def calc_correction_vector_tip(pt_new, base_pts):
"""Computing correction vector to meet the distance threshold.
return vector P-P_c (figure below).
.. image:: ../images/vertex_correction_to_top_connection.png
:scale: 80 %
:align: center
Parameters
----------
pt_new : [type]
[description]
base_pts : list of three points
contact base points for the base bars
"""
assert len(base_pts) == 3
vec_x = normalize_vector(vector_from_points(base_pts[0], base_pts[1]))
vec_y = normalize_vector(vector_from_points(base_pts[0], base_pts[2]))
vec_z = normalize_vector(cross_vectors(vec_x, vec_y))
pl_test = (base_pts[0], vec_z)
dist_p = distance_point_plane(pt_new, pl_test)
pt_proj = project_point_plane(pt_new, pl_test)
if dist_p < NODE_CORRECTION_TOP_DISTANCE:
vec_m = scale_vector(normalize_vector(vector_from_points(pt_proj, pt_new)), NODE_CORRECTION_TOP_DISTANCE)
pt_n = add_vectors(pt_proj, vec_m)
else:
pt_n = None
return pt_n
def board_setup(self):
for my_layer in range(layer_no):
if my_layer % 2 == 0:
my_frame = self.origin_fr
my_grid = self.ceiling_grids[0]
else:
my_frame = self.sec_fr
my_grid = self.ceiling_grids[1][0]
my_dir1 = normalize_vector(my_frame[1])
my_dir2 = normalize_vector(my_frame[2])
# we have to separate i/board_code because of possible exceptions in the centre
board_code = 0
for i, dist in enumerate(my_grid):
my_board = self.timberboards[my_layer][board_code]
# for the inner parts
if self.skipping and 0 < my_layer < self.layer_no - 1 and my_layer%2 == 0 and \
0 < i < len(my_grid) - 1 and i%2 != 0:
continue
# build the three vectors with which we later find he centre point
my_vec1 = scale_vector(my_dir1, my_board.length / 2)
my_vec2 = scale_vector(my_dir2, dist)
my_vec3 = Vector(0, 0, my_board.z_drop - my_board.height / 2)
my_centre = self.origin_pt + my_vec1 + my_vec2 + my_vec3
my_board.centre_point = my_centre
my_board.drop_point = my_centre + Vector(
0, 0, my_board.height / 2)
my_board.length_vector = normalize_vector(my_vec1)
my_board.width_vector = normalize_vector(my_vec2)
my_board.box_update()
board_code += 1
def find_points_extreme(pts_all, pts_init):
"""update a bar's axis end point based on all the contact projected points specified in `pts_all`
Parameters
----------
pts_all : list of points
all the contact points projected on the axis (specified by pts_init)
pts_init : list of two points
the initial axis end points
Returns
-------
[type]
[description]
"""
vec_init = normalize_vector(vector_from_points(*pts_init))
# * find the pair of points with maximal distance
sorted_pt_pairs = sorted(combinations(pts_all, 2), key=lambda pt_pair: distance_point_point(*pt_pair))
pts_draw = sorted_pt_pairs[-1]
vec_new = normalize_vector(vector_from_points(*pts_draw))
if angle_vectors(vec_init, vec_new, deg=True) > 90:
# angle can only be 0 or 180
pts_draw = pts_draw[::-1]
# ext_len = 30
# pts_draw = (add_vectors(pts_draw[0], scale_vector(normalize_vector(vector_from_points(pts_draw[1], pts_draw[0])), ext_len)), add_vectors(pts_draw[1], scale_vector(normalize_vector(vector_from_points(pts_draw[0], pts_draw[1])), ext_len)))
return pts_draw
def set_wait_time_on_sharp_corners(print_organizer, threshold=0.5 * math.pi, wait_time=0.3):
"""
Sets a wait time at the sharp corners of the path, based on the angle threshold.
Parameters
----------
print_organizer: :class:`compas_slicer.print_organization.BasePrintOrganizer`
threshold: float
angle_threshold
wait_time: float
Time in seconds to introduce to add as a wait time
"""
number_of_wait_points = 0
for printpoint, i, j, k in print_organizer.printpoints_indices_iterator():
neighbors = print_organizer.get_printpoint_neighboring_items('layer_%d' % i, 'path_%d' % j, k)
prev_ppt = neighbors[0]
next_ppt = neighbors[1]
if prev_ppt and next_ppt:
v_to_prev = normalize_vector(Vector.from_start_end(printpoint.pt, prev_ppt.pt))
v_to_next = normalize_vector(Vector.from_start_end(printpoint.pt, next_ppt.pt))
a = abs(Vector(*v_to_prev).angle(v_to_next))
if a < threshold:
printpoint.wait_time = wait_time
printpoint.blend_radius = 0.0 # 0.0 blend radius for points where the robot will wait
number_of_wait_points += 1
logger.info('Added wait times for %d points' % number_of_wait_points)
def from_basis_vectors(cls, xaxis, yaxis):
"""Creates a ``Rotation`` from basis vectors (= orthonormal vectors).
