Class: Geo3d::Matrix

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

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(*args) ⇒ Matrix

Returns a new instance of Matrix.



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

def initialize *args
  @_11 = 0
  @_12 = 0
  @_13 = 0
  @_14 = 0
  @_21 = 0
  @_22 = 0
  @_23 = 0
  @_24 = 0
  @_31 = 0
  @_32 = 0
  @_33 = 0
  @_34 = 0
  @_41 = 0
  @_42 = 0
  @_43 = 0
  @_44 = 0
  @_11 = args[0] if args.size > 0
  @_12 = args[1] if args.size > 1
  @_13 = args[2] if args.size > 2
  @_14 = args[3] if args.size > 3
  @_21 = args[4] if args.size > 4
  @_22 = args[5] if args.size > 5
  @_23 = args[6] if args.size > 6
  @_24 = args[7] if args.size > 7
  @_31 = args[8] if args.size > 8
  @_32 = args[9] if args.size > 9
  @_33 = args[10] if args.size > 10
  @_34 = args[11] if args.size > 11
  @_41 = args[12] if args.size > 12
  @_42 = args[13] if args.size > 13
  @_43 = args[14] if args.size > 14
  @_44 = args[15] if args.size > 15
end

Instance Attribute Details

#_11 ⇒ Object

Returns the value of attribute _11.



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# File 'lib/matrix.rb', line 5

def _11
  @_11
end

#_12 ⇒ Object

Returns the value of attribute _12.



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# File 'lib/matrix.rb', line 5

def _12
  @_12
end

#_13 ⇒ Object

Returns the value of attribute _13.



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# File 'lib/matrix.rb', line 5

def _13
  @_13
end

#_14 ⇒ Object

Returns the value of attribute _14.



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# File 'lib/matrix.rb', line 5

def _14
  @_14
end

#_21 ⇒ Object

Returns the value of attribute _21.



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# File 'lib/matrix.rb', line 6

def _21
  @_21
end

#_22 ⇒ Object

Returns the value of attribute _22.



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# File 'lib/matrix.rb', line 6

def _22
  @_22
end

#_23 ⇒ Object

Returns the value of attribute _23.



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# File 'lib/matrix.rb', line 6

def _23
  @_23
end

#_24 ⇒ Object

Returns the value of attribute _24.



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# File 'lib/matrix.rb', line 6

def _24
  @_24
end

#_31 ⇒ Object

Returns the value of attribute _31.



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# File 'lib/matrix.rb', line 7

def _31
  @_31
end

#_32 ⇒ Object

Returns the value of attribute _32.



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# File 'lib/matrix.rb', line 7

def _32
  @_32
end

#_33 ⇒ Object

Returns the value of attribute _33.



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# File 'lib/matrix.rb', line 7

def _33
  @_33
end

#_34 ⇒ Object

Returns the value of attribute _34.



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# File 'lib/matrix.rb', line 7

def _34
  @_34
end

#_41 ⇒ Object

Returns the value of attribute _41.



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# File 'lib/matrix.rb', line 8

def _41
  @_41
end

#_42 ⇒ Object

Returns the value of attribute _42.



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# File 'lib/matrix.rb', line 8

def _42
  @_42
end

#_43 ⇒ Object

Returns the value of attribute _43.



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# File 'lib/matrix.rb', line 8

def _43
  @_43
end

#_44 ⇒ Object

Returns the value of attribute _44.



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# File 'lib/matrix.rb', line 8

def _44
  @_44
end

Class Method Details

.identity ⇒ Object 



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# File 'lib/matrix.rb', line 255

def self.identity
  identity_matrix = self.new
  identity_matrix._12 = identity_matrix._13 = identity_matrix._14 = 0
  identity_matrix._21 = identity_matrix._23 = identity_matrix._24 = 0
  identity_matrix._31 = identity_matrix._32 = identity_matrix._34 = 0
  identity_matrix._41 = identity_matrix._42 = identity_matrix._43 = 0
  identity_matrix._11 = identity_matrix._22 = identity_matrix._33 = identity_matrix._44 = 1
  identity_matrix
end

