Class: Engine::Quaternion

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

Constant Summary collapse

EULER_ORDER = 
"XYZ"

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(w, x, y, z) ⇒ Quaternion

Returns a new instance of Quaternion.



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# File 'lib/engine/quaternion.rb', line 8

def initialize(w, x, y, z)
  @w = w
  @x = x
  @y = y
  @z = z
end

Instance Attribute Details

#euler_order ⇒ Object

Returns the value of attribute euler_order.



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# File 'lib/engine/quaternion.rb', line 6

def euler_order
  @euler_order
end

#w ⇒ Object

Returns the value of attribute w.



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# File 'lib/engine/quaternion.rb', line 6

def w
  @w
end

#x ⇒ Object

Returns the value of attribute x.



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# File 'lib/engine/quaternion.rb', line 6

def x
  @x
end

#y ⇒ Object

Returns the value of attribute y.



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# File 'lib/engine/quaternion.rb', line 6

def y
  @y
end

#z ⇒ Object

Returns the value of attribute z.



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# File 'lib/engine/quaternion.rb', line 6

def z
  @z
end

Class Method Details

.from_angle_axis(angle, axis) ⇒ Object 



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# File 'lib/engine/quaternion.rb', line 204

def self.from_angle_axis(angle, axis)
  axis = axis.normalize
  angle = angle * Math::PI / 180

  half_angle = angle / 2
  sin_half_angle = Math.sin(half_angle)
  cos_half_angle = Math.cos(half_angle)

  Quaternion.new(
    cos_half_angle,
    axis[0] * sin_half_angle,
    axis[1] * sin_half_angle,
    axis[2] * sin_half_angle
  )
end

.from_euler(euler) ⇒ Object

taken from github.com/mrdoob/three.js/blob/134ff886792734a75c0a9b30aa816d19270f8526/src/math/Quaternion.js#L229



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# File 'lib/engine/quaternion.rb', line 29

def self.from_euler(euler)
  e_1 = euler[0] * Math::PI / 180
  e_2 = euler[1] * Math::PI / 180
  e_3 = euler[2] * Math::PI / 180

  c_1 = Math.cos(e_1 / 2)
  c_2 = Math.cos(e_2 / 2)
  c_3 = Math.cos(e_3 / 2)

  s_1 = Math.sin(e_1 / 2)
  s_2 = Math.sin(e_2 / 2)
  s_3 = Math.sin(e_3 / 2)

  case EULER_ORDER
  when "XYZ"
    Quaternion.new(
      c_1 * c_2 * c_3 - s_1 * s_2 * s_3,
      s_1 * c_2 * c_3 + c_1 * s_2 * s_3,
      c_1 * s_2 * c_3 - s_1 * c_2 * s_3,
      c_1 * c_2 * s_3 + s_1 * s_2 * c_3
    )
  when "YXZ"
    Quaternion.new(
      c_1 * c_2 * c_3 + s_1 * s_2 * s_3,
      s_1 * c_2 * c_3 + c_1 * s_2 * s_3,
      c_1 * s_2 * c_3 - s_1 * c_2 * s_3,
      c_1 * c_2 * s_3 - s_1 * s_2 * c_3
    )
  when "ZXY"
    Quaternion.new(
      c_1 * c_2 * c_3 - s_1 * s_2 * s_3,
      s_1 * c_2 * c_3 - c_1 * s_2 * s_3,
      c_1 * s_2 * c_3 + s_1 * c_2 * s_3,
      c_1 * c_2 * s_3 + s_1 * s_2 * c_3
    )
  when "ZYX"
    Quaternion.new(
      c_1 * c_2 * c_3 + s_1 * s_2 * s_3,
      s_1 * c_2 * c_3 - c_1 * s_2 * s_3,
      c_1 * s_2 * c_3 + s_1 * c_2 * s_3,
      c_1 * c_2 * s_3 - s_1 * s_2 * c_3
    )
  when "YZX"
    Quaternion.new(
      s_1 * c_2 * c_3 + c_1 * s_2 * s_3,
      c_1 * s_2 * c_3 + s_1 * c_2 * s_3,
      c_1 * c_2 * s_3 - s_1 * s_2 * c_3,
      c_1 * c_2 * c_3 - s_1 * s_2 * s_3
    )
  when "XZY"
    Quaternion.new(
      c_1 * c_2 * c_3 + s_1 * s_2 * s_3,
      s_1 * c_2 * c_3 - c_1 * s_2 * s_3,
      c_1 * s_2 * c_3 - s_1 * c_2 * s_3,
      c_1 * c_2 * s_3 + s_1 * s_2 * c_3
    )
  end
end

