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; Quat.bb : v1.0 : 15/11/02
; A tutorial on how to use this file is at http://www.dscho.co.uk/blitz/tutorials/quaternions.shtml
; Types
Type Rotation
Field pitch#, yaw#, roll#
End Type
Type Quat
Field w#, x#, y#, z#
End Type
; Change these constants if you notice slips in accuracy
Const QuatToEulerAccuracy# = 0.001
Const QuatSlerpAccuracy# = 0.0001
; convert a Rotation to a Quat
Function EulerToQuat(out.Quat, src.Rotation)
; NB roll is inverted due to change in handedness of coordinate systems
Local cr# = Cos(-src\roll/2)
Local cp# = Cos(src\pitch/2)
Local cy# = Cos(src\yaw/2)
Local sr# = Sin(-src\roll/2)
Local sp# = Sin(src\pitch/2)
Local sy# = Sin(src\yaw/2)
; These variables are only here to cut down on the number of multiplications
Local cpcy# = cp * cy
Local spsy# = sp * sy
Local spcy# = sp * cy
Local cpsy# = cp * sy
; Generate the output quat
out\w = cr * cpcy + sr * spsy
out\x = sr * cpcy - cr * spsy
out\y = cr * spcy + sr * cpsy
out\z = cr * cpsy - sr * spcy
End Function
; convert a Quat to a Rotation
Function QuatToEuler(out.Rotation, src.Quat)
Local sint#, cost#, sinv#, cosv#, sinf#, cosf#
Local cost_temp#
sint = (2 * src\w * src\y) - (2 * src\x * src\z)
cost_temp = 1.0 - (sint * sint)
If Abs(cost_temp) > QuatToEulerAccuracy
cost = Sqr(cost_temp)
Else
cost = 0
EndIf
If Abs(cost) > QuatToEulerAccuracy
sinv = ((2 * src\y * src\z) + (2 * src\w * src\x)) / cost
cosv = (1 - (2 * src\x * src\x) - (2 * src\y * src\y)) / cost
sinf = ((2 * src\x * src\y) + (2 * src\w * src\z)) / cost
cosf = (1 - (2 * src\y * src\y) - (2 * src\z * src\z)) / cost
Else
sinv = (2 * src\w * src\x) - (2 * src\y * src\z)
cosv = 1 - (2 * src\x * src\x) - (2 * src\z * src\z)
sinf = 0
cosf = 1
EndIf
; Generate the output rotation
out\roll = -ATan2(sinv, cosv); inverted due to change in handedness of coordinate system
out\pitch = ATan2(sint, cost)
out\yaw = ATan2(sinf, cosf)
End Function
; use this to interpolate between quaternions
Function QuatSlerp(res.Quat, start.Quat, fin.Quat, t#)
Local scaler_w#, scaler_x#, scaler_y#, scaler_z#
Local omega#, cosom#, sinom#, scale0#, scale1#
cosom = start\x * fin\x + start\y * fin\y + start\z * fin\z + start\w * fin\w
If cosom <= 0.0
cosom = -cosom
scaler_w = -fin\w
scaler_x = -fin\x
scaler_y = -fin\y
scaler_z = -fin\z
Else
scaler_w = fin\w
scaler_x = fin\x
scaler_y = fin\y
scaler_z = fin\z
EndIf
If (1 - cosom) > QuatSlerpAccuracy
omega = ACos(cosom)
sinom = Sin(omega)
scale0 = Sin((1 - t) * omega) / sinom
scale1 = Sin(t * omega) / sinom
Else
; Angle too small: use linear interpolation instead
scale0 = 1 - t
scale1 = t
EndIf
res\x = scale0 * start\x + scale1 * scaler_x
res\y = scale0 * start\y + scale1 * scaler_y
res\z = scale0 * start\z + scale1 * scaler_z
res\w = scale0 * start\w + scale1 * scaler_w
End Function
; result will be the same rotation as doing q1 then q2 (order matters!)
Function MultiplyQuat(result.Quat, q1.Quat, q2.Quat)
Local a#, b#, c#, d#, e#, f#, g#, h#
a = (q1\w + q1\x) * (q2\w + q2\x)
b = (q1\z - q1\y) * (q2\y - q2\z)
c = (q1\w - q1\x) * (q2\y + q2\z)
d = (q1\y + q1\z) * (q2\w - q2\x)
e = (q1\x + q1\z) * (q2\x + q2\y)
f = (q1\x - q1\z) * (q2\x - q2\y)
g = (q1\w + q1\y) * (q2\w - q2\z)
h = (q1\w - q1\y) * (q2\w + q2\z)
result\w = b + (-e - f + g + h) / 2
result\x = a - ( e + f + g + h) / 2
result\y = c + ( e - f + g - h) / 2
result\z = d + ( e - f - g + h) / 2
End Function
; convenience function to fill in a rotation structure
Function FillRotation(r.Rotation, pitch#, yaw#, roll#)
r\pitch = pitch
r\yaw = yaw
r\roll = roll
End Function