Class: RMath3D::RQuat

Inherits:
Object
  • Object
show all
Defined in:
lib/rmath3d/rmath3d_plain.rb

Overview

Document-class: RMath3D::RQuat provies quaternion arithmetic.

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(*a) ⇒ RQuat

call-seq:

RQuat.new -> (0,0,0,0)
RQuat.new(e) -> (e,e,e,e)
RQuat.new( other ) : Copy Constructor
RQuat.new( e0, e1, e2, e3 ) -> (e0,e1,e2,e3)

Creates a new quaternion.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1692

def initialize( *a )
  @e = []
  case a.length
  when 0
    @e = [0.0, 0.0, 0.0, 0.0]
  when 1
    case a[0]
    when Fixnum, Float
      @e = [ a[0], a[0], a[0], a[0] ]
    when RQuat
      @e = [ a[0].x, a[0].y, a[0].z, a[0].w ]
    else
      raise TypeError, "RQuat#initialize : Unknown type #{a[0].class}."
      return nil
    end
  when 4
    a.each_with_index do |elem, index|
      case elem
      when Fixnum, Float
        @e[index] = elem
      else
        raise TypeError, "RQuat#initialize : Unknown type #{elem.class}."
        return nil
      end
    end
  else
    raise RuntimeError, "RQuat#initialize : wrong # of arguments (#{a.length})"
    return nil
  end
  return self
end

Class Method Details

.dot(q1, q2) ⇒ Object

call-seq: RQuat.dot(q_a,q_b) -> value

Calculates the dot product of q_a and q_b.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1891

def RQuat.dot( q1, q2 )
  if q1.class != RQuat || q2.class != RQuat
    raise TypeError, "RQuat#dot : Unknown type q1:#{q2.class}, q2:#{q2.class}."
    return nil
  end
  return q1.x*q2.x + q1.y*q2.y + q1.z*q2.z + q1.w*q2.w
end

.slerp(q1, q2, t) ⇒ Object

call-seq: RQuat.slerp( q_a, q_b, t ) -> interpolated quaternion

Calculates the spherical linear interpolation between q_a and q_b at time t (0.0~1.0).



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1905

def RQuat.slerp( q1, q2, t )
  if q1.class != RQuat || q2.class != RQuat
    raise TypeError, "RQuat#slerp : Unknown type q1:#{q2.class}, q2:#{q2.class}."
    return nil
  end
  s1 = 0.0
  s2 = 0.0
  it = 1.0 - t
  cosine = RQuat.dot( q1, q2 )

  qn1 = q1
  qn2 = q2

  if ( cosine < 0.0 )
    cosine *= -1.0
    qn1 *= -1.0
  end

  if ( (1.0 - cosine) > TOLERANCE )
    theta = Math.acos( cosine )
    sin_theta = Math.sin( theta )

    s1 = Math.sin( it * theta ) / sin_theta
    s2 = Math.sin(  t * theta ) / sin_theta
  else
    s1 = it
    s2 = t
  end

  qn1 *= s1
  qn2 *= s2
  qResult = qn1 + qn2

  return qResult
end

Instance Method Details

#*(arg) ⇒ Object

call-seq: *

quat1 * quat2 : Binary multiply operator.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2072

def *( arg )
  case arg
  when RQuat
    q1x = self.x
    q1y = self.y
    q1z = self.z
    q1w = self.w
    q2x = arg.x
    q2y = arg.y
    q2z = arg.z
    q2w = arg.w
    x = q1w*q2x + q1x*q2w + q1y*q2z - q1z*q2y
    y = q1w*q2y - q1x*q2z + q1y*q2w + q1z*q2x
    z = q1w*q2z + q1x*q2y - q1y*q2x + q1z*q2w
    w = q1w*q2w - q1x*q2x - q1y*q2y - q1z*q2z
    return RQuat.new( x, y, z, w )
  when Fixnum, Float
    return RQuat.new( @e[0]*arg, @e[1]*arg, @e[2]*arg, @e[3]*arg )
  else
    raise TypeError, "RQuat#* : Unknown type #{arg}."
    return nil
  end
end