Instance Method Details

#*(other) ⇒ Object 



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# File 'lib/engine/quaternion.rb', line 19

def *(other)
  Quaternion.new(
    @w * other.w - @x * other.x - @y * other.y - @z * other.z,
    @w * other.x + @x * other.w + @y * other.z - @z * other.y,
    @w * other.y - @x * other.z + @y * other.w + @z * other.x,
    @w * other.z + @x * other.y - @y * other.x + @z * other.w
  )
end

#te ⇒ Object 



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# File 'lib/engine/quaternion.rb', line 166

def te
  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

  [
    1 - (yy + zz),
    xy + wz,
    xz - wy,
    0,

    xy - wz,
    1 - (xx + zz),
    yz + wx,
    0,

    xz + wy,
    yz - wx,
    1 - (xx + yy),
    0,

    0,
    0,
    0,
    1,
  ]
end

#to_angle_axis ⇒ Object 



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# File 'lib/engine/quaternion.rb', line 220

def to_angle_axis
  angle = 2 * Math.acos(@w)
  s = Math.sqrt(1 - @w * @w)
  s = 1 if s < 0.0001
  axis = Vector[@x / s, @y / s, @z / s]
  [angle * 180 / Math::PI, axis]
end

#to_euler ⇒ Object

taken from github.com/mrdoob/three.js/blob/134ff886792734a75c0a9b30aa816d19270f8526/src/math/Euler.js#L134



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# File 'lib/engine/quaternion.rb', line 89

def to_euler
  m11 = te[0]
  m12 = te[4]
  m13 = te[8]
  m21 = te[1]
  m22 = te[5]
  m23 = te[9]
  m31 = te[2]
  m32 = te[6]
  m33 = te[10]

  case EULER_ORDER
  when "XYZ"
    e_y = Math.asin(m13.clamp(-1, 1))

    if m13.abs < 0.9999999
      e_x = Math.atan2(-m23, m33)
      e_z = Math.atan2(-m12, m11)
    else
      e_x = Math.atan2(m32, m22)
      e_z = 0
    end
  when "YXZ"
    e_x = Math.asin(-m23.clamp(-1, 1))

    if m23.abs < 0.9999999
      e_y = Math.atan2(m13, m33)
      e_z = Math.atan2(m21, m22)
    else
      e_y = Math.atan2(-m31, m11)
      e_z = 0
    end
  when "ZXY"
    e_x = Math.asin(m32.clamp(-1, 1))

    if m32.abs < 0.9999999
      e_y = Math.atan2(-m31, m33)
      e_z = Math.atan2(-m12, m22)
    else
      e_y = 0
      e_z = Math.atan2(m21, m11)
    end
  when "ZYX"
    e_y = Math.asin(-m31.clamp(-1, 1))

    if m31.abs < 0.9999999
      e_x = Math.atan2(m32, m33)
      e_z = Math.atan2(m21, m11)
    else
      e_x = 0
      e_z = Math.atan2(-m12, m22)
    end
  when "YZX"
    e_z = Math.asin(m21.clamp(-1, 1))

    if m21.abs < 0.9999999
      e_x = Math.atan2(-m23, m22)
      e_y = Math.atan2(-m31, m11)
    else
      e_x = 0
      e_y = Math.atan2(m13, m33)
    end
  when "XZY"
    e_z = Math.asin(-m12.clamp(-1, 1))

    if m12.abs < 0.9999999
      e_x = Math.atan2(m32, m22)
      e_y = Math.atan2(m13, m11)
    else
      e_x = Math.atan2(-m23, m33)
      e_y = 0
    end
  end

  Vector[e_x, e_y, e_z] * 180 / Math::PI
end

#to_s ⇒ Object 



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# File 'lib/engine/quaternion.rb', line 15

def to_s
  "Quaternion(w: #{@w}, x: #{@x}, y: #{@y}, z: #{@z})"
end