Class: RMath3D::RMtx3

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

Overview

Document-class: RMath3D::RMtx3 provies 3x3 matrix arithmetic.

Notice

  • elements are stored in column-major order.

Instance Method Summary collapse

Constructor Details

#initialize(*a) ⇒ RMtx3

call-seq:

RMtx3.new -> ((1,0,0),(0,1,0),(0,0,1))
RMtx3.new(e) -> ((e,e,e), (e,e,e), (e,e,e))
RMtx3.new( other ) : Copy Constructor
RMtx3.new( e0, e1, ..., e8 ) -> ((e0,e1,e2), (e3,e4,e5), (e6,e7,e8))

Creates a new 3x3 matrix.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 554

def initialize( *a )
  # [NOTE] elemetns are stored in column-major order.

  @e = []
  case a.length
  when 0
    @e = [ 0.0, 0.0, 0.0,
           0.0, 0.0, 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], a[0], a[0],
             a[0], a[0], a[0] ]
    when RMtx3
      # Copy Constructor

      @e = [ a[0].e00, a[0].e10, a[0].e20,
             a[0].e01, a[0].e11, a[0].e21,
             a[0].e02, a[0].e12, a[0].e22 ]
    else
      raise TypeError, "RMtx3#initialize : Unknown type #{a[0].class}."
      return nil
    end
  when 9
    # Element-wise setter

    for row in 0...3 do
      for col in 0...3 do
        index = 3*row + col
        case a[index]
        when Fixnum, Float
          setElement( row, col, a[index] )
        else
          raise TypeError, "RMtx3#initialize : Unknown type #{a[0].class}."
          return nil
        end
      end
    end
  else
    raise RuntimeError, "RMtx3#initialize : wrong # of arguments (#{a.length})"
    return nil
  end

  return self
end

Instance Method Details

#*(arg) ⇒ Object

call-seq: *

mtx1 * mtx2 : Binary multiply operator.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1100

def *( arg )
  case arg
  when Fixnum, Float, Bignum
    return RMtx3.new( arg*self.e00, arg*self.e01, arg*self.e02,
                      arg*self.e10, arg*self.e11, arg*self.e12,
                      arg*self.e20, arg*self.e21, arg*self.e22 )

  when RMtx3
    result = RMtx3.new
    for row in 0...3 do
      for col in 0...3 do
        sum = 0.0
        for i in 0...3 do
          sum += getElement( row, i ) * arg.getElement( i, col )
        end
        result.setElement( row, col, sum )
      end
    end
    return result

  else
    raise TypeError, "RMtx3#*(arg) : Unknown type #{arg.class} given."
    return nil
  end
end

#+(arg) ⇒ Object

call-seq: +

mtx1 + mtx2 : Binary plus operator.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1058

def +( arg )
  if ( arg.class != RMtx3 )
    raise TypeError, "RMtx3#+(arg) : Unknown type #{arg.class} given as RMtx3."
    return nil
  end

  result = RMtx3.new
  for row in 0...3 do
    for col in 0...3 do
      result.setElement( row, col, getElement(row,col) + arg.getElement(row,col) )
    end
  end

  return result
end

#+@ ⇒ Object

call-seq: +

+mtx : Unary plus operator.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1040

def +@
  return self
end

#-(arg) ⇒ Object

call-seq: -

mtx1 - mtx2 : Binary minus operator.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1079

def -( arg )
  if ( arg.class != RMtx3 )
    raise TypeError, "RMtx3#-(arg) : Unknown type #{arg.class} given as RMtx3."
    return nil
  end

  result = RMtx3.new
  for row in 0...3 do
    for col in 0...3 do
      result.setElement( row, col, getElement(row,col) - arg.getElement(row,col) )
    end
  end

  return result
end

#-@ ⇒ Object

call-seq: -

-mtx : Unary minus operator.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1049

def -@
  return RMtx3.new( self * -1.0 )
end

#==(other) ⇒ Object

call-seq: ==

mtx1 == mtx2 : evaluates equality.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1131

def ==( other )
  if ( other.class != RMtx3 )
    raise TypeError, "RMtx3#==(other) : Unknown type #{other.class} given as RMtx3."
    return nil
  end

  for row in 0...3 do
    for col in 0...3 do
      if ( (getElement(row,col) - other.getElement(row,col)).abs > TOLERANCE )
        return false
      end
    end
  end
  return true
end

#[](row, col) ⇒ Object Also known as: getElement

call-seq: [row,col] -> value

Returns the element at (row,col).