#+(arg) ⇒ Object

call-seq: +

quat1 + quat2 : Binary plus operator.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2046

def +( arg )
  if arg.class != RQuat
    raise TypeError, "RQuat#+ : Unknown type #{arg.class}."
    return nil
  end
  RQuat.new( x+arg.x, y+arg.y, z+arg.z, w+arg.w )
end

#+@ ⇒ Object

call-seq: +

+quat : Unary plus operator.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2028

def +@
  return self
end

#-(arg) ⇒ Object

call-seq: -

quat1 - quat2 : Binary minus operator.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2059

def -( arg )
  if arg.class != RQuat
    raise TypeError, "RQuat#- : Unknown type #{arg.class}."
    return nil
  end
  RQuat.new( x-arg.x, y-arg.y, z-arg.z, w-arg.w )
end

#-@ ⇒ Object

call-seq: -

-quat : Unary minus operator.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2037

def -@
  return RQuat.new( -@e[0], -@e[1], -@e[2], -@e[3] )
end

#==(other) ⇒ Object

call-seq: ==

quat1 == quat2 : evaluates equality.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2101

def ==( other )
  if other.class != RQuat
    raise TypeError, "RQuat#== : Unknown type #{other.class}."
    return nil
  end

  if  (x-other.x).abs<=Float::EPSILON &&
      (y-other.y).abs<=Float::EPSILON &&
      (z-other.z).abs<=Float::EPSILON &&
      (w-other.w).abs<=Float::EPSILON
    return true
  else
    return false
  end
end

#[](i) ⇒ Object

call-seq: quat -> value

Returns the element at i.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1826

def [](i)
  @e[i]
end

#[]=(i, value) ⇒ Object

call-seq: quat= value

Stores value at i.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1774

def []=(i,value)
  @e[i] = value
end

#add!(other) ⇒ Object

call-seq: quat1.add!( quat2 )

quat1 += quat2 : appends the elements of quat2 into corresponding quat1 elements.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2122

def add!( other )
  if other.class != RQuat
    raise TypeError, "RQ#add! : Unknown type #{other.class}."
    return nil
  end

  self.x += other.x
  self.y += other.y
  self.z += other.z
  self.w += other.w

  return self
end

#coerce(arg) ⇒ Object

call-seq: coerse(other)

Resolves type mismatch.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1747

def coerce( arg )
  case arg
  when Fixnum, Float, Bignum
    return [ self, arg ]
  else
    raise TypeError, "RQuat#coerce : #{arg.self} can't be coerced into  #{self.class}."
    return nil
  end
end

#conjugate! ⇒ Object

call-seq: conjugate!

Conjugates itself.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1968

def conjugate!
  @e[0] *= -1.0
  @e[1] *= -1.0
  @e[2] *= -1.0
  return self
end

#getConjugated ⇒ Object

call-seq: getConjugated

Returns its conjugate quaternion.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1959

def getConjugated
  return RQuat.new( -@e[0], -@e[1], -@e[2], @e[3] )
end

#getInverse ⇒ Object

call-seq: getInverse -> inverse quaternion

Returns the inverse.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1980

def getInverse
  length_sq = getLengthSq()
  return RQuat.new( -@e[0]/length_sq, -@e[1]/length_sq, -@e[2]/length_sq, @e[3]/length_sq )
end

#getLength ⇒ Object

call-seq: getLength

Returns the Euclidean length.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1873

def getLength
  return Math.sqrt( @e[0]*@e[0] + @e[1]*@e[1] + @e[2]*@e[2] + @e[3]*@e[3] )
end

#getLengthSq ⇒ Object

call-seq: getLengthSq

Returns the squared Euclidean length.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1882

def getLengthSq
  return (@e[0]*@e[0] + @e[1]*@e[1] + @e[2]*@e[2] + @e[3]*@e[3]).to_f
end