Parameters
----------
xaxis : compas.geometry.Vector or list
The x-axis of the frame.
yaxis : compas.geometry.Vector or list
The y-axis of the frame.
Examples
--------
>>> xaxis = [0.68, 0.68, 0.27]
>>> yaxis = [-0.67, 0.73, -0.15]
>>> R = Rotation.from_basis_vectors(xaxis, yaxis)
"""
xaxis = normalize_vector(list(xaxis))
yaxis = normalize_vector(list(yaxis))
zaxis = cross_vectors(xaxis, yaxis)
yaxis = cross_vectors(zaxis, xaxis)
matrix = [[xaxis[0], yaxis[0], zaxis[0], 0],
[xaxis[1], yaxis[1], zaxis[1], 0],
[xaxis[2], yaxis[2], zaxis[2], 0], [0, 0, 0, 1]]
R = cls()
R.matrix = matrix
return R
def orthonormalize_axes(xaxis, yaxis):
"""Corrects xaxis and yaxis to be unit vectors and orthonormal.
Parameters
----------
xaxis: :class:`Vector` or list of float
yaxis: :class:`Vector` or list of float
Returns
-------
tuple: (xaxis, yaxis)
The corrected axes.
Raises
------
ValueError: If xaxis and yaxis cannot span a plane.
Examples
--------
>>> xaxis = [1, 4, 5]
>>> yaxis = [1, 0, -2]
>>> xaxis, yaxis = orthonormalize_axes(xaxis, yaxis)
>>> allclose(xaxis, [0.1543, 0.6172, 0.7715], tol=0.001)
True
>>> allclose(yaxis, [0.6929, 0.4891, -0.5298], tol=0.001)
True
"""
xaxis = normalize_vector(xaxis)
yaxis = normalize_vector(yaxis)
zaxis = cross_vectors(xaxis, yaxis)
if not norm_vector(zaxis):
raise ValueError("Xaxis and yaxis cannot span a plane.")
yaxis = cross_vectors(normalize_vector(zaxis), xaxis)
return xaxis, yaxis
def match_paths_orientations(pts, reference_points, is_closed):
"""
Check if new curve has same direction as prev curve, otherwise reverse.
Parameters
----------
pts: list, :class: 'compas.geometry.Point'. The list of points whose direction we are fixing.
reference_points: list, :class: 'compas.geometry.Point'. [p1, p2] Two reference points.
is_closed : bool, Determines if the path is closed or open
"""
if len(pts) > 2 and len(reference_points) > 2:
v1 = normalize_vector(subtract_vectors(pts[0], pts[2]))
v2 = normalize_vector(
subtract_vectors(reference_points[0], reference_points[2]))
else:
v1 = normalize_vector(subtract_vectors(pts[0], pts[1]))
v2 = normalize_vector(
subtract_vectors(reference_points[0], reference_points[1]))
if dot_vectors(v1, v2) < 0:
if is_closed:
items = deque(reversed(pts))
items.rotate(1) # bring last point again in the front
pts = list(items)
else:
pts.reverse()
return pts
def board_geometry_setup(self):
for my_layer in range(layer_no):
if my_layer % 2 == 0:
my_frame = self.origin_fr
my_grid = self.ceiling_grids[0][0]
else:
my_frame = self.sec_fr
my_grid = self.ceiling_grids[1][0]
my_dir1 = normalize_vector(my_frame[1])
my_dir2 = normalize_vector(my_frame[2])
# we have to separate i/board_code because of possible exceptions in the centre
board_code = 0
for my_board in self.timberboards[my_layer]:
dist = my_board.grid_position
# build the three vectors with which we later find he centre point
# one advanced case
if my_board.location == "high":
