Class: Three::Matrix4

Inherits:
Object
  • Object
show all
Defined in:
lib/three/math/matrix4.rb

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(*values) ⇒ Matrix4

Returns a new instance of Matrix4.



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# File 'lib/three/math/matrix4.rb', line 9

def initialize(*values)
  @elements = [
    1, 0, 0, 0,
    0, 1, 0, 0,
    0, 0, 1, 0,
    0, 0, 0, 1
  ]

  set(*values) unless values.empty?
end

Instance Attribute Details

#elements ⇒ Object (readonly)

Returns the value of attribute elements.



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# File 'lib/three/math/matrix4.rb', line 7

def elements
  @elements
end

Instance Method Details

#==(other) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 440

def ==(other)
  other.is_a?(self.class) && equals?(other)
end

#clone ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 49

def clone
  self.class.new.from_array(@elements)
end

#compose(position, quaternion, scale) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 346

def compose(position, quaternion, scale)
  x = quaternion.x
  y = quaternion.y
  z = quaternion.z
  w = quaternion.w
  x2 = x + x
  y2 = y + y
  z2 = z + z
  xx = x * x2
  xy = x * y2
  xz = x * z2
  yy = y * y2
  yz = y * z2
  zz = z * z2
  wx = w * x2
  wy = w * y2
  wz = w * z2
  sx = scale.x
  sy = scale.y
  sz = scale.z

  @elements[0] = (1 - (yy + zz)) * sx
  @elements[1] = (xy + wz) * sx
  @elements[2] = (xz - wy) * sx
  @elements[3] = 0

  @elements[4] = (xy - wz) * sy
  @elements[5] = (1 - (xx + zz)) * sy
  @elements[6] = (yz + wx) * sy
  @elements[7] = 0

  @elements[8] = (xz + wy) * sz
  @elements[9] = (yz - wx) * sz
  @elements[10] = (1 - (xx + yy)) * sz
  @elements[11] = 0

  @elements[12] = position.x
  @elements[13] = position.y
  @elements[14] = position.z
  @elements[15] = 1
  self
end

#copy(matrix) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 53

def copy(matrix)
  @elements = matrix.elements.dup
  self
end

#copy_position(matrix) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 58

def copy_position(matrix)
  @elements[12] = matrix.elements[12]
  @elements[13] = matrix.elements[13]
  @elements[14] = matrix.elements[14]
  self
end

#decompose(position, quaternion, scale) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 389

def decompose(position, quaternion, scale)
  position.set(@elements[12], @elements[13], @elements[14])

  det = determinant
  if det.zero?
    scale.set(1, 1, 1)
    quaternion.identity
    return self
  end

  sx = Vector3.new(@elements[0], @elements[1], @elements[2]).length
  sy = Vector3.new(@elements[4], @elements[5], @elements[6]).length
  sz = Vector3.new(@elements[8], @elements[9], @elements[10]).length
  sx = -sx if det.negative?

  matrix = clone
  matrix.elements[0] *= 1.0 / sx
  matrix.elements[1] *= 1.0 / sx
  matrix.elements[2] *= 1.0 / sx
  matrix.elements[4] *= 1.0 / sy
  matrix.elements[5] *= 1.0 / sy
  matrix.elements[6] *= 1.0 / sy
  matrix.elements[8] *= 1.0 / sz
  matrix.elements[9] *= 1.0 / sz
  matrix.elements[10] *= 1.0 / sz

  quaternion.set_from_rotation_matrix(matrix)
  scale.set(sx, sy, sz)
  self
end

#determinant ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 180

def determinant
  n11 = @elements[0]
  n12 = @elements[4]
  n13 = @elements[8]
  n14 = @elements[12]
  n21 = @elements[1]
  n22 = @elements[5]
  n23 = @elements[9]
  n24 = @elements[13]
  n31 = @elements[2]
  n32 = @elements[6]
  n33 = @elements[10]
  n34 = @elements[14]
  n41 = @elements[3]
  n42 = @elements[7]
  n43 = @elements[11]
  n44 = @elements[15]

  t11 = n23 * n34 - n24 * n33
  t12 = n22 * n34 - n24 * n32
  t13 = n22 * n33 - n23 * n32
  t21 = n21 * n34 - n24 * n31
  t22 = n21 * n33 - n23 * n31
  t23 = n21 * n32 - n22 * n31

  n11 * (n42 * t11 - n43 * t12 + n44 * t13) -
    n12 * (n41 * t11 - n43 * t21 + n44 * t22) +
    n13 * (n41 * t12 - n42 * t21 + n44 * t23) -
    n14 * (n41 * t13 - n42 * t22 + n43 * t23)
end

#equals?(matrix, epsilon: 0.0) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/three/math/matrix4.rb', line 434

def equals?(matrix, epsilon: 0.0)
  @elements.each_with_index.all? do |value, index|
    (value - matrix.elements[index]).abs <= epsilon
  end
end

