Class: Mittsu::Quaternion
- Inherits:
-
Object
- Object
- Mittsu::Quaternion
- Defined in:
- lib/mittsu/math/quaternion.rb
Constant Summary collapse
- EPS =
0.000001
Instance Attribute Summary collapse
-
#w ⇒ Object
Returns the value of attribute w.
-
#x ⇒ Object
Returns the value of attribute x.
-
#y ⇒ Object
Returns the value of attribute y.
-
#z ⇒ Object
Returns the value of attribute z.
Class Method Summary collapse
Instance Method Summary collapse
- #==(quaternion) ⇒ Object
- #clone ⇒ Object
- #conjugate ⇒ Object
- #copy(quaternion) ⇒ Object
- #dot(v) ⇒ Object
- #from_array(array, offset = 0) ⇒ Object
-
#initialize(x = 0.0, y = 0.0, z = 0.0, w = 1.0) ⇒ Quaternion
constructor
A new instance of Quaternion.
- #inverse ⇒ Object
- #length ⇒ Object
- #length_sq ⇒ Object
- #multiply(q) ⇒ Object
- #multiply_quaternions(a, b) ⇒ Object
- #normalize ⇒ Object
- #on_change(&callback) ⇒ Object
- #on_change_callback ⇒ Object
- #set(x, y, z, w) ⇒ Object
- #set_from_axis_angle(axis, angle) ⇒ Object
- #set_from_euler(euler, update = true) ⇒ Object
- #set_from_rotation_matrix(m) ⇒ Object
- #set_from_unit_vectors(v_from, v_to) ⇒ Object
- #slerp(qb, t) ⇒ Object
- #to_array(array = [], offset = 0) ⇒ Object
Constructor Details
#initialize(x = 0.0, y = 0.0, z = 0.0, w = 1.0) ⇒ Quaternion
Returns a new instance of Quaternion.
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# File 'lib/mittsu/math/quaternion.rb', line 7 def initialize(x = 0.0, y = 0.0, z = 0.0, w = 1.0) @x, @y, @z, @w = x, y, z, w @on_change_callback = nil end |
Instance Attribute Details
#w ⇒ Object
Returns the value of attribute w.
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# File 'lib/mittsu/math/quaternion.rb', line 5 def w @w end |
#x ⇒ Object
Returns the value of attribute x.
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# File 'lib/mittsu/math/quaternion.rb', line 5 def x @x end |
#y ⇒ Object
Returns the value of attribute y.
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# File 'lib/mittsu/math/quaternion.rb', line 5 def y @y end |
#z ⇒ Object
Returns the value of attribute z.
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# File 'lib/mittsu/math/quaternion.rb', line 5 def z @z end |
Class Method Details
.slerp(qa, qb, qm, t) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 303 def self.slerp(qa, qb, qm, t) qm.copy(qa).slerp(qb, t) end |
Instance Method Details
#==(quaternion) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 268 def ==(quaternion) (quaternion.x == @x) && (quaternion.y == @y) && (quaternion.z == @z) && (quaternion.w == @w) end |
#clone ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 299 def clone Mittsu::Quaternion.new(@x, @y, @z, @w) end |
#conjugate ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 173 def conjugate @x *= -1.0 @y *= -1.0 @z *= -1.0 self.on_change_callback self end |
#copy(quaternion) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 41 def copy(quaternion) @x = quaternion.x @y = quaternion.y @z = quaternion.z @w = quaternion.w self.on_change_callback self end |
#dot(v) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 181 def dot(v) @x * v._x + @y * v._y + @z * v._z + @w * v._w end |