#getNormalized ⇒ Object

call-seq: getNormalized -> RQuat

Returns normalized quaternion.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2004

def getNormalized
  length = getLength()
  return RQuat.new( @e[0]/length, @e[1]/length, @e[2]/length, @e[3]/length )
end

#invert! ⇒ Object

call-seq: invert! -> self

Inverts itself.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1990

def invert!
  length_sq = getLengthSq()
  @e[0] /= -length_sq
  @e[1] /= -length_sq
  @e[2] /= -length_sq
  @e[3] /= length_sq
  return self
end

#mul!(other) ⇒ Object

call-seq: quat1.mul!( quat2 )

quat1 *= quat2



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2160

def mul!( other )
  case other
  when RQuat
    q1x = self.x
    q1y = self.y
    q1z = self.z
    q1w = self.w
    q2x = other.x
    q2y = other.y
    q2z = other.z
    q2w = other.w

    x = q1w*q2x + q1x*q2w + q1y*q2z - q1z*q2y
    y = q1w*q2y - q1x*q2z + q1y*q2w + q1z*q2x
    z = q1w*q2z + q1x*q2y - q1y*q2x + q1z*q2w
    w = q1w*q2w - q1x*q2x - q1y*q2y - q1z*q2z

    self.x = x
    self.y = y
    self.z = z
    self.w = w

    return self

  when Fixnum, Float
    self.x *= other
    self.y *= other
    self.z *= other
    self.w *= other
    return self

  else
    raise TypeError, "RQuat#mul! : Unknown type #{other.class}."
    return nil
  end
end

#normalize! ⇒ Object

call-seq: normalize! -> self

Normalizes itself.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2014

def normalize!
  length = getLength()
  @e[0] /= length
  @e[1] /= length
  @e[2] /= length
  @e[3] /= length
  return self
end

#rotationAxis(axis, radian) ⇒ Object

call-seq: rotationAxis(axis,radian) -> self

Makes a quaternion that rotates around the axis.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2250

def rotationAxis( axis, radian )
  if axis.class != RVec3
    raise TypeError, "RQuat#rotationAxis : Unknown type #{axis.class}."
    return nil
  end

  s = Math.sin( radian / 2.0 )
  self.x = s * axis.x
  self.y = s * axis.y
  self.z = s * axis.z
  self.w = Math.cos( radian / 2.0 )

  return self
end

#rotationMatrix(mtx) ⇒ Object

call-seq: rotationMarix(mtx4) -> self

Makes a rotation quaternion from a rotation matrix mtx4 (RMtx4).



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2202

def rotationMatrix( mtx )
  if mtx.class != RMtx3 && mtx.class != RMtx4
    raise TypeError, "RQuat#rotationMatrix : Unknown type #{mtx.class}."
    return nil
  end

  diag00 = mtx.getElement(0,0)
  diag11 = mtx.getElement(1,1)
  diag22 = mtx.getElement(2,2)

  if ( diag00 + diag11 + diag22 > 0.0 )
    t = diag00 + diag11 + diag22 + 1.0
    s = 1.0 / ( Math.sqrt( t ) * 2.0 )
    self.w = s * t
    self.z = (mtx.getElement(1,0) - mtx.getElement(0,1)) * s
    self.y = (mtx.getElement(0,2) - mtx.getElement(2,0)) * s
    self.x = (mtx.getElement(2,1) - mtx.getElement(1,2)) * s
  elsif ( diag00 > diag11 && diag00 > diag22 )
    t = diag00 - diag11 - diag22 + 1.0
    s = 1.0 / ( Math.sqrt( t ) * 2.0 )
    self.x = s * t
    self.y = (mtx.getElement(1,0) + mtx.getElement(0,1)) * s
    self.z = (mtx.getElement(0,2) + mtx.getElement(2,0)) * s
    self.w = (mtx.getElement(2,1) - mtx.getElement(1,2)) * s
  elsif ( diag11 > diag22 )
    t = -diag00 + diag11 - diag22 + 1.0
    s = 1.0 / ( Math.sqrt( t ) * 2.0 )
    self.y = s * t
    self.x = (mtx.getElement(1,0) + mtx.getElement(0,1)) * s
    self.w = (mtx.getElement(0,2) - mtx.getElement(2,0)) * s
    self.z = (mtx.getElement(2,1) + mtx.getElement(1,2)) * s
  else
    t = -diag00 - diag11 + diag22 + 1.0
    s = 1.0 / ( Math.sqrt( t ) * 2.0 )
    self.z = s * t
    self.w = (mtx.getElement(1,0) - mtx.getElement(0,1)) * s
    self.x = (mtx.getElement(0,2) + mtx.getElement(2,0)) * s
    self.y = (mtx.getElement(2,1) + mtx.getElement(1,2)) * s
  end

