Class: Mittsu::Matrix4

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

Constant Summary collapse

DIMENSIONS = 
4

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize ⇒ Matrix4

Returns a new instance of Matrix4.



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

def initialize()
  @elements = [
    1.0, 0.0, 0.0, 0.0,
    0.0, 1.0, 0.0, 0.0,
    0.0, 0.0, 1.0, 0.0,
    0.0, 0.0, 0.0, 1.0
  ]
end

Instance Attribute Details

#elements ⇒ Object

Returns the value of attribute elements.



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# File 'lib/mittsu/math/matrix4.rb', line 5

def elements
  @elements
end

Instance Method Details

#==(other) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 568

def ==(other)
  other.elements == @elements
end

#apply_to_vector3_array(array, offset = 0, length = array.length) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 277

def apply_to_vector3_array(array, offset = 0, length = array.length)
  v1 = Mittsu::Vector3.new
  i = 0
  j = offset
  while i < length
    v1.x = array[j].to_f
    v1.y = array[j + 1].to_f
    v1.z = array[j + 2].to_f
    v1.apply_matrix4(self)
    array[j]     = v1.x
    array[j + 1] = v1.y
    array[j + 2] = v1.z
    i += 3
    j += 3
  end
  array
end

#clone ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 582

def clone
  Mittsu::Matrix4.new.from_array(self.elements)
end

#compose(position, quaternion, scale) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 476

def compose(position, quaternion, scale)
  self.make_rotation_from_quaternion(quaternion)
  self.scale(scale)
  self.set_position(position)
  self
end

#copy(m) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 37

def copy(m)
  self.from_array(m.elements)
  self
end

#copy_position(m) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 42

def copy_position(m)
  te = self.elements
  me = m.elements
  te[12] = me[12]
  te[13] = me[13]
  te[14] = me[14]
  self
end

#decompose(position, quaternion, scale) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 483

def decompose(position, quaternion, scale)
  vector = Mittsu::Vector3.new
  matrix = Mittsu::Matrix4.new
  te = self.elements
  sx = vector.set(te[0], te[1],  te[2]).length
  sy = vector.set(te[4], te[5],  te[6]).length
  sz = vector.set(te[8], te[9], te[10]).length
  # if determine is negative, we need to invert one scale
  det = self.determinant
  if det < 0.0
    sx = -sx
  end
  position.x = te[12]
  position.y = te[13]
  position.z = te[14]
  # scale the rotation part
  matrix.elements[0...15] = self.elements # at this point matrix is incomplete so we can't use .copy
  inv_sx = 1.0 / sx
  inv_sy = 1.0 / sy
  inv_sz = 1.0 / sz
  matrix.elements[0]  *= inv_sx
  matrix.elements[1]  *= inv_sx
  matrix.elements[2]  *= inv_sx
  matrix.elements[4]  *= inv_sy
  matrix.elements[5]  *= inv_sy
  matrix.elements[6]  *= inv_sy
  matrix.elements[8]  *= inv_sz
  matrix.elements[9]  *= inv_sz
  matrix.elements[10] *= inv_sz
  quaternion.set_from_rotation_matrix(matrix)
  scale.x = sx
  scale.y = sy
  scale.z = sz
  self
end

#determinant ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 295

def determinant
  te = self.elements
  n11 = te[0]; n12 = te[4]; n13 = te[8]; n14 = te[12]
  n21 = te[1]; n22 = te[5]; n23 = te[9]; n24 = te[13]
  n31 = te[2]; n32 = te[6]; n33 = te[10]; n34 = te[14]
  n41 = te[3]; n42 = te[7]; n43 = te[11]; n44 = te[15]
  #TODO: make this more efficient
  #(based on http:#www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm)
  n41 * (n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34) +
  n42 * (n11 * n23 * n34 - n11 * n24 * n33 + n14 * n21 * n33 - n13 * n21 * n34 + n13 * n24 * n31 - n14 * n23 * n31) +
  n43 * (n11 * n24 * n32 - n11 * n22 * n34 - n14 * n21 * n32 + n12 * n21 * n34 + n14 * n22 * n31 - n12 * n24 * n31) +
  n44 * (-n13 * n22 * n31 - n11 * n23 * n32 + n11 * n22 * n33 + n13 * n21 * n32 - n12 * n21 * n33 + n12 * n23 * n31)
end