.look_at_lh(eye_position, look_at_position, up_direction) ⇒ Object 



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# File 'lib/matrix.rb', line 503

def self.look_at_lh eye_position, look_at_position, up_direction
  zaxis = (look_at_position - eye_position).normalize
  xaxis = up_direction.cross(zaxis).normalize
  yaxis = zaxis.cross xaxis

  matrix = self.new

  # set column one
  matrix._11 = xaxis.x
  matrix._21 = xaxis.y
  matrix._31 = xaxis.z
  matrix._41 = -xaxis.dot(eye_position)

  # set column two
  matrix._12 = yaxis.x
  matrix._22 = yaxis.y
  matrix._32 = yaxis.z
  matrix._42 = -yaxis.dot(eye_position)

  # set column three
  matrix._13 = zaxis.x
  matrix._23 = zaxis.y
  matrix._33 = zaxis.z
  matrix._43 = -zaxis.dot(eye_position)

  # set column four
  matrix._14 = matrix._24 = matrix._34 = 0
  matrix._44 = 1

  matrix
end

.look_at_rh(eye_position, look_at_position, up_direction) ⇒ Object 



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# File 'lib/matrix.rb', line 471

def self.look_at_rh eye_position, look_at_position, up_direction
  zaxis = (eye_position - look_at_position).normalize
  xaxis = up_direction.cross(zaxis).normalize
  yaxis = zaxis.cross xaxis

  matrix = self.new

  # set column one
  matrix._11 = xaxis.x
  matrix._21 = xaxis.y
  matrix._31 = xaxis.z
  matrix._41 = -xaxis.dot(eye_position)

  # set column two
  matrix._12 = yaxis.x
  matrix._22 = yaxis.y
  matrix._32 = yaxis.z
  matrix._42 = -yaxis.dot(eye_position)

  # set column three
  matrix._13 = zaxis.x
  matrix._23 = zaxis.y
  matrix._33 = zaxis.z
  matrix._43 = -zaxis.dot(eye_position)

  # set column four
  matrix._14 = matrix._24 = matrix._34 = 0
  matrix._44 = 1

  matrix
end

.ortho_off_center_lh(l, r, b, t, zn, zf) ⇒ Object 



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# File 'lib/matrix.rb', line 454

def self.ortho_off_center_lh l, r, b, t, zn, zf
  l = l.to_f
  r = r.to_f
  b = b.to_f
  t = t.to_f
  zn = zn.to_f
  zf = zf.to_f
  m = identity
  m._11 = 2.0 / (r - l)
  m._22 = 2.0 / (t - b)
  m._33 = 1.0 / (zf -zn)
  m._41 = -1.0 -2.0 *l / (r - l)
  m._42 = 1.0 + 2.0 * t / (b - t)
  m._43 = zn / (zn -zf)
  m
end

.ortho_off_center_rh(l, r, b, t, zn, zf) ⇒ Object 



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# File 'lib/matrix.rb', line 437

def self.ortho_off_center_rh l, r, b, t, zn, zf
  l = l.to_f
  r = r.to_f
  b = b.to_f
  t = t.to_f
  zn = zn.to_f
  zf = zf.to_f
  m = identity
  m._11 = 2.0 / (r - l)
  m._22 = 2.0 / (t - b)
  m._33 = 1.0 / (zn -zf)
  m._41 = -1.0 -2.0 *l / (r - l)
  m._42 = 1.0 + 2.0 * t / (b - t)
  m._43 = zn / (zn -zf)
  m
end

.perspective_fov_lh(fovy, aspect, zn, zf) ⇒ Object 



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# File 'lib/matrix.rb', line 421

def self.perspective_fov_lh fovy, aspect, zn, zf
  fovy = fovy.to_f
  aspect = aspect.to_f
  zn = zn.to_f
  zf = zf.to_f
  y_scale = 1.0 / Math.tan(0.5*fovy)
  x_scale = y_scale / aspect
  matrix = self.new
  matrix._11 = x_scale
  matrix._22 = y_scale
  matrix._33 = zf/(zf - zn)
  matrix._34 = 1
  matrix._43 = zn*zf/(zn - zf)
  matrix
end

.perspective_fov_rh(fovy, aspect, zn, zf) ⇒ Object 



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# File 'lib/matrix.rb', line 405

def self.perspective_fov_rh fovy, aspect, zn, zf
  fovy = fovy.to_f
  aspect = aspect.to_f
  zn = zn.to_f
  zf = zf.to_f
  y_scale = 1.0 / Math.tan(0.5*fovy)
  x_scale = y_scale / aspect
  matrix = self.new
  matrix._11 = x_scale
  matrix._22 = y_scale
  matrix._33 = zf/(zn - zf)
  matrix._34 = -1
  matrix._43 = zn*zf/(zn - zf)
  matrix
end

