Class: GMath3D::Quat

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

Overview

Quat represents quaternion.

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(x = 0.0, y = 0.0, z = 0.0, w = 0.0) ⇒ Quat

[Input] x, y, z, _w_should be Numeric. [Output] return new instance of Quat.



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# File 'lib/quat.rb', line 18

def initialize(x=0.0,y=0.0,z=0.0,w=0.0)
  Util3D.check_arg_type(Numeric, x)
  Util3D.check_arg_type(Numeric, y)
  Util3D.check_arg_type(Numeric, z)
  Util3D.check_arg_type(Numeric, w)
  super()
  @x = x
  @y = y
  @z = z
  @w = w
end

Instance Attribute Details

#w ⇒ Object

Returns the value of attribute w.



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# File 'lib/quat.rb', line 12

def w
  @w
end

#x ⇒ Object

Returns the value of attribute x.



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# File 'lib/quat.rb', line 9

def x
  @x
end

#y ⇒ Object

Returns the value of attribute y.



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# File 'lib/quat.rb', line 10

def y
  @y
end

#z ⇒ Object

Returns the value of attribute z.



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# File 'lib/quat.rb', line 11

def z
  @z
end

Class Method Details

.from_axis(axis, angle) ⇒ Object

[Input] axsi should be Vector3 and angle should be Numeric. [Output] return new instance of Quat.



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# File 'lib/quat.rb', line 34

def self.from_axis(axis, angle)
  Util3D.check_arg_type(Vector3, axis)
  Util3D.check_arg_type(Numeric, angle)
  s = Math.sin(0.5*angle)
  x = s * axis.x
  y = s * axis.y
  z = s * axis.z
  w = Math.cos(0.5*angle)
  return Quat.new(x,y,z,w)
end

.from_matrix(mat) ⇒ Object

[Input] matrix should be Matrix which row and column size are 3. [Output] return new instance of Quat.



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# File 'lib/quat.rb', line 49

def self.from_matrix(mat)
  fourWSquaredMinus1 = mat[0,0] + mat[1,1] + mat[2,2]
  fourXSquaredMinus1 = mat[0,0] - mat[1,1] - mat[2,2]
  fourYSquaredMinus1 = mat[1,1] - mat[0,0] - mat[2,2]
  fourZSquaredMinus1 = mat[2,2] - mat[0,0] - mat[1,1]

  biggestIndex = 0
  fourBiggestSquaredMinus1 = fourWSquaredMinus1
  if(fourXSquaredMinus1 > fourBiggestSquaredMinus1)
    fourBiggestSquaredMinus1 = fourXSquaredMinus1
    biggestIndex = 1
  end
  if(fourYSquaredMinus1 > fourBiggestSquaredMinus1)
    fourBiggestSquaredMinus1 = fourYSquaredMinus1
    biggestIndex = 2
  end
  if(fourZSquaredMinus1 > fourBiggestSquaredMinus1)
    fourBiggestSquaredMinus1 = fourZSquaredMinus1
    biggestIndex = 3
  end

  biggestVal = Math.sqrt(fourBiggestSquaredMinus1 + 1.0) * 0.5
  multi = 0.25 / biggestVal

  case biggestIndex
  when 0
    w = biggestVal
    x = (mat[1,2] - mat[2,1]) *multi
    y = (mat[2,0] - mat[0,2]) *multi
    z = (mat[0,1] - mat[1,0]) *multi
  when 1
    x = biggestVal;
    w = (mat[1,2] - mat[2,1]) *multi
    y = (mat[0,1] + mat[1,0]) *multi
    z = (mat[2,0] + mat[0,2]) *multi
  when 2
    y = biggestVal;
    w = (mat[2,0] - mat[0,2]) *multi
    x = (mat[0,1] + mat[1,0]) *multi
    z = (mat[1,2] + mat[2,1]) *multi
  when 3
    z = biggestVal;
    w = (mat[0,1] - mat[1,0]) *multi
    x = (mat[2,0] + mat[0,2]) *multi
    y = (mat[1,2] + mat[2,1]) *multi
  end
  return Quat.new(x,y,z,w)
end

Instance Method Details

#*(rhs) ⇒ Object

[Input] rsh should be Quat. [Output] return (outer products) multiplyed result as Quat.



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# File 'lib/quat.rb', line 156

def *(rhs)
  Util3D.check_arg_type(Quat, rhs)

  pw = self.w; px = self.x; py = self.y; pz = self.z;
  qw = rhs.w ; qx = rhs.x ; qy = rhs.y ; qz = rhs.z;

  w = pw * qw - px * qx - py * qy - pz * qz
  x = pw * qx + px * qw + py * qz - pz * qy
  y = pw * qy - px * qz + py * qw + pz * qx
  z = pw * qz + px * qy - py * qx + pz * qw
  return Quat.new( x,y,z,w )
end

#+(rhs) ⇒ Object

[Input] rhs should be Quat. [Output] return added result as Quat.



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# File 'lib/quat.rb', line 136

def +(rhs)
  Util3D.check_arg_type(Quat, rhs)
  t1 = Vector3.new(self.x, self.y, self.z)
  t2 = Vector3.new(rhs.x, rhs.y, rhs.z)
  dot = t1.dot(t2)
  t3 = t2.cross(t1)

  t1 *= rhs.w
  t2 *= self.w

  tf = t1 + t2 + t3
  rtn_w = self.w * rhs.w - dot

  return Quat.new(tf.x, tf.y, tf.z, rtn_w)
end

#==(rhs) ⇒ Object

[Input] rhs should be Quat. [Output] return true if rhs equals myself.



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# File 'lib/quat.rb', line 110

def ==(rhs)
  return false if( !rhs.kind_of?(Quat) )
  return false if(self.x != rhs.x)
  return false if(self.y != rhs.y)
  return false if(self.z != rhs.z)
  return false if(self.w != rhs.w)
  true
end

#conjugate ⇒ Object

[Output] return conjugated Quat.



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# File 'lib/quat.rb', line 121

def conjugate
  return Quat.new( -self.x, -self.y, -self.z, self.w)
end

#normalize ⇒ Object

[Output] return normalized result as Quat.



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# File 'lib/quat.rb', line 127

def normalize()
  mag = Math.sqrt(self.x*self.x + self.y*self.y + self.z*self.z)
  return Quat.new(self.x/mag, self.y/mag, self.z/mag, self.w/mag)
end

#to_element_s ⇒ Object 



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# File 'lib/quat.rb', line 98

def to_element_s
  "[#{@x}, #{@y}, #{@z}, #{@w}]"
end

#to_s ⇒ Object 



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

def to_s
  "Quat" + to_element_s
end