#extract_basis(x_axis, y_axis, z_axis) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 51

def extract_basis(x_axis, y_axis, z_axis)
  te = self.elements
  x_axis.set(te[0], te[1], te[2])
  y_axis.set(te[4], te[5], te[6])
  z_axis.set(te[8], te[9], te[10])
  self
end

#extract_rotation(m) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 69

def extract_rotation(m)
  v1 = Mittsu::Vector3.new
  te = self.elements
  me = m.elements
  scale_x = 1.0 / v1.set(me[0], me[1], me[2]).length
  scale_y = 1.0 / v1.set(me[4], me[5], me[6]).length
  scale_z = 1.0 / v1.set(me[8], me[9], me[10]).length
  te[0] = me[0] * scale_x
  te[1] = me[1] * scale_x
  te[2] = me[2] * scale_x
  te[4] = me[4] * scale_y
  te[5] = me[5] * scale_y
  te[6] = me[6] * scale_y
  te[8] = me[8] * scale_z
  te[9] = me[9] * scale_z
  te[10] = me[10] * scale_z
  self
end

#flatten_to_array_offset(array, offset) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 320

def flatten_to_array_offset(array, offset)
  te = self.elements
  array[offset    ] = te[0]
  array[offset + 1] = te[1]
  array[offset + 2] = te[2]
  array[offset + 3] = te[3]
  array[offset + 4] = te[4]
  array[offset + 5] = te[5]
  array[offset + 6] = te[6]
  array[offset + 7] = te[7]
  array[offset + 8]  = te[8]
  array[offset + 9]  = te[9]
  array[offset + 10] = te[10]
  array[offset + 11] = te[11]
  array[offset + 12] = te[12]
  array[offset + 13] = te[13]
  array[offset + 14] = te[14]
  array[offset + 15] = te[15]
  array
end

#from_array(array) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 563

def from_array(array)
  self.elements[0..array.length] = array
  self
end

#identity ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 27

def identity
  self.set(
    1.0, 0.0, 0.0, 0.0,
    0.0, 1.0, 0.0, 0.0,
    0.0, 0.0, 1.0, 0.0,
    0.0, 0.0, 0.0, 1.0
  )
  self
end

#inverse(m, throw_on_invertable = false) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 349

def inverse(m, throw_on_invertable = false)
  # based on http:#www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
  te = @elements
  me = m.elements
  n11 = me[0]; n12 = me[4]; n13 = me[8];  n14 = me[12]
  n21 = me[1]; n22 = me[5]; n23 = me[9];  n24 = me[13]
  n31 = me[2]; n32 = me[6]; n33 = me[10]; n34 = me[14]
  n41 = me[3]; n42 = me[7]; n43 = me[11]; n44 = me[15]
  te[0] = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44
  te[4] = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44
  te[8] = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44
  te[12] = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34
  te[1] = n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44
  te[5] = n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44
  te[9] = n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44
  te[13] = n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34
  te[2] = n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44
  te[6] = n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44
  te[10] = n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44
  te[14] = n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34
  te[3] = n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43
  te[7] = n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43
  te[11] = n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43
  te[15] = n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33
  det = n11 * te[0] + n21 * te[4] + n31 * te[8] + n41 * te[12]
  if det.zero?
    msg = "Mittsu::Matrix4#inverse: can't invert matrix, determinant is 0"
    if throw_on_invertable
      raise Error.new(msg)
    else
      # THREE.warn(msg)
      puts "WARNING: #{msg}"
    end
    self.identity
    return self
  end
  self.multiply_scalar(1.0 / det)
  self
end

#look_at(eye, target, up) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 201

def look_at(eye, target, up)
  x = Mittsu::Vector3.new
  y = Mittsu::Vector3.new
  z = Mittsu::Vector3.new
  te = self.elements
  z.sub_vectors(eye, target).normalize
  if z.length.zero?
    z.z = 1.0
  end
  x.cross_vectors(up, z).normalize
  if x.length.zero?
    z.x += 0.0001
    x.cross_vectors(up, z).normalize
  end
  y.cross_vectors(z, x)
  te[0] = x.x; te[4] = y.x; te[8] = z.x
  te[1] = x.y; te[5] = y.y; te[9] = z.y
  te[2] = x.z; te[6] = y.z; te[10] = z.z
  self
end