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# File 'lib/rmath3d/rmath3d_plain.rb', line 669

def [](row,col)
  # [NOTE] elemetns are stored in column-major order.

  return @e[col*3+row]
end

#[]=(row, col, value) ⇒ Object Also known as: setElement

call-seq: [row,col]= value

Stores value at (row,col).



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# File 'lib/rmath3d/rmath3d_plain.rb', line 658

def []=(row,col,value)
  # [NOTE] elemetns are stored in column-major order.

  @e[col*3+row] = value
end

#add!(other) ⇒ Object

call-seq: mtx1.add!( mtx2 )

mtx1 += mtx2 : appends the elements of mtx2 into corresponding mtx1 elements.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1152

def add!( other )
  if ( other.class != RMtx3 )
    raise TypeError, "RMtx3#add! : Unknown type #{other.class} given as RMtx3."
    return nil
  end

  result = RMtx3.new
  for row in 0...3 do
    for col in 0...3 do
      self.setElement( row, col, getElement(row,col) + other.getElement(row,col) )
    end
  end

  return self
end

#coerce ⇒ Object

call-seq: coerse(other)

Resolves type mismatch.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 624

def coerce
  case arg
  when Fixnum, Float, Bignum
    return [ self, arg ]
  else
    raise TypeError, "RMtx3#coerce : #{arg.self} can't be coerced into  #{self.class}."
    return nil
  end
end

#e00 ⇒ Object

Returns the element at row 0 and column 0.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 676

def e00() getElement(0,0) end

#e00=(value) ⇒ Object

Replaces the element at row 0 and column 0 by value.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 695

def e00=(value) setElement(0,0,value) end

#e01 ⇒ Object

Returns the element at row 0 and column 1.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 678

def e01() getElement(0,1) end

#e01=(value) ⇒ Object

Replaces the element at row 0 and column 1 by value.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 697

def e01=(value) setElement(0,1,value) end

#e02 ⇒ Object

Returns the element at row 0 and column 2.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 680

def e02() getElement(0,2) end

#e02=(value) ⇒ Object

Replaces the element at row 0 and column 2 by value.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 699

def e02=(value) setElement(0,2,value) end

#e10 ⇒ Object

Returns the element at row 1 and column 0.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 682

def e10() getElement(1,0) end

#e10=(value) ⇒ Object

Replaces the element at row 1 and column 0 by value.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 701

def e10=(value) setElement(1,0,value) end

#e11 ⇒ Object

Returns the element at row 1 and column 1.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 684

def e11() getElement(1,1) end

#e11=(value) ⇒ Object

Replaces the element at row 1 and column 1 by value.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 703

def e11=(value) setElement(1,1,value) end

#e12 ⇒ Object

Returns the element at row 1 and column 2.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 686

def e12() getElement(1,2) end

#e12=(value) ⇒ Object

Replaces the element at row 1 and column 2 by value.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 705

def e12=(value) setElement(1,2,value) end

#e20 ⇒ Object

Returns the element at row 2 and column 0.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 688

def e20() getElement(2,0) end

#e20=(value) ⇒ Object

Replaces the element at row 2 and column 0 by value.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 707

def e20=(value) setElement(2,0,value) end

#e21 ⇒ Object

Returns the element at row 2 and column 1.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 690

def e21() getElement(2,1) end

#e21=(value) ⇒ Object

Replaces the element at row 2 and column 1 by value.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 709