.reflection(reflection_plane) ⇒ Object 



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# File 'lib/matrix.rb', line 535

def self.reflection reflection_plane
  reflection_matrix = self.new

  plane_magnitude = Vector.new(reflection_plane.x, reflection_plane.y, reflection_plane.z, 0).length
  normalized_plane = reflection_plane / plane_magnitude

  # row one
  reflection_matrix._11 = -2 * normalized_plane.x * normalized_plane.x + 1
  reflection_matrix._12 = -2 * normalized_plane.y * normalized_plane.x
  reflection_matrix._13 = -2 * normalized_plane.z * normalized_plane.x
  reflection_matrix._14 = 0

  # row two
  reflection_matrix._21 = -2 * normalized_plane.x * normalized_plane.y
  reflection_matrix._22 = -2 * normalized_plane.y * normalized_plane.y + 1
  reflection_matrix._23 = -2 * normalized_plane.z * normalized_plane.y
  reflection_matrix._24 = 0

  # row three
  reflection_matrix._31 = -2 * normalized_plane.x * normalized_plane.z
  reflection_matrix._32 = -2 * normalized_plane.y * normalized_plane.z
  reflection_matrix._33 = -2 * normalized_plane.z * normalized_plane.z + 1
  reflection_matrix._34 = 0

  # row four
  reflection_matrix._41 = -2 * normalized_plane.x * normalized_plane.w
  reflection_matrix._42 = -2 * normalized_plane.y * normalized_plane.w
  reflection_matrix._43 = -2 * normalized_plane.z * normalized_plane.w
  reflection_matrix._44 = 1

  reflection_matrix
end

.rotation(axis, angle) ⇒ Object 



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# File 'lib/matrix.rb', line 651

def self.rotation axis, angle
  v = axis.normalize
  m = identity
  m._11 = (1.0 - Math.cos(angle)) * v.x * v.x + Math.cos(angle)
  m._21 = (1.0 - Math.cos(angle)) * v.x * v.y - Math.sin(angle) * v.z
  m._31 = (1.0 - Math.cos(angle)) * v.x * v.z + Math.sin(angle) * v.y
  m._12 = (1.0 - Math.cos(angle)) * v.y * v.x + Math.sin(angle) * v.z
  m._22 = (1.0 - Math.cos(angle)) * v.y * v.y + Math.cos(angle)
  m._32 = (1.0 - Math.cos(angle)) * v.y * v.z - Math.sin(angle) * v.x
  m._13 = (1.0 - Math.cos(angle)) * v.z * v.x - Math.sin(angle) * v.y
  m._23 = (1.0 - Math.cos(angle)) * v.z * v.y + Math.sin(angle) * v.x
  m._33 = (1.0 - Math.cos(angle)) * v.z * v.z + Math.cos(angle)
  m
end

.rotation_x(angle) ⇒ Object 



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# File 'lib/matrix.rb', line 618

def self.rotation_x angle
  m = identity
  sine = Math.sin angle
  cosine = Math.cos angle
  m._22 = cosine
  m._33 = cosine
  m._23 = sine
  m._32 = -sine
  m
end

.rotation_y(angle) ⇒ Object 



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# File 'lib/matrix.rb', line 629

def self.rotation_y angle
  m = identity
  sine = Math.sin angle
  cosine = Math.cos angle
  m._11 = cosine
  m._33 = cosine
  m._13 = -sine
  m._31 = sine
  m
end

.rotation_z(angle) ⇒ Object 



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# File 'lib/matrix.rb', line 640

def self.rotation_z angle
  m = identity
  sine = Math.sin angle
  cosine = Math.cos angle
  m._11 = cosine
  m._22 = cosine
  m._12 = sine
  m._21 = -sine
  m
end

.scaling(x, y, z) ⇒ Object 



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# File 'lib/matrix.rb', line 605

def self.scaling x, y, z
  scaling_matrix = self.new
  scaling_matrix._11 = x
  scaling_matrix._22 = y
  scaling_matrix._33 = z
  scaling_matrix._44 = 1
  scaling_matrix
end