my_vec1 = scale_vector(my_dir1, primary_length - my_board.length / 2)
# all other cases
else:
my_vec1 = scale_vector(my_dir1, my_board.length / 2)
my_vec2 = scale_vector(my_dir2, dist)
my_vec3 = Vector(0, 0, my_board.z_drop - my_board.height / 2)
my_centre = self.origin_pt + my_vec1 + my_vec2 + my_vec3
my_board.centre_point = my_centre
my_board.drop_point = my_centre + Vector(0, 0, my_board.height / 2)
my_board.length_vector = normalize_vector(my_vec1)
my_board.width_vector = normalize_vector(my_vec2)
my_board.box_update()
board_code += 1
def draw_circle(circle, color=None, n=100):
(center, normal), radius = circle
cx, cy, cz = center
a, b, c = normal
u = -1.0, 0.0, a
v = 0.0, -1.0, b
w = cross_vectors(u, v)
uvw = [normalize_vector(u), normalize_vector(v), normalize_vector(w)]
color = color if color else (1.0, 0.0, 0.0, 0.5)
sector = 2 * pi / n
glColor4f(*color)
glBegin(GL_POLYGON)
for i in range(n):
a = i * sector
x = radius * cos(a)
y = radius * sin(a)
z = 0
x, y, z = global_coords_numpy(center, uvw, [[x, y, z]]).tolist()[0]
glVertex3f(x, y, z)
glEnd()
glBegin(GL_POLYGON)
for i in range(n):
a = -i * sector
x = radius * cos(a)
y = radius * sin(a)
z = 0
x, y, z = global_coords_numpy(center, uvw, [[x, y, z]]).tolist()[0]
glVertex3f(x, y, z)
glEnd()
def matrix_from_basis_vectors(xaxis, yaxis):
"""Creates a rotation matrix from basis vectors (= orthonormal vectors).
Parameters
----------
xaxis : list of float
The x-axis of the frame.
yaxis : list of float
The y-axis of the frame.
Examples
--------
>>> xaxis = [0.68, 0.68, 0.27]
>>> yaxis = [-0.67, 0.73, -0.15]
>>> R = matrix_from_basis_vectors(xaxis, yaxis)
"""
xaxis = normalize_vector(list(xaxis))
yaxis = normalize_vector(list(yaxis))
zaxis = cross_vectors(xaxis, yaxis)
yaxis = cross_vectors(zaxis, xaxis) # correction
R = identity_matrix(4)
R[0][0], R[1][0], R[2][0] = xaxis
R[0][1], R[1][1], R[2][1] = yaxis
R[0][2], R[1][2], R[2][2] = zaxis
return R
def from_basis_vectors(cls, xaxis, yaxis):
"""Construct a rotation transformation from basis vectors (= orthonormal vectors).
Parameters
----------
xaxis : [float, float, float] | :class:`compas.geometry.Vector`
The x-axis of the frame.
yaxis : [float, float, float] | :class:`compas.geometry.Vector`
The y-axis of the frame.
Returns
-------
:class:`compas.geometry.Rotation`
Examples
--------
>>> xaxis = [0.68, 0.68, 0.27]
>>> yaxis = [-0.67, 0.73, -0.15]
>>> R = Rotation.from_basis_vectors(xaxis, yaxis)
"""
xaxis = normalize_vector(list(xaxis))
yaxis = normalize_vector(list(yaxis))
zaxis = cross_vectors(xaxis, yaxis)
yaxis = cross_vectors(zaxis, xaxis)
matrix = [[xaxis[0], yaxis[0], zaxis[0], 0],
[xaxis[1], yaxis[1], zaxis[1], 0],
[xaxis[2], yaxis[2], zaxis[2], 0], [0, 0, 0, 1]]
R = cls()
R.matrix = matrix
return R
def from_basis_vectors(cls, xaxis, yaxis):
"""Creates a ``Rotation`` from basis vectors (= orthonormal vectors).
Parameters
----------
xaxis : :class:`Vector`
The x-axis of the frame.
yaxis : :class:`Vector`
The y-axis of the frame.