#make_basis(x_axis, y_axis, z_axis) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 59

def make_basis(x_axis, y_axis, z_axis)
  self.set(
    x_axis.x, y_axis.x, z_axis.x, 0.0,
    x_axis.y, y_axis.y, z_axis.y, 0.0,
    x_axis.z, y_axis.z, z_axis.z, 0.0,
        0.0,     0.0,     0.0, 1.0
  )
  self
end

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



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# File 'lib/mittsu/math/matrix4.rb', line 519

def make_frustum(left, right, bottom, top, near, far)
  left, right, bottom, top, near, far =
    left.to_f, right.to_f, bottom.to_f, top.to_f, near.to_f, far.to_f
  te = self.elements
  x = 2.0 * near / (right - left)
  y = 2.0 * near / (top - bottom)
  a = (right + left) / (right - left)
  b = (top + bottom) / (top - bottom)
  c =     -(far + near) / (far - near)
  d = -2.0 * far * near / (far - near)
  te[0] =   x; te[4] = 0.0;  te[8]  =    a;  te[12] = 0.0
  te[1] = 0.0; te[5] =   y;  te[9]  =    b;  te[13] = 0.0
  te[2] = 0.0; te[6] = 0.0;  te[10] =    c;  te[14] =   d
  te[3] = 0.0; te[7] = 0.0;  te[11] = -1.0;  te[15] = 0.0
  self
end

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



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# File 'lib/mittsu/math/matrix4.rb', line 546

def make_orthographic(left, right, top, bottom, near, far)
  left, right, top, bottom, near, far =
    left.to_f, right.to_f, top.to_f, bottom.to_f, near.to_f, far.to_f
  te = self.elements
  w = right - left
  h = top - bottom
  p = far - near
  x = (right + left) / w
  y = (top + bottom) / h
  z = (far + near) / p
  te[0] = 2.0 / w; te[4] =     0.0; te[8]  =      0.0; te[12] =  -x
  te[1] =     0.0; te[5] = 2.0 / h; te[9]  =      0.0; te[13] =  -y
  te[2] =     0.0; te[6] =     0.0; te[10] = -2.0 / p; te[14] =  -z
  te[3] =     0.0; te[7] =     0.0; te[11] =      0.0; te[15] = 1.0
  self
end

#make_perspective(fov, aspect, near, far) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 536

def make_perspective(fov, aspect, near, far)
  fov, aspect, near, far =
    fov.to_f, aspect.to_f, near.to_f, far.to_f
  ymax = near * Math.tan(Math.deg_to_rad(fov * 0.5))
  ymin = -ymax
  xmin = ymin * aspect
  xmax = ymax * aspect
  self.make_frustum(xmin, xmax, ymin, ymax, near, far)
end

#make_rotation_axis(axis, angle) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 450

def make_rotation_axis(axis, angle)
  # Based on http:#www.gamedev.net/reference/articles/article1199.asp
  c = Math.cos(angle)
  s = Math.sin(angle)
  t = 1.0 - c
  x, y, z = axis.x, axis.y, axis.z
  tx, ty = t * x, t * y
  self.set(
        tx * x + c, tx * y - s * z, tx * z + s * y, 0.0,
    tx * y + s * z,     ty * y + c, ty * z - s * x, 0.0,
    tx * z - s * y, ty * z + s * x,  t * z * z + c, 0.0,
               0.0,            0.0,            0.0, 1.0
  )
  self
end

#make_rotation_from_euler(euler) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 88