def e21=(value) setElement(2,1,value) end

#e22 ⇒ Object

Returns the element at row 2 and column 2.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 692

def e22() getElement(2,2) end

#e22=(value) ⇒ Object

Replaces the element at row 2 and column 2 by value.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 711

def e22=(value) setElement(2,2,value) end

#getColumn(column) ⇒ Object

call-seq: mtx3.getColumn© -> RVec3

Returns c-th column vector.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 728

def getColumn( column )
  return RVec3.new( self[0,column], self[1,column], self[2,column] )
end

#getDeterminant ⇒ Object

call-seq: getDeterminant -> determinant

Calculates determinant.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 790

def getDeterminant
  e00 * (e11*e22 - e12*e21) -
  e01 * (e10*e22 - e12*e20) +
  e02 * (e10*e21 - e11*e20)
end

#getInverse ⇒ Object

call-seq: getInverse -> inverse

Returns the inverse.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 823

def getInverse
  result = RMtx3.new

  result.e00 =  (self.e11*self.e22 - self.e12*self.e21)
  result.e01 = -(self.e01*self.e22 - self.e02*self.e21)
  result.e02 =  (self.e01*self.e12 - self.e02*self.e11)

  result.e10 = -(self.e10*self.e22 - self.e12*self.e20)
  result.e11 =  (self.e00*self.e22 - self.e02*self.e20)
  result.e12 = -(self.e00*self.e12 - self.e02*self.e10)

  result.e20 =  (self.e10*self.e21 - self.e11*self.e20)
  result.e21 = -(self.e00*self.e21 - self.e01*self.e20)
  result.e22 =  (self.e00*self.e11 - self.e01*self.e10)

  det = e00 * result.e00 + e01 * result.e10 + e02 * result.e20

  if ( det.abs < TOLERANCE )
    raise RuntimeError, "RMtx3#getInverse : det.abs < TOLERANCE"
    return nil
  end

  d = 1.0 / det

  result.mul!( d )

  return result
end

#getRow(row) ⇒ Object

call-seq: mtx3.getRow® -> RVec3

Returns r-th row vector.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 719

def getRow( row )
  return RVec3.new( self[row,0], self[row,1], self[row,2] )
end

#getTransposed ⇒ Object

call-seq: getTransposed

Returns transposed matrix.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 801

def getTransposed
  return RMtx3.new( @e[0], @e[1], @e[2],
                    @e[3], @e[4], @e[5],
                    @e[6], @e[7], @e[8] )
end

#invert! ⇒ Object

call-seq: invert! -> self

Makes itself as the inverse of the original matrix.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 857

def invert!
  elements = Array.new( 9 )

  elements[3*0+0] =  (self.e11*self.e22 - self.e12*self.e21)
  elements[3*0+1] = -(self.e01*self.e22 - self.e02*self.e21)
  elements[3*0+2] =  (self.e01*self.e12 - self.e02*self.e11)

  elements[3*1+0] = -(self.e10*self.e22 - self.e12*self.e20)
  elements[3*1+1] =  (self.e00*self.e22 - self.e02*self.e20)
  elements[3*1+2] = -(self.e00*self.e12 - self.e02*self.e10)

  elements[3*2+0] =  (self.e10*self.e21 - self.e11*self.e20)
  elements[3*2+1] = -(self.e00*self.e21 - self.e01*self.e20)
  elements[3*2+2] =  (self.e00*self.e11 - self.e01*self.e10)

  det = e00 * elements[3*0+0] + e01 * elements[3*1+0] + e02 * elements[3*2+0]

  if ( det.abs < TOLERANCE )
    raise RuntimeError, "RMtx3#invert! : det.abs < TOLERANCE"
    return nil
  end