  return self
end

#setElements(x, y, z, w) ⇒ Object

call-seq: setElements( e0, e1, e2, e3 )

Stores given 4 new values.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1762

def setElements( x, y, z, w )
  self.x = x
  self.y = y
  self.z = z
  self.w = w
end

#setIdentity ⇒ Object

call-seq: setIdentity

Sets as identity quaternion.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1946

def setIdentity
  self.x = 0.0
  self.y = 0.0
  self.z = 0.0
  self.w = 1.0
  return self
end

#sub!(other) ⇒ Object

call-seq: quat1.sub!( quat2 )

quat1 -= quat2 : subtracts the elements of quat2 from corresponding quat1 elements.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2141

def sub!( other )
  if other.class != RQuat
    raise TypeError, "RQuat#sub! : Unknown type #{other.class}."
    return nil
  end

  self.x -= other.x
  self.y -= other.y
  self.z -= other.z
  self.w -= other.w

  return self
end

#to_a ⇒ Object

call-seq: to_a

Returns its elements as a new Array.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1738

def to_a
  return @e
end

#to_s ⇒ Object

call-seq: to_s

Returns human-readable string.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1729

def to_s
  return "( #{@e[0]}, #{@e[1]}, #{@e[2]}, #{@e[3]} )\n"
end

#toAxisAngle ⇒ Object

call-seq: toAxisAngle -> [axis,radian]

Returns its rotation axis (RVec3) and rotation angle (in radian).



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# File 'lib/rmath3d/rmath3d_plain.rb', line 2270

def toAxisAngle
  axis = RVec3.new( self.x, self.y, self.z ).normalize!
  radian = 2.0 * Math.acos( self.w )

  return [ axis, radian ]
end

#w ⇒ Object

call-seq: w -> value

Returns the value of w.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1857

def w() return @e[3] end

#w=(value) ⇒ Object

call-seq: w= value

Stores value as w.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1804

def w=(value) @e[3] = value end

#x ⇒ Object

call-seq: x -> value

Returns the value of x.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1836

def x() return @e[0] end

#x=(value) ⇒ Object

call-seq: x= value

Stores value as x.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1783

def x=(value) @e[0] = value end

#xyz ⇒ Object

call-seq: xyz -> RVec3

Returns the values of x, y and z with new RVec3(x,y,z).



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1864

def xyz()
  return RVec3.new( @e[0], @e[1], @e[2] )
end

#xyz=(arg) ⇒ Object

call-seq: xyz= vXYZ

Copies the values of vXYZ(RVec3) into x, y and z.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1811

def xyz=( arg )
  if arg.class != RVec3
    raise TypeError, "RQuat#xyz= : Unknown type #{arg.class}."
    return nil
  end
  @e[0] = arg.x
  @e[1] = arg.y
  @e[2] = arg.z
end

#y ⇒ Object

call-seq: y -> value

Returns the value of y.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1843

def y() return @e[1] end

#y=(value) ⇒ Object

call-seq: y= value

Stores value as y.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1790

def y=(value) @e[1] = value end

#z ⇒ Object

call-seq: z -> value

Returns the value of z.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1850

def z() return @e[2] end

#z=(value) ⇒ Object

call-seq: z= value

Stores value as z.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1797

def z=(value) @e[2] = value end