#from_array(array, offset = 0) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 420

def from_array(array, offset = 0)
  16.times { |index| @elements[index] = array[index + offset] }
  self
end

#identity ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 40

def identity
  set(
    1, 0, 0, 0,
    0, 1, 0, 0,
    0, 0, 1, 0,
    0, 0, 0, 1
  )
end

#inspect ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 444

def inspect
  "#<#{self.class} elements=#{@elements.inspect}>"
end

#invert ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 221

def invert
  n11 = @elements[0]
  n21 = @elements[1]
  n31 = @elements[2]
  n41 = @elements[3]
  n12 = @elements[4]
  n22 = @elements[5]
  n32 = @elements[6]
  n42 = @elements[7]
  n13 = @elements[8]
  n23 = @elements[9]
  n33 = @elements[10]
  n43 = @elements[11]
  n14 = @elements[12]
  n24 = @elements[13]
  n34 = @elements[14]
  n44 = @elements[15]

  t1 = n11 * n22 - n21 * n12
  t2 = n11 * n32 - n31 * n12
  t3 = n11 * n42 - n41 * n12
  t4 = n21 * n32 - n31 * n22
  t5 = n21 * n42 - n41 * n22
  t6 = n31 * n42 - n41 * n32
  t7 = n13 * n24 - n23 * n14
  t8 = n13 * n34 - n33 * n14
  t9 = n13 * n44 - n43 * n14
  t10 = n23 * n34 - n33 * n24
  t11 = n23 * n44 - n43 * n24
  t12 = n33 * n44 - n43 * n34

  det = t1 * t12 - t2 * t11 + t3 * t10 + t4 * t9 - t5 * t8 + t6 * t7
  return set(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) if det.zero?

  det_inv = 1.0 / det

  @elements[0] = (n22 * t12 - n32 * t11 + n42 * t10) * det_inv
  @elements[1] = (n31 * t11 - n21 * t12 - n41 * t10) * det_inv
  @elements[2] = (n24 * t6 - n34 * t5 + n44 * t4) * det_inv
  @elements[3] = (n33 * t5 - n23 * t6 - n43 * t4) * det_inv
  @elements[4] = (n32 * t9 - n12 * t12 - n42 * t8) * det_inv
  @elements[5] = (n11 * t12 - n31 * t9 + n41 * t8) * det_inv
  @elements[6] = (n34 * t3 - n14 * t6 - n44 * t2) * det_inv
  @elements[7] = (n13 * t6 - n33 * t3 + n43 * t2) * det_inv
  @elements[8] = (n12 * t11 - n22 * t9 + n42 * t7) * det_inv
  @elements[9] = (n21 * t9 - n11 * t11 - n41 * t7) * det_inv
  @elements[10] = (n14 * t5 - n24 * t3 + n44 * t1) * det_inv
  @elements[11] = (n23 * t3 - n13 * t5 - n43 * t1) * det_inv
  @elements[12] = (n22 * t8 - n12 * t10 - n32 * t7) * det_inv
  @elements[13] = (n11 * t10 - n21 * t8 + n31 * t7) * det_inv
  @elements[14] = (n24 * t2 - n14 * t4 - n34 * t1) * det_inv
  @elements[15] = (n13 * t4 - n23 * t2 + n33 * t1) * det_inv
  self
end

#make_orthographic(left, right, top, bottom, near, far) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 319

def make_orthographic(left, right, top, bottom, near, far)
  w = 1.0 / (right - left)
  h = 1.0 / (top - bottom)
  p = 1.0 / (far - near)
  x = (right + left) * w
  y = (top + bottom) * h
  z = (far + near) * p

  @elements[0] = 2 * w
  @elements[4] = 0
  @elements[8] = 0
  @elements[12] = -x
  @elements[1] = 0
  @elements[5] = 2 * h
  @elements[9] = 0
  @elements[13] = -y
  @elements[2] = 0
  @elements[6] = 0
  @elements[10] = -2 * p
  @elements[14] = -z
  @elements[3] = 0
  @elements[7] = 0
  @elements[11] = 0
  @elements[15] = 1
  self
end

#make_perspective(left, right, top, bottom, near, far) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 292

def make_perspective(left, right, top, bottom, near, far)
  x = 2.0 * near / (right - left)
  y = 2.0 * near / (top - bottom)
  a = (right + left).to_f / (right - left)
  b = (top + bottom).to_f / (top - bottom)
  c = -(far + near).to_f / (far - near)
  d = (-2.0 * far * near) / (far - near)

  @elements[0] = x
  @elements[4] = 0
  @elements[8] = a
  @elements[12] = 0
  @elements[1] = 0
  @elements[5] = y
  @elements[9] = b
  @elements[13] = 0
  @elements[2] = 0
  @elements[6] = 0
  @elements[10] = c
  @elements[14] = d
  @elements[3] = 0
  @elements[7] = 0
  @elements[11] = -1
  @elements[15] = 0
  self
end