  d = 1.0 / det

  setElement( 0, 0, d * elements[3*0+0] )
  setElement( 0, 1, d * elements[3*0+1] )
  setElement( 0, 2, d * elements[3*0+2] )
  setElement( 1, 0, d * elements[3*1+0] )
  setElement( 1, 1, d * elements[3*1+1] )
  setElement( 1, 2, d * elements[3*1+2] )
  setElement( 2, 0, d * elements[3*2+0] )
  setElement( 2, 1, d * elements[3*2+1] )
  setElement( 2, 2, d * elements[3*2+2] )

  return self
end

#mul!(other) ⇒ Object

call-seq: mtx1.mul!( mtx2 )

mtx1 *= mtx2



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1194

def mul!( other )
  case other
  when Fixnum, Float, Bignum
    self.e00 = other*self.e00
    self.e01 = other*self.e01
    self.e02 = other*self.e02
    self.e10 = other*self.e10
    self.e11 = other*self.e11
    self.e12 = other*self.e12
    self.e20 = other*self.e20
    self.e21 = other*self.e21
    self.e22 = other*self.e22

    return self
  when RMtx3
    result = RMtx3.new
    for row in 0...3 do
      for col in 0...3 do
        sum = 0.0
        for i in 0...3 do
          sum += getElement( row, i ) * other.getElement( i, col )
        end
        result.setElement( row, col, sum )
      end
    end

    self.e00 = result.e00
    self.e01 = result.e01
    self.e02 = result.e02
    self.e10 = result.e10
    self.e11 = result.e11
    self.e12 = result.e12
    self.e20 = result.e20
    self.e21 = result.e21
    self.e22 = result.e22

    return self
  end
end

#rotationAxis(axis, radian) ⇒ Object

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

Makes a matrix that rotates around the axis.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 953

def rotationAxis( axis, radian )
  if ( axis.class != RVec3 )
    raise TypeError, "RMtx3#rotationAxis : Unknown type #{axis.class} given as axis."
    return nil
  end
  s   = Math.sin( radian )
  c   = Math.cos( radian )
  omc = 1.0 - c
  x   = axis.x.to_f
  y   = axis.y.to_f
  z   = axis.z.to_f

  self.e00 = x*x*omc + c
  self.e01 = x*y*omc - z*s
  self.e02 = z*x*omc + y*s
  self.e10 = x*y*omc + z*s
  self.e11 = y*y*omc + c
  self.e12 = y*z*omc - x*s
  self.e20 = z*x*omc - y*s
  self.e21 = y*z*omc + x*s
  self.e22 = z*z*omc + c

  return self
end

#rotationQuaternion(q) ⇒ Object

call-seq: rotationQuaternion(q) -> self

Makes a rotation matrix from a normalized quaternion q.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 983

def rotationQuaternion( q )
  if ( q.class != RQuat )
    raise TypeError, "RMtx3#rotationQuaternion : Unknown type #{q.class} given as RQuat."
    return nil
  end
  x  = q.x
  y  = q.y
  z  = q.z
  w  = q.w

  x2 = 2.0 * x
  y2 = 2.0 * y
  z2 = 2.0 * z

  xx2 = x * x2
  yy2 = y * y2
  zz2 = z * z2

  yz2 = y * z2
  wx2 = w * x2
  xy2 = x * y2
  wz2 = w * z2
  xz2 = x * z2
  wy2 = w * y2

  self.e00 = 1.0 - yy2 - zz2
  self.e10 = xy2 + wz2
  self.e20 = xz2 - wy2
  self.e01 = xy2 - wz2
  self.e11 = 1.0 - xx2 - zz2
  self.e21 = yz2 + wx2
  self.e02 = xz2 + wy2
  self.e12 = yz2 - wx2
  self.e22 = 1.0 - xx2 - yy2

  return self
end

#rotationX(radian) ⇒ Object

call-seq: rotationX(radian) -> self

Makes a matrix that rotates around the x-axis.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 899

def rotationX( radian )
  s = Math.sin( radian )
  c = Math.cos( radian )