.shadow(light_position, plane) ⇒ Object 



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# File 'lib/matrix.rb', line 568

def self.shadow light_position, plane
  norm = plane.x * plane.x + plane.y * plane.y + plane.z * plane.z
  normalized_plane = plane / norm
  dot = normalized_plane.dot(light_position)

  m = self.new
  m._11 = dot - normalized_plane.a * light_position.x
  m._12 = -normalized_plane.a * light_position.y
  m._13 = -normalized_plane.a * light_position.z
  m._14 = -normalized_plane.a * light_position.w
  m._21 = -normalized_plane.b * light_position.x
  m._22 = dot - normalized_plane.b * light_position.y
  m._23 = -normalized_plane.b * light_position.z
  m._24 = -normalized_plane.b * light_position.w
  m._31 = -normalized_plane.c * light_position.x
  m._32 = -normalized_plane.c * light_position.y
  m._33 = dot - normalized_plane.c * light_position.z
  m._34 = -normalized_plane.c * light_position.w
  m._41 = -normalized_plane.d * light_position.x
  m._42 = -normalized_plane.d * light_position.y
  m._43 = -normalized_plane.d * light_position.z
  m._44 = dot - normalized_plane.d * light_position.w

  m
end

.translation(x, y, z) ⇒ Object 



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# File 'lib/matrix.rb', line 595

def self.translation x, y, z
  translation_matrix = self.new
  translation_matrix._11 = translation_matrix._22 = translation_matrix._33 = translation_matrix._44 = 1
  #todo: consider simplifying with identity
  translation_matrix._41 = x
  translation_matrix._42 = y
  translation_matrix._43 = z
  translation_matrix
end

.uniform_scaling(scale) ⇒ Object 



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# File 'lib/matrix.rb', line 614

def self.uniform_scaling scale
  scaling scale, scale, scale
end

Instance Method Details

#!=(m) ⇒ Object 



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# File 'lib/matrix.rb', line 66

def != m
  !(self == m)
end

#*(v) ⇒ Object 



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# File 'lib/matrix.rb', line 130

def * v
  result = self.class.new

  if self.class == v.class
    matrix = v

    result._11 = _11 * matrix._11 + _12 * matrix._21 + _13 * matrix._31 + _14 * matrix._41
    result._12 = _11 * matrix._12 + _12 * matrix._22 + _13 * matrix._32 + _14 * matrix._42
    result._13 = _11 * matrix._13 + _12 * matrix._23 + _13 * matrix._33 + _14 * matrix._43
    result._14 = _11 * matrix._14 + _12 * matrix._24 + _13 * matrix._34 + _14 * matrix._44

    result._21 = _21 * matrix._11 + _22 * matrix._21 + _23 * matrix._31 + _24 * matrix._41
    result._22 = _21 * matrix._12 + _22 * matrix._22 + _23 * matrix._32 + _24 * matrix._42
    result._23 = _21 * matrix._13 + _22 * matrix._23 + _23 * matrix._33 + _24 * matrix._43
    result._24 = _21 * matrix._14 + _22 * matrix._24 + _23 * matrix._34 + _24 * matrix._44

    result._31 = _31 * matrix._11 + _32 * matrix._21 + _33 * matrix._31 + _34 * matrix._41
    result._32 = _31 * matrix._12 + _32 * matrix._22 + _33 * matrix._32 + _34 * matrix._42
    result._33 = _31 * matrix._13 + _32 * matrix._23 + _33 * matrix._33 + _34 * matrix._43
    result._34 = _31 * matrix._14 + _32 * matrix._24 + _33 * matrix._34 + _34 * matrix._44

    result._41 = _41 * matrix._11 + _42 * matrix._21 + _43 * matrix._31 + _44 * matrix._41
    result._42 = _41 * matrix._12 + _42 * matrix._22 + _43 * matrix._32 + _44 * matrix._42
    result._43 = _41 * matrix._13 + _42 * matrix._23 + _43 * matrix._33 + _44 * matrix._43
    result._44 = _41 * matrix._14 + _42 * matrix._24 + _43 * matrix._34 + _44 * matrix._44
  elsif Vector == v.class
    vec = v
    transformed_vector = Vector.new
    transformed_vector.x = _11 * vec.x + _21 * vec.y + _31 * vec.z + _41
    transformed_vector.y = _12 * vec.x + _22 * vec.y + _32 * vec.z + _42
    transformed_vector.z = _13 * vec.x + _23 * vec.y + _33 * vec.z + _43
    transformed_vector.w = _14 * vec.x + _24 * vec.y + _34 * vec.z + _44
    return transformed_vector
  else
    scalar = v
    result._11 = _11 * scalar
    result._12 = _12 * scalar
    result._13 = _13 * scalar
    result._14 = _14 * scalar
    result._21 = _21 * scalar
    result._22 = _22 * scalar
    result._23 = _23 * scalar
    result._24 = _24 * scalar
    result._31 = _31 * scalar
    result._32 = _32 * scalar
    result._33 = _33 * scalar
    result._34 = _34 * scalar
    result._41 = _41 * scalar
    result._42 = _42 * scalar
    result._43 = _43 * scalar
    result._44 = _44 * scalar
  end