def make_rotation_from_euler(euler)
  te = self.elements
  x, y, z = euler.x, euler.y, euler.z
  a, b = Math.cos(x), Math.sin(x)
  c, d = Math.cos(y), Math.sin(y)
  e, f = Math.cos(z), Math.sin(z)
  if euler.order == 'XYZ'
    ae = a * e; af = a * f; be = b * e; bf = b * f
    te[0] = c * e
    te[4] = - c * f
    te[8] = d
    te[1] = af + be * d
    te[5] = ae - bf * d
    te[9] = - b * c
    te[2] = bf - ae * d
    te[6] = be + af * d
    te[10] = a * c
  elsif euler.order == 'YXZ'
    ce = c * e; cf = c * f; de = d * e; df = d * f
    te[0] = ce + df * b
    te[4] = de * b - cf
    te[8] = a * d
    te[1] = a * f
    te[5] = a * e
    te[9] = - b
    te[2] = cf * b - de
    te[6] = df + ce * b
    te[10] = a * c
  elsif euler.order == 'ZXY'
    ce = c * e; cf = c * f; de = d * e; df = d * f
    te[0] = ce - df * b
    te[4] = - a * f
    te[8] = de + cf * b
    te[1] = cf + de * b
    te[5] = a * e
    te[9] = df - ce * b
    te[2] = - a * d
    te[6] = b
    te[10] = a * c
  elsif euler.order == 'ZYX'
    ae = a * e; af = a * f; be = b * e; bf = b * f
    te[0] = c * e
    te[4] = be * d - af
    te[8] = ae * d + bf
    te[1] = c * f
    te[5] = bf * d + ae
    te[9] = af * d - be
    te[2] = - d
    te[6] = b * c
    te[10] = a * c
  elsif euler.order == 'YZX'
    ac = a * c; ad = a * d; bc = b * c; bd = b * d
    te[0] = c * e
    te[4] = bd - ac * f
    te[8] = bc * f + ad
    te[1] = f
    te[5] = a * e
    te[9] = - b * e
    te[2] = - d * e
    te[6] = ad * f + bc
    te[10] = ac - bd * f
  elsif euler.order == 'XZY'
    ac = a * c; ad = a * d; bc = b * c; bd = b * d
    te[0] = c * e
    te[4] = - f
    te[8] = d * e
    te[1] = ac * f + bd
    te[5] = a * e
    te[9] = ad * f - bc
    te[2] = bc * f - ad
    te[6] = b * e
    te[10] = bd * f + ac
  end
  # last column
  te[3] = 0.0
  te[7] = 0.0
  te[11] = 0.0
  # bottom row
  te[12] = 0.0
  te[13] = 0.0
  te[14] = 0.0
  te[15] = 1.0
  self
end

#make_rotation_from_quaternion(q) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 173

def make_rotation_from_quaternion(q)
  te = self.elements
  x, y, z, w = q.x, q.y, q.z, q.w
  x2, y2, z2 = x + x, y + y, z + z
  xx, xy, xz = x * x2, x * y2, x * z2
  yy, yz, zz = y * y2, y * z2, z * z2
  wx, wy, wz = w * x2, w * y2, w * z2
  te[0] = 1.0 - (yy + zz)
  te[4] = xy - wz
  te[8] = xz + wy
  te[1] = xy + wz
  te[5] = 1.0 - (xx + zz)
  te[9] = yz - wx
  te[2] = xz - wy
  te[6] = yz + wx
  te[10] = 1.0 - (xx + yy)
  # last column
  te[3] = 0.0
  te[7] = 0.0
  te[11] = 0.0
  # bottom row
  te[12] = 0.0
  te[13] = 0.0
  te[14] = 0.0
  te[15] = 1.0
  self
end

#make_rotation_x(theta) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 417

def make_rotation_x(theta)
  c, s = Math.cos(theta), Math.sin(theta)
  self.set(
    1.0, 0.0,  0.0, 0.0,
    0.0,   c,   -s, 0.0,
    0.0,   s,    c, 0.0,
    0.0, 0.0,  0.0, 1.0
  )
  self
end

#make_rotation_y(theta) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 428

def make_rotation_y(theta)
  c, s = Math.cos(theta), Math.sin(theta)
  self.set(
       c, 0.0,   s, 0.0,
     0.0, 1.0, 0.0, 0.0,
      -s, 0.0,   c, 0.0,
     0.0, 0.0, 0.0, 1.0
  )
  self
end

#make_rotation_z(theta) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 439

def make_rotation_z(theta)
  c, s = Math.cos(theta), Math.sin(theta)
  self.set(
      c,   -s, 0.0, 0.0,
      s,    c, 0.0, 0.0,
    0.0,  0.0, 1.0, 0.0,
    0.0,  0.0, 0.0, 1.0
  )
  self
end