  setIdentity()
  self.e11 =  c
  self.e12 = -s
  self.e21 =  s
  self.e22 =  c

  return self
end

#rotationY(radian) ⇒ Object

call-seq: rotationY(radian) -> self

Makes a matrix that rotates around the y-axis.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 917

def rotationY( radian )
  s = Math.sin( radian )
  c = Math.cos( radian )

  setIdentity()
  self.e00 =  c
  self.e02 =  s
  self.e20 = -s
  self.e22 =  c

  return self
end

#rotationZ(radian) ⇒ Object

call-seq: rotationZ(radian) -> self

Makes a matrix that rotates around the z-axis.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 935

def rotationZ( radian )
  s = Math.sin( radian )
  c = Math.cos( radian )

  setIdentity()
  self.e00 =  c
  self.e01 = -s
  self.e10 =  s
  self.e11 =  c

  return self
end

#scaling(sx, sy, sz) ⇒ Object

call-seq: scaling(sx,sy,sz) -> self

Makes itself as a scaling matrix.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1026

def scaling( sx, sy, sz )
  setIdentity()
  setElement( 0, 0, sx )
  setElement( 1, 1, sy )
  setElement( 2, 2, sz )

  return self
end

#setColumn(v, column) ⇒ Object

call-seq: mtx3.setColumn(v,c)

Returns sets c-th column by vector v.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 748

def setColumn( v, column )
  self[0,column] = v.x
  self[1,column] = v.y
  self[2,column] = v.z
end

#setElements(*a) ⇒ Object

call-seq: setElements( e0, e1, …, e8 )

Stores given 9 new values.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 639

def setElements( *a )
  if a.length != 9
    raise RuntimeError, "RMtx3#setElements : wrong # of arguments (#{a.length})"
    return nil
  end

  for row in 0...3 do
    for col in 0...3 do
      index = 3*row + col
      setElement( row, col, a[index] )
    end
  end
end

#setIdentity ⇒ Object

call-seq: setIdentity

Sets as identity matrix.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 771

def setIdentity
  for row in 0...3 do
    for col in 0...3 do
      index = 3*row + col
      if ( row == col )
        setElement( row, col, 1.0 )
      else
        setElement( row, col, 0.0 )
      end
    end
  end
  return self
end

#setRow(v, row) ⇒ Object

call-seq: mtx3.setRow(v,r)

Returns sets r-th row by vector v.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 737

def setRow( v, row )
  self[row,0] = v.x
  self[row,1] = v.y
  self[row,2] = v.z
end

#setZero ⇒ Object

call-seq: setZero

Clears all elements by 0.0



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# File 'lib/rmath3d/rmath3d_plain.rb', line 759

def setZero
  9.times do |i|
    @e[i] = 0.0
  end
  return self
end

#sub!(other) ⇒ Object

call-seq: mtx1.sub!( mtx2 )

mtx1 -= mtx2 : subtracts the elements of mtx2 from corresponding mtx1 elements.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 1173

def sub!( other )
  if ( other.class != RMtx3 )
    raise TypeError, "RMtx3#sub! : Unknown type #{other.class} given as RMtx3."
    return nil
  end

  result = RMtx3.new
  for row in 0...3 do
    for col in 0...3 do
      self.setElement( row, col, getElement(row,col) - other.getElement(row,col) )
    end
  end

  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 615

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 604

def to_s
  "( #{@e[0]}, #{@e[3]}, #{@e[6]} )\n" +
  "( #{@e[1]}, #{@e[4]}, #{@e[7]} )\n" +
  "( #{@e[2]}, #{@e[5]}, #{@e[8]} )\n"
end

#transpose! ⇒ Object

call-seq: transpose!

Transposeas its elements.



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# File 'lib/rmath3d/rmath3d_plain.rb', line 812

def transpose!
  @e[1], @e[3] = @e[3], @e[1]
  @e[2], @e[6] = @e[6], @e[2]
  @e[5], @e[7] = @e[7], @e[5]
end