  result
end

#+(mat) ⇒ Object 



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# File 'lib/matrix.rb', line 78

def + mat
  sum = self.class.new

  sum._11 = _11 + mat._11
  sum._12 = _12 + mat._12
  sum._13 = _13 + mat._13
  sum._14 = _14 + mat._14

  sum._21 = _21 + mat._21
  sum._22 = _22 + mat._22
  sum._23 = _23 + mat._23
  sum._24 = _24 + mat._24

  sum._31 = _31 + mat._31
  sum._32 = _32 + mat._32
  sum._33 = _33 + mat._33
  sum._34 = _34 + mat._34

  sum._41 = _41 + mat._41
  sum._42 = _42 + mat._42
  sum._43 = _43 + mat._43
  sum._44 = _44 + mat._44

  sum
end

#+@ ⇒ Object 



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# File 'lib/matrix.rb', line 70

def +@
  self * 1
end

#-(mat) ⇒ Object 



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# File 'lib/matrix.rb', line 104

def - mat
  sum = self.class.new

  sum._11 = _11 - mat._11
  sum._12 = _12 - mat._12
  sum._13 = _13 - mat._13
  sum._14 = _14 - mat._14

  sum._21 = _21 - mat._21
  sum._22 = _22 - mat._22
  sum._23 = _23 - mat._23
  sum._24 = _24 - mat._24

  sum._31 = _31 - mat._31
  sum._32 = _32 - mat._32
  sum._33 = _33 - mat._33
  sum._34 = _34 - mat._34

  sum._41 = _41 - mat._41
  sum._42 = _42 - mat._42
  sum._43 = _43 - mat._43
  sum._44 = _44 - mat._44

  sum
end

#-@ ⇒ Object 



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# File 'lib/matrix.rb', line 74

def -@
  self * -1
end

#/(v) ⇒ Object 



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# File 'lib/matrix.rb', line 186

def / v
  if self.class == v.class
    self * v.inverse
  elsif Vector == v.class
    raise 'dividing matrices by vectors not currently supported'
  else
    result = self.class.new
    scalar = v
    result._11 = _11 / scalar
    result._12 = _12 / scalar
    result._13 = _13 / scalar
    result._14 = _14 / scalar
    result._21 = _21 / scalar
    result._22 = _22 / scalar
    result._23 = _23 / scalar
    result._24 = _24 / scalar
    result._31 = _31 / scalar
    result._32 = _32 / scalar
    result._33 = _33 / scalar
    result._34 = _34 / scalar
    result._41 = _41 / scalar
    result._42 = _42 / scalar
    result._43 = _43 / scalar
    result._44 = _44 / scalar
    result
  end
end

#==(m) ⇒ Object 



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# File 'lib/matrix.rb', line 57

def == m
  a = to_a
  b = m.to_a
  for i in 0..15
    return false unless Geo3d::Utils.float_cmp a[i], b[i]
  end
  true
end

#[](x, y) ⇒ Object 



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

def [] x, y
  to_a[4*x + y]
end

#[]=(x, y, v) ⇒ Object 



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# File 'lib/matrix.rb', line 53

def []= x, y, v
  send (%w{_11 _12 _13 _14 _21 _22 _23 _24 _31 _32 _33 _34 _41 _42 _43 _44}[4*x + y] + '=').to_sym, v
end

#determinant ⇒ Object 



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# File 'lib/matrix.rb', line 265

def determinant
  inverse(true).last
end

#identity? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/matrix.rb', line 227

