_root_of_trace)
    pout.y = (pm._31 - pm._13) / (2.0 * sq_root_of_trace)
    pout.z = (pm._12- pm._21) / (2.0 * sq_root_of_trace)
    pout.w = sq_root_of_trace / 2.0
    #puts "a and pout is #{pout.inspect}"

    return pout
  end
  maxi = 0
  maxdiag = pm._11


  for i in 1..2
    if pm[i, i] > maxdiag #todo: indexing might need to be fixed > maxdiag
      maxi = i
      maxdiag = pm[i, i] #todo: indexing might need to be fixed
    end
  end
  case maxi
    when 0
      s = 2.0 * Math.sqrt(1.0 + pm._11 - pm._22 - pm._33)
      pout.x = 0.25 * s
      pout.y = (pm._12 + pm._21) / s
      pout.z = (pm._13 + pm._31) / s
      pout.w = (pm._23 - pm._32) / s

    when 1
      s = 2.0 * Math.sqrt(1.0 + pm._22 - pm._11 - pm._33)
      pout.x = (pm._12 + pm._21) / s
      pout.y = 0.25 * s
      pout.z = (pm._23 + pm._32) / s
      pout.w = (pm._31 - pm._13) / s

    when 2
      s = 2.0 * Math.sqrt(1.0 + pm._33 - pm._11 - pm._22)
      pout.x = (pm._13 + pm._31) / s
      pout.y = (pm._23 + pm._32) / s
      pout.z = 0.25 * s
      pout.w = (pm._12 - pm._21) / s
  end
  #puts "b"
  pout
end

.identity ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 212

def self.identity
  self.new 0, 0, 0, 1
end

Instance Method Details

#!=(vec) ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 45

def != vec
  !(self == vec)
end

#*(v) ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 122

def * v
  if Quaternion == v.class
    quat = v
    out = self.class.new
    out.w = w * quat.w - x * quat.x - y * quat.y - z * quat.z
    out.x = w * quat.x + x * quat.w + y * quat.z - z * quat.y
    out.y = w * quat.y - x * quat.z + y * quat.w + z * quat.x
    out.z = w * quat.z + x * quat.y - y * quat.x + z * quat.w
    out
  else
    self.class.new x*v, y*v, z*v, w*v
  end
end

#+(quat) ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 114

def + quat
  self.class.new x + quat.x, y + quat.y, z + quat.z, w + quat.w
end

#+@ ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 33

def +@
  self.class.new x, y, z, w
end

#-(quat) ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 118

def - quat
  self.class.new x - quat.x, y - quat.y, z - quat.z, w - quat.w
end

#-@ ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 37

def -@
  self.class.new -x, -y, -z, -w
end

#/(v) ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 136

def / v
  self.class.new x/v, y/v, z/v, w/v
end

#==(q) ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 41

def == q
  Geo3d::Utils.float_cmp(x, q.x) && Geo3d::Utils.float_cmp(y, q.y) && Geo3d::Utils.float_cmp(z, q.z) && Geo3d::Utils.float_cmp(w, q.w)
end

#angle ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 159

def angle
  Math.acos(normalize.w) * 2.0
end

#angle_degrees ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 163

def angle_degrees
  Geo3d::Utils.to_degrees angle
end

#axis ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 155

def axis
  Vector.new( *(normalize / Math.sin( angle / 2.0 )).to_a ).zero_w
end

#conjugate ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 195

def conjugate
  self.class.new -x, -y, -z, w
end

#dot(quat) ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 175

def dot quat
  x * quat.x + y * quat.y + z * quat.z + w * quat.w
end

#identity? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/geo3d/quaternion.rb', line 208

def identity?
  self == self.class.identity
end

#inverse ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 199

def inverse
  norm = length_squared
  if norm.zero?
    self.class.new 0, 0, 0, 0
  else
    conjugate / norm
  end
end

#length ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 171

def length
  Math.sqrt length_squared
end

#length_squared ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 167

def length_squared
  dot self
end

#normalize ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 189

def normalize
  q = self.class.new x, y, z, w
  q.normalize!
  q
end

#normalize! ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 179

def normalize!
  len = length
  if length > 0
    @x /= len
    @y /= len
    @z /= len
    @w /= len
  end
end

#to_a ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 13

def to_a
  [x,y,z,w]
end

#to_matrix ⇒ Object 



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# File 'lib/geo3d/quaternion.rb', line 140

def to_matrix
  v = normalize
  matrix = Matrix.identity
  matrix._11 = 1.0 - 2.0 * (v.y * v.y + v.z * v.z)
  matrix._12 = 2.0 * (v.x * v.y + v.z * v.w)
  matrix._13 = 2.0 * (v.x * v.z - v.y * v.w)
  matrix._21 = 2.0 * (v.x * v.y - v.z * v.w)
  matrix._22 = 1.0 - 2.0 * (v.x * v.x + v.z * v.z)
  matrix._23 = 2.0 * (v.y * v.z + v.x * v.w)
  matrix._31 = 2.0 * (v.x * v.z + v.y * v.w)
  matrix._32 = 2.0 * (v.y * v.z - v.x * v.w)
  matrix._33 = 1.0 - 2.0 * (v.x * v.x + v.y * v.y)
  matrix
end