#make_rotation_from_quaternion(quaternion) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 89

def make_rotation_from_quaternion(quaternion)
  compose(Vector3.new, quaternion, Vector3.new(1, 1, 1))
end

#make_scale(x, y, z) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 80

def make_scale(x, y, z)
  set(
    x, 0, 0, 0,
    0, y, 0, 0,
    0, 0, z, 0,
    0, 0, 0, 1
  )
end

#make_translation(x, y = nil, z = nil) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 65

def make_translation(x, y = nil, z = nil)
  if y.nil? && z.nil?
    y = x.y
    z = x.z
    x = x.x
  end

  set(
    1, 0, 0, x,
    0, 1, 0, y,
    0, 0, 1, z,
    0, 0, 0, 1
  )
end

#multiply(matrix) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 107

def multiply(matrix)
  multiply_matrices(self, matrix)
end

#multiply_matrices(a, b) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 115

def multiply_matrices(a, b)
  ae = a.elements
  be = b.elements

  a11 = ae[0]
  a12 = ae[4]
  a13 = ae[8]
  a14 = ae[12]
  a21 = ae[1]
  a22 = ae[5]
  a23 = ae[9]
  a24 = ae[13]
  a31 = ae[2]
  a32 = ae[6]
  a33 = ae[10]
  a34 = ae[14]
  a41 = ae[3]
  a42 = ae[7]
  a43 = ae[11]
  a44 = ae[15]

  b11 = be[0]
  b12 = be[4]
  b13 = be[8]
  b14 = be[12]
  b21 = be[1]
  b22 = be[5]
  b23 = be[9]
  b24 = be[13]
  b31 = be[2]
  b32 = be[6]
  b33 = be[10]
  b34 = be[14]
  b41 = be[3]
  b42 = be[7]
  b43 = be[11]
  b44 = be[15]

  @elements[0] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41
  @elements[4] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42
  @elements[8] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43
  @elements[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44

  @elements[1] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41
  @elements[5] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42
  @elements[9] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43
  @elements[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44

  @elements[2] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41
  @elements[6] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42
  @elements[10] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43
  @elements[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44

  @elements[3] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41
  @elements[7] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42
  @elements[11] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43
  @elements[15] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44
  self
end

#multiply_scalar(scalar) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 175

def multiply_scalar(scalar)
  @elements.map! { |value| value * scalar }
  self
end

#premultiply(matrix) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 111

def premultiply(matrix)
  multiply_matrices(matrix, self)
end

#scale(vector) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 276

def scale(vector)
  @elements[0] *= vector.x
  @elements[4] *= vector.y
  @elements[8] *= vector.z
  @elements[1] *= vector.x
  @elements[5] *= vector.y
  @elements[9] *= vector.z
  @elements[2] *= vector.x
  @elements[6] *= vector.y
  @elements[10] *= vector.z
  @elements[3] *= vector.x
  @elements[7] *= vector.y
  @elements[11] *= vector.z
  self
end

#set(n11, n12, n13, n14, n21, n22, n23, n24, n31, n32, n33, n34, n41, n42, n43, n44) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 20

def set(n11, n12, n13, n14, n21, n22, n23, n24, n31, n32, n33, n34, n41, n42, n43, n44)
  @elements[0] = n11
  @elements[4] = n12
  @elements[8] = n13
  @elements[12] = n14
  @elements[1] = n21
  @elements[5] = n22
  @elements[9] = n23
  @elements[13] = n24
  @elements[2] = n31
  @elements[6] = n32
  @elements[10] = n33
  @elements[14] = n34
  @elements[3] = n41
  @elements[7] = n42
  @elements[11] = n43
  @elements[15] = n44
  self
end

#set_position(x, y = nil, z = nil) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 93

def set_position(x, y = nil, z = nil)
  if y.nil? && z.nil?
    @elements[12] = x.x
    @elements[13] = x.y
    @elements[14] = x.z
  else
    @elements[12] = x
    @elements[13] = y
    @elements[14] = z
  end

  self
end

#to_a ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 425

def to_a
  @elements.dup
end

#to_array(array = [], offset = 0) ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 429

def to_array(array = [], offset = 0)
  16.times { |index| array[index + offset] = @elements[index] }
  array
end

#transpose ⇒ Object 



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# File 'lib/three/math/matrix4.rb', line 211

def transpose
  @elements[1], @elements[4] = @elements[4], @elements[1]
  @elements[2], @elements[8] = @elements[8], @elements[2]
  @elements[6], @elements[9] = @elements[9], @elements[6]
  @elements[3], @elements[12] = @elements[12], @elements[3]
  @elements[7], @elements[13] = @elements[13], @elements[7]
  @elements[11], @elements[14] = @elements[14], @elements[11]
  self
end