#make_scale(x, y, z) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 466

def make_scale(x, y, z)
  self.set(
    x.to_f, 0.0,    0.0,    0.0,
    0.0,    y.to_f, 0.0,    0.0,
    0.0,    0.0,    z.to_f, 0.0,
    0.0,    0.0,    0.0,    1.0
  )
  self
end

#make_translation(x, y, z) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 407

def make_translation(x, y, z)
  self.set(
    1.0, 0.0, 0.0, x.to_f,
    0.0, 1.0, 0.0, y.to_f,
    0.0, 0.0, 1.0, z.to_f,
    0.0, 0.0, 0.0, 1.0
  )
  self
end

#max_scale_on_axis ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 399

def max_scale_on_axis
  te = self.elements
  scale_x_sq = te[0] * te[0] + te[1] * te[1] + te[2] * te[2]
  scale_y_sq = te[4] * te[4] + te[5] * te[5] + te[6] * te[6]
  scale_z_sq = te[8] * te[8] + te[9] * te[9] + te[10] * te[10]
  Math.sqrt([scale_x_sq, scale_y_sq, scale_z_sq].max)
end

#multiply(m) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 222

def multiply(m)
  self.multiply_matrices(self, m)
end

#multiply_matrices(a, b) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 226

def multiply_matrices(a, b)
  ae = a.elements
  be = b.elements
  te = self.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]
  te[0]  = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41
  te[4]  = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42
  te[8]  = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43
  te[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44
  te[1]  = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41
  te[5]  = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42
  te[9]  = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43
  te[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44
  te[2]  = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41
  te[6]  = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42
  te[10] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43
  te[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44
  te[3]  = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41
  te[7]  = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42
  te[11] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43
  te[15] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44
  self
end

#multiply_scalar(s) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 267

def multiply_scalar(s)
  te = self.elements
  s = s.to_f
  te[0] *= s; te[4] *= s; te[8]  *= s; te[12] *= s
  te[1] *= s; te[5] *= s; te[9]  *= s; te[13] *= s
  te[2] *= s; te[6] *= s; te[10] *= s; te[14] *= s
  te[3] *= s; te[7] *= s; te[11] *= s; te[15] *= s
  self
end

#multiply_to_array(a, b, r) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 257

def multiply_to_array(a, b, r)
  te = self.elements
  self.multiply_matrices(a, b)
  r[0]  = te[0];  r[1]  = te[1];  r[2]  = te[2];  r[3]  = te[3]
  r[4]  = te[4];  r[5]  = te[5];  r[6]  = te[6];  r[7]  = te[7]
  r[8]  = te[8];  r[9]  = te[9];  r[10] = te[10]; r[11] = te[11]
  r[12] = te[12]; r[13] = te[13]; r[14] = te[14]; r[15] = te[15]
  self
end

#scale(v) ⇒ Object 



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

def scale(v)
  te = self.elements
  x = v.x; y = v.y; z = v.z
  te[0] *= x; te[4] *= y; te[8]  *= z
  te[1] *= x; te[5] *= y; te[9]  *= z
  te[2] *= x; te[6] *= y; te[10] *= z
  te[3] *= x; te[7] *= y; te[11] *= 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/mittsu/math/matrix4.rb', line 18

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

#set_position(v) ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 341

def set_position(v)
  te = self.elements
  te[12] = v.x
  te[13] = v.y
  te[14] = v.z
  self
end

#to_a ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 572

def to_a
  te = self.elements
  [
    te[0], te[1], te[2], te[3],
    te[4], te[5], te[6], te[7],
    te[8], te[9], te[10], te[11],
    te[12], te[13], te[14], te[15]
  ]
end

#transpose ⇒ Object 



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# File 'lib/mittsu/math/matrix4.rb', line 309

def transpose
  te = self.elements
  tmp = te[1];  te[1]  = te[4];  te[4]  = tmp
  tmp = te[2];  te[2]  = te[8];  te[8]  = tmp
  tmp = te[6];  te[6]  = te[9];  te[9]  = tmp
  tmp = te[3];  te[3]  = te[12]; te[12] = tmp
  tmp = te[7];  te[7]  = te[13]; te[13] = tmp
  tmp = te[11]; te[11] = te[14]; te[14] = tmp
  self
end