#from_array(array, offset = 0) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 272 def from_array(array, offset = 0) @x = array[offset] @y = array[offset + 1] @z = array[offset + 2] @w = array[offset + 3] self.on_change_callback self end |
#inverse ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 168 def inverse self.conjugate.normalize self end |
#length ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 189 def length ::Math.sqrt(@x * @x + @y * @y + @z * @z + @w * @w) end |
#length_sq ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 185 def length_sq @x * @x + @y * @y + @z * @z + @w * @w end |
#multiply(q) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 211 def multiply(q) self.multiply_quaternions(self, q) end |
#multiply_quaternions(a, b) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 215 def multiply_quaternions(a, b) # from http:#www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/code/index.htm qax = a.x; qay = a.y; qaz = a.z; qaw = a.w qbx = b.x; qby = b.y; qbz = b.z; qbw = b.w @x = qax * qbw + qaw * qbx + qay * qbz - qaz * qby @y = qay * qbw + qaw * qby + qaz * qbx - qax * qbz @z = qaz * qbw + qaw * qbz + qax * qby - qay * qbx @w = qaw * qbw - qax * qbx - qay * qby - qaz * qbz self.on_change_callback self end |
#normalize ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 193 def normalize l = self.length if l == 0.0 @x = 0.0 @y = 0.0 @z = 0.0 @w = 1.0 else l = 1.0 / l @x = @x * l @y = @y * l @z = @z * l @w = @w * l end self.on_change_callback self end |
#on_change(&callback) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 289 def on_change(&callback) @on_change_callback = callback self end |
#on_change_callback ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 294 def on_change_callback return unless @on_change_callback @on_change_callback.call end |
#set(x, y, z, w) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 12 def set(x, y, z, w) @x = x.to_f @y = y.to_f @z = z.to_f @w = w.to_f self.on_change_callback self end |
#set_from_axis_angle(axis, angle) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 95 def set_from_axis_angle(axis, angle) # http:#www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm # assumes axis is normalized half_angle = angle / 2.0 s = ::Math.sin(half_angle) @x = axis.x * s @y = axis.y * s @z = axis.z * s @w = ::Math.cos(half_angle) self.on_change_callback self end |
#set_from_euler(euler, update = true) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 50 def set_from_euler(euler, update = true) # http:#www.mathworks.com/matlabcentral/fileexchange/ # 20696-function-to-convert-between-dcm-euler-angles-quaternions-and-euler-vectors/ # content/SpinCalc.m c1 = ::Math.cos(euler.x / 2.0) c2 = ::Math.cos(euler.y / 2.0) c3 = ::Math.cos(euler.z / 2.0) s1 = ::Math.sin(euler.x / 2.0) s2 = ::Math.sin(euler.y / 2.0) s3 = ::Math.sin(euler.z / 2.0) if euler.order == 'XYZ' @x = s1 * c2 * c3 + c1 * s2 * s3 @y = c1 * s2 * c3 - s1 * c2 * s3 @z = c1 * c2 * s3 + s1 * s2 * c3 @w = c1 * c2 * c3 - s1 * s2 * s3 elsif euler.order == 'YXZ' @x = s1 * c2 * c3 + c1 * s2 * s3 @y = c1 * s2 * c3 - s1 * c2 * s3 @z = c1 * c2 * s3 - s1 * s2 * c3 @w = c1 * c2 * c3 + s1 * s2 * s3 elsif euler.order == 'ZXY' @x = s1 * c2 * c3 - c1 * s2 * s3 @y = c1 * s2 * c3 + s1 * c2 * s3 @z = c1 * c2 * s3 + s1 * s2 * c3 @w = c1 * c2 * c3 - s1 * s2 * s3 elsif euler.order == 'ZYX' @x = s1 * c2 * c3 - c1 * s2 * s3 @y = c1 * s2 * c3 + s1 * c2 * s3 @z = c1 * c2 * s3 - s1 * s2 * c3 @w = c1 * c2 * c3 + s1 * s2 * s3 elsif euler.order == 'YZX' @x = s1 * c2 * c3 + c1 * s2 * s3 @y = c1 * s2 * c3 + s1 * c2 * s3 @z = c1 * c2 * s3 - s1 * s2 * c3 @w = c1 * c2 * c3 - s1 * s2 * s3 elsif euler.order == 'XZY' @x = s1 * c2 * c3 - c1 * s2 * s3 @y = c1 * s2 * c3 - s1 * c2 * s3 @z = c1 * c2 * s3 + s1 * s2 * c3 @w = c1 * c2 * c3 + s1 * s2 * s3 end self.on_change_callback if update self end |
#set_from_rotation_matrix(m) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 108 def set_from_rotation_matrix(m) # http:#www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm # assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled) te = m.elements 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] trace = m11 + m22 + m33 if trace > 0 s = 0.5 / ::Math.sqrt(trace + 1.0) @w = 0.25 / s @x = (m32 - m23) * s @y = (m13 - m31) * s @z = (m21 - m12) * s elsif m11 > m22 && m11 > m33 s = 2.0 * ::Math.sqrt(1.0 + m11 - m22 - m33) @w = (m32 - m23) / s @x = 0.25 * s @y = (m12 + m21) / s @z = (m13 + m31) / s elsif m22 > m33 s = 2.0 * ::Math.sqrt(1.0 + m22 - m11 - m33) @w = (m13 - m31) / s @x = (m12 + m21) / s @y = 0.25 * s @z = (m23 + m32) / s else s = 2.0 * ::Math.sqrt(1.0 + m33 - m11 - m22) @w = (m21 - m12) / s @x = (m13 + m31) / s @y = (m23 + m32) / s @z = 0.25 * s end self.on_change_callback self end |
#set_from_unit_vectors(v_from, v_to) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 145 def set_from_unit_vectors(v_from, v_to) # http:#lolengine.net/blog/2014/02/24/quaternion-from-two-vectors-final # assumes direction vectors v_from and v_to are normalized v1 = Mittsu::Vector3.new r = v_from.dot(v_to) + 1.0 if r < EPS r = 0.0 if v_from.x.abs > v_from.z.abs v1.set(-v_from.y, v_from.x, 0.0) else v1.set(0.0, -v_from.z, v_from.y) end else v1.cross_vectors(v_from, v_to) end @x = v1.x @y = v1.y @z = v1.z @w = r self.normalize self end |
#slerp(qb, t) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 227 def slerp(qb, t) return self if t.zero? return self.copy(qb) if t == 1.0 _x, _y, _z, _w = @x, @y, @z, @w # http:#www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/ cos_half_theta = _w * qb.w + _x * qb.x + _y * qb.y + _z * qb.z if cos_half_theta < 0.0 @w = -qb.w @x = -qb.x @y = -qb.y @z = -qb.z cos_half_theta = - cos_half_theta else self.copy(qb) end if cos_half_theta >= 1.0 @w = _w @x = _x @y = _y @z = _z return self end half_theta = ::Math.acos(cos_half_theta) sin_half_theta = ::Math.sqrt(1.0 - cos_half_theta * cos_half_theta) if sin_half_theta.abs < 0.001 @w = 0.5 * (_w + @w) @x = 0.5 * (_x + @x) @y = 0.5 * (_y + @y) @z = 0.5 * (_z + @z) return self end ratio_a = ::Math.sin((1.0. - t) * half_theta) / sin_half_theta, ratio_b = ::Math.sin(t * half_theta) / sin_half_theta @w = (_w * ratio_a + @w * ratio_b) @x = (_x * ratio_a + @x * ratio_b) @y = (_y * ratio_a + @y * ratio_b) @z = (_z * ratio_a + @z * ratio_b) self.on_change_callback self end |
#to_array(array = [], offset = 0) ⇒ Object
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# File 'lib/mittsu/math/quaternion.rb', line 281 def to_array(array = [], offset = 0) array[offset] = @x array[offset + 1] = @y array[offset + 2] = @z array[offset + 3] = @w array end |