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

#inverse(with_determinant = false) ⇒ Object 



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# File 'lib/matrix.rb', line 269

def inverse with_determinant = false
  mat = to_a
  dst = Array.new 16
  tmp = Array.new 12
  src = Array.new 16

  for i in 0..3
    src[i] = mat[i*4]
    src[i + 4] = mat[i*4 + 1]
    src[i + 8] = mat[i*4 + 2]
    src[i + 12] = mat[i*4 + 3]
  end

  # calculate pairs for first 8 elements (cofactors)
  tmp[0] = src[10] * src[15]
  tmp[1] = src[11] * src[14]
  tmp[2] = src[9] * src[15]
  tmp[3] = src[11] * src[13]
  tmp[4] = src[9] * src[14]
  tmp[5] = src[10] * src[13]
  tmp[6] = src[8] * src[15]
  tmp[7] = src[11] * src[12]
  tmp[8] = src[8] * src[14]
  tmp[9] = src[10] * src[12]
  tmp[10] = src[8] * src[13]
  tmp[11] = src[9] * src[12]

  # calculate first 8 elements (cofactors)
  dst[0] = tmp[0]*src[5] + tmp[3]*src[6] + tmp[4]*src[7]
  dst[0] -= tmp[1]*src[5] + tmp[2]*src[6] + tmp[5]*src[7]
  dst[1] = tmp[1]*src[4] + tmp[6]*src[6] + tmp[9]*src[7]
  dst[1] -= tmp[0]*src[4] + tmp[7]*src[6] + tmp[8]*src[7]
  dst[2] = tmp[2]*src[4] + tmp[7]*src[5] + tmp[10]*src[7]
  dst[2] -= tmp[3]*src[4] + tmp[6]*src[5] + tmp[11]*src[7]
  dst[3] = tmp[5]*src[4] + tmp[8]*src[5] + tmp[11]*src[6]
  dst[3] -= tmp[4]*src[4] + tmp[9]*src[5] + tmp[10]*src[6]
  dst[4] = tmp[1]*src[1] + tmp[2]*src[2] + tmp[5]*src[3]
  dst[4] -= tmp[0]*src[1] + tmp[3]*src[2] + tmp[4]*src[3]
  dst[5] = tmp[0]*src[0] + tmp[7]*src[2] + tmp[8]*src[3]
  dst[5] -= tmp[1]*src[0] + tmp[6]*src[2] + tmp[9]*src[3]
  dst[6] = tmp[3]*src[0] + tmp[6]*src[1] + tmp[11]*src[3]
  dst[6] -= tmp[2]*src[0] + tmp[7]*src[1] + tmp[10]*src[3]
  dst[7] = tmp[4]*src[0] + tmp[9]*src[1] + tmp[10]*src[2]
  dst[7] -= tmp[5]*src[0] + tmp[8]*src[1] + tmp[11]*src[2]

  # calculate pairs for second 8 elements (cofactors)
  tmp[0] = src[2]*src[7]
  tmp[1] = src[3]*src[6]
  tmp[2] = src[1]*src[7]
  tmp[3] = src[3]*src[5]
  tmp[4] = src[1]*src[6]
  tmp[5] = src[2]*src[5]
  tmp[6] = src[0]*src[7]
  tmp[7] = src[3]*src[4]
  tmp[8] = src[0]*src[6]
  tmp[9] = src[2]*src[4]
  tmp[10] = src[0]*src[5]
  tmp[11] = src[1]*src[4]

  # calculate second 8 elements (cofactors)
  dst[8] = tmp[0]*src[13] + tmp[3]*src[14] + tmp[4]*src[15]
  dst[8] -= tmp[1]*src[13] + tmp[2]*src[14] + tmp[5]*src[15]
  dst[9] = tmp[1]*src[12] + tmp[6]*src[14] + tmp[9]*src[15]
  dst[9] -= tmp[0]*src[12] + tmp[7]*src[14] + tmp[8]*src[15]
  dst[10] = tmp[2]*src[12] + tmp[7]*src[13] + tmp[10]*src[15]
  dst[10]-= tmp[3]*src[12] + tmp[6]*src[13] + tmp[11]*src[15]
  dst[11] = tmp[5]*src[12] + tmp[8]*src[13] + tmp[11]*src[14]
  dst[11]-= tmp[4]*src[12] + tmp[9]*src[13] + tmp[10]*src[14]
  dst[12] = tmp[2]*src[10] + tmp[5]*src[11] + tmp[1]*src[9]
  dst[12]-= tmp[4]*src[11] + tmp[0]*src[9] + tmp[3]*src[10]
  dst[13] = tmp[8]*src[11] + tmp[0]*src[8] + tmp[7]*src[10]
  dst[13]-= tmp[6]*src[10] + tmp[9]*src[11] + tmp[1]*src[8]
  dst[14] = tmp[6]*src[9] + tmp[11]*src[11] + tmp[3]*src[8]
  dst[14]-= tmp[10]*src[11] + tmp[2]*src[8] + tmp[7]*src[9]
  dst[15] = tmp[10]*src[10] + tmp[4]*src[8] + tmp[9]*src[9]
  dst[15]-= tmp[8]*src[9] + tmp[11]*src[10] + tmp[5]*src[8]

