def rotate(u,angle,axis=Vector(0,0,1)):
'''rotate(Vector,Float,axis=Vector): rotates the first Vector
around the given axis, at the given angle.
If axis is omitted, the rotation is made on the xy plane.'''
typecheck ([(u,Vector), (angle,(int,float)), (axis,Vector)], "rotate")
if angle == 0:
return u
l=axis.Length
x=axis.x/l
y=axis.y/l
z=axis.z/l
c = math.cos(angle)
s = math.sin(angle)
t = 1 - c
xyt = x*y*t
xzt = x*z*t
yzt = y*z*t
xs = x*s
ys = y*s
zs = z*s
m = Matrix(c + x*x*t, xyt - zs, xzt + ys, 0,
xyt + zs, c + y*y*t, yzt - xs, 0,
xzt - ys, yzt + xs, c + z*z*t, 0)
return m.multiply(u)
def rotate(u, angle, axis=Vector(0, 0, 1)):
'''rotate(Vector,Float,axis=Vector): rotates the first Vector
around the given axis, at the given angle.
If axis is omitted, the rotation is made on the xy plane.'''
typecheck([(u, Vector), (angle, (int, long, float)), (axis, Vector)],
"rotate")
if angle == 0:
return u
l = axis.Length
x = axis.x / l
y = axis.y / l
z = axis.z / l
c = math.cos(angle)
s = math.sin(angle)
t = 1 - c
xyt = x * y * t
xzt = x * z * t
yzt = y * z * t
xs = x * s
ys = y * s
zs = z * s
m = Matrix(c + x * x * t, xyt - zs, xzt + ys, 0, xyt + zs, c + y * y * t,
yzt - xs, 0, xzt - ys, yzt + xs, c + z * z * t, 0)
return m.multiply(u)
def __valueAtEllipse__(ra, rb, center, axis, u): x = VEC(cos(u) * ra, sin(u) * rb, 0) theta = axis.getAngle(DIR_Z) if (abs(theta) < 1e-06): n = DIR_X elif (abs(theta - pi) < 1e-06): n = -DIR_X else: n = DIR_Z.cross(axis) if (n.Length == 0): return x n = n.normalize() a = cos(theta/2) b = n.x*sin(theta/2) c = n.y*sin(theta/2) d = n.z*sin(theta/2) aa, bb, cc, dd = a*a, b*b, c*c, d*d bc, ad, ac, ab, bd, cd = b*c, a*d, a*c, a*b, b*d, c*d m = MAT(aa+bb-cc-dd, 2*(bc+ad), 2*(bd-ac), 0, 2*(bc-ad), aa+cc-bb-dd, 2*(cd+ab), 0, 2*(bd+ac), 2*(cd-ab), aa+dd-bb-cc, 0, 0, 0, 0, 1) return center + m.multiply(x)
def rotate(u, angle, axis=Vector(0, 0, 1)):
"""Rotate the vector by the specified angle, around the given axis.
If the axis is omitted, the rotation is made around the Z axis
(on the XY plane).
It uses a 3x3 rotation matrix.
::
u_rot = R u
(c + x*x*t xyt - zs xzt + ys )
u_rot = (xyt + zs c + y*y*t yzt - xs ) * u
(xzt - ys yzt + xs c + z*z*t)
Where `x`, `y`, `z` indicate unit components of the axis;
`c` denotes a cosine of the angle; `t` indicates a complement
of that cosine; `xs`, `ys`, `zs` indicate products of the unit
components and the sine of the angle; and `xyt`, `xzt`, `yzt`
indicate products of two unit components and the complement
of the cosine.
Parameters
----------
u : Base::Vector3
The vector.
angle : float
The angle of rotation given in radians.
axis : Base::Vector3, optional
The vector specifying the axis of rotation.
It defaults to `(0, 0, 1)`, the +Z axis.
Returns
-------
Base::Vector3
The new rotated vector.
If the `angle` is zero, return the original vector `u`.
"""
typecheck([(u, Vector), (angle, (int, float)), (axis, Vector)], "rotate")
if angle == 0:
return u
# Unit components, so that x**2 + y**2 + z**2 = 1
L = axis.Length
x = axis.x / L
y = axis.y / L
z = axis.z / L
c = math.cos(angle)
s = math.sin(angle)
t = 1 - c
# Various products
xyt = x * y * t
xzt = x * z * t
yzt = y * z * t
xs = x * s
ys = y * s
zs = z * s
m = Matrix(c + x * x * t, xyt - zs, xzt + ys, 0, xyt + zs, c + y * y * t,
yzt - xs, 0, xzt - ys, yzt + xs, c + z * z * t, 0)
return m.multiply(u)
