def test(axis, equiv_ang: Py_Angle):
for ang in range(0, 360, 15):
assert_rot(Matrix.axis_angle(axis, ang),
Matrix.from_angle(ang * equiv_ang),
f'{axis} * {ang} != {equiv_ang}')
# Inverse axis = reversed rotation.
assert_rot(Matrix.axis_angle(-axis, ang),
Matrix.from_angle(-ang * equiv_ang),
f'{-axis} * {ang} != {equiv_ang}')
def res_rotate_inst(inst: Entity, res: Property) -> None:
"""Rotate the instance around an axis.
If `axis` is specified, it should be a normal vector and the instance will
be rotated `angle` degrees around it.
Otherwise, `angle` is a pitch-yaw-roll angle which is applied.
`around` can be a point (local, pre-rotation) which is used as the origin.
"""
angles = Angle.from_str(inst['angles'])
if 'axis' in res:
orient = Matrix.axis_angle(
Vec.from_str(inst.fixup.substitute(res['axis'])),
conv_float(inst.fixup.substitute(res['angle'])),
)
else:
orient = Matrix.from_angle(
Angle.from_str(inst.fixup.substitute(res['angle'])))
try:
offset = Vec.from_str(inst.fixup.substitute(res['around']))
except NoKeyError:
pass
else:
origin = Vec.from_str(inst['origin'])
inst['origin'] = origin + (-offset @ orient + offset) @ angles
inst['angles'] = (orient @ angles).to_angle()
def compute_orients(nodes: Iterable[Node]) -> None:
"""Compute the appropriate orientation for each node."""
# This is based on the info at:
# https://janakiev.com/blog/framing-parametric-curves/
tangents: Dict[Node, Vec] = {}
all_nodes: Set[Node] = set()
for node in nodes:
if node.prev is node.next is None:
continue
node_prev = node.prev if node.prev is not None else node
node_next = node.next if node.next is not None else node
tangents[node] = (node_next.pos - node_prev.pos).norm()
all_nodes.add(node)
while all_nodes:
node1 = all_nodes.pop()
node1 = node1.find_start()
tanj1 = tangents[node1]
# Start with an arbitrary roll for the first orientation.
node1.orient = Matrix.from_angle(tanj1.to_angle())
while node1.next is not None:
node2 = node1.next
all_nodes.discard(node2)
tanj1 = tangents[node1]
tanj2 = tangents[node2]
b = Vec.cross(tanj1, tanj2)
if b.mag_sq() < 0.001:
node2.orient = node1.orient.copy()
else:
b = b.norm()
phi = math.acos(Vec.dot(tanj1, tanj2))
up = node1.orient.up() @ Matrix.axis_angle(
b, math.degrees(phi))
node2.orient = Matrix.from_basis(x=tanj2, z=up)
node1 = node2