  # calculate determinant
  det=src[0]*dst[0]+src[1]*dst[1]+src[2]*dst[2]+src[3]*dst[3]


  # calculate matrix inverse
  det = 1.0/det
  for j in 0..15
    dst[j] *= det
  end

  inverted_matrix = self.class.new *dst

  if with_determinant
    [inverted_matrix, det]
  else
    inverted_matrix
  end
end

#print ⇒ Object 



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# File 'lib/matrix.rb', line 386

def print
  puts "_11: #{_11}\n"
  puts "_12: #{_12}\n"
  puts "_13: #{_13}\n"
  puts "_14: #{_14}\n"
  puts "_21: #{_21}\n"
  puts "_22: #{_22}\n"
  puts "_23: #{_23}\n"
  puts "_24: #{_24}\n"
  puts "_31: #{_31}\n"
  puts "_32: #{_32}\n"
  puts "_33: #{_33}\n"
  puts "_34: #{_34}\n"
  puts "_41: #{_41}\n"
  puts "_42: #{_42}\n"
  puts "_43: #{_43}\n"
  puts "_44: #{_44}\n"
end

#rotation_component ⇒ Object 



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# File 'lib/matrix.rb', line 239

def rotation_component
  scaling = scaling_component
  return nil if scaling.x.zero? || scaling.y.zero? || scaling.z.zero?
  m = Matrix.new
  m._11=_11 / scaling.x
  m._12=_12/scaling.x
  m._13=_13/scaling.x
  m._21=_21/scaling.y
  m._22=_22/scaling.y
  m._23=_23/scaling.y
  m._31=_31/scaling.z
  m._32=_32/scaling.z
  m._33=_33/scaling.z
  Quaternion.from_matrix m
end

#scaling_component ⇒ Object 



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# File 'lib/matrix.rb', line 235

def scaling_component
  Vector.new Vector.new(_11, _12, _13).length, Vector.new(_21, _22, _23).length, Vector.new(_31, _32, _33).length
end

#to_a ⇒ Object 



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# File 'lib/matrix.rb', line 45

def to_a
  [_11, _12, _13, _14, _21, _22, _23, _24, _31, _32, _33, _34, _41, _42, _43, _44]
end

#transform(vec) ⇒ Object 



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# File 'lib/matrix.rb', line 223

def transform vec
  self * vec
end

#transform_coord(vec) ⇒ Object 



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# File 'lib/matrix.rb', line 214

def transform_coord vec
  norm =_14 * vec.x + _24 * vec.y + _34 * vec.z + _44
  transformed_vector = self * vec
  transformed_vector.x /= norm
  transformed_vector.y /= norm
  transformed_vector.z /= norm
  transformed_vector
end

#translation_component ⇒ Object 



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# File 'lib/matrix.rb', line 231

def translation_component
  Vector.new _41, _42, _43
end

#transpose ⇒ Object 



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# File 'lib/matrix.rb', line 365

def transpose
  transposed_matrix = self.class.new
  transposed_matrix._11 = _11
  transposed_matrix._12 = _21
  transposed_matrix._13 = _31
  transposed_matrix._14 = _41
  transposed_matrix._21 = _12
  transposed_matrix._22 = _22
  transposed_matrix._23 = _32
  transposed_matrix._24 = _42
  transposed_matrix._31 = _13
  transposed_matrix._32 = _23
  transposed_matrix._33 = _33
  transposed_matrix._34 = _43
  transposed_matrix._41 = _14
  transposed_matrix._42 = _24
  transposed_matrix._43 = _34
  transposed_matrix._44 = _44
  transposed_matrix
end