Examples
--------
>>> xaxis = [0.68, 0.68, 0.27]
>>> yaxis = [-0.67, 0.73, -0.15]
>>> R = Rotation.from_basis_vectors(xaxis, yaxis)
"""
xaxis = normalize_vector(list(xaxis))
yaxis = normalize_vector(list(yaxis))
zaxis = cross_vectors(xaxis, yaxis)
yaxis = cross_vectors(zaxis, xaxis) # correction
R = cls()
R.matrix[0][0], R.matrix[1][0], R.matrix[2][0] = xaxis
R.matrix[0][1], R.matrix[1][1], R.matrix[2][1] = yaxis
R.matrix[0][2], R.matrix[1][2], R.matrix[2][2] = zaxis
return R
def separate(self, dst, boids, mxf=0.02, mxs=0.02):
count = 0
sum_vec = [0, 0, 0]
tol = 1e-6
for boid in boids:
d = cg.distance_point_point(self.pos, boid.pos)
print('distance is {}'.format(d))
if d > tol and d < dst:
dif = subtract_vectors(self.pos, boid.pos)
dif = cg.normalize_vector(cg.scale_vector(dif, 1/d))
sum_vec = cg.add_vectors(dif, sum_vec)
count += 1
if count > 0:
sum_vec = cg.normalize_vector(cg.scale_vector(sum_vec,
1/count)
)
sum_vec = cg.scale_vector(sum_vec, mxs)
# Reynold's steering formula
steer = subtract_vectors(sum_vec, self.vel)
steer = ut.limit_vector(steer, mxf)
return steer
return sum_vec
def _cross_edges(edge1, edge2):
a, b = edge1
c, d = edge2
edge1_vec = normalize_vector(subtract_vectors(b, a))
edge2_vec = normalize_vector(subtract_vectors(d, c))
cross = cross_vectors(edge1_vec, edge2_vec)
return cross
def calc_correction_vector(b_struct, pt_new, bar_pair):
"""Computing correction vector to meet the angle threshold.
return vector P-P_c (figure below).
.. image:: ../images/vertex_correction_to_base.png
:scale: 80 %
:align: center
Parameters
----------
b_struct : [type]
[description]
pt_new : [type]
[description]
bar_pair : list of two int
BarS vertex key, representing two bars
Returns
-------
list of two points
return None if feasible (bigger than the angle threshold), otherwise return the line connecting pt_int and modified pt
"""
bar1 = b_struct.vertex[bar_pair[0]]
bar2 = b_struct.vertex[bar_pair[1]]
pt_int = intersection_bars_base(b_struct, bar_pair)
vec_x = normalize_vector(vector_from_points(bar1["axis_endpoints"][0], bar1["axis_endpoints"][1]))
vec_y = normalize_vector(vector_from_points(bar2["axis_endpoints"][0], bar2["axis_endpoints"][1]))
# contact vector
vec_z = normalize_vector(cross_vectors(vec_x, vec_y))
# test plane
pl_test = (pt_int, vec_z)
vec_m = correct_angle(pt_new, pt_int, pl_test)
return vec_m
def matrix_from_shear(angle, direction, point, normal):
"""Constructs a shear matrix by an angle along the direction vector on the
shear plane (defined by point and normal).
Parameters
----------
angle : float
The angle in radians.
direction : list of float
The direction vector as list of 3 numbers.
It must be orthogonal to the normal vector.
point : list of float
The point of the shear plane as list of 3 numbers.
normal : list of float
The normal of the shear plane as list of 3 numbers.
Raises
------
ValueError
If direction and normal are not orthogonal.
Notes
-----
A point P is transformed by the shear matrix into P" such that
the vector P-P" is parallel to the direction vector and its extent is
given by the angle of P-P'-P", where P' is the orthogonal projection
of P onto the shear plane (defined by point and normal).
Examples
--------
>>> angle = 0.1
>>> direction = [0.1, 0.2, 0.3]
>>> point = [4, 3, 1]
>>> normal = cross_vectors(direction, [1, 0.3, -0.1])
>>> S = matrix_from_shear(angle, direction, point, normal)
"""
fabs = math.fabs
normal = normalize_vector(normal)
direction = normalize_vector(direction)
if fabs(dot_vectors(normal, direction)) > _EPS:
raise ValueError('Direction and normal vectors are not orthogonal')
angle = math.tan(angle)
M = identity_matrix(4)
for j in range(3):
for i in range(3):
M[i][j] += angle * direction[i] * normal[j]
M[0][3], M[1][3], M[2][3] = scale_vector(
direction, -angle * dot_vectors(point, normal))
return M
def transformed_stress_vector_fields(mesh, vector_fields, stress_type,
ref_vector):
"""
Rescales a vector field based on a plane stress transformation.
"""
vf1, vf2 = vector_fields
# TODO: mapping is not robust! depends on naming convention
stress_components = {
"bending": {
"names": ["mx", "my", "mxy"],
"ps": "m_1"
},
"axial": {
"names": ["nx", "ny", "nxy"],
"ps": "n_1"
}
}
stress_names = stress_components[stress_type]["names"]
vf_ps = mesh.vector_field(stress_components[stress_type]["ps"])
vf1_transf = VectorField()
vf2_transf = VectorField()
for fkey in mesh.faces():
# query stress components
sx, sy, sxy = mesh.face_attributes(fkey, names=stress_names)
# generate principal stresses and angles
s1a, s1 = principal_stresses_and_angles(sx, sy, sxy)
s1, angle1 = s1a
vector_ps = vf_ps[fkey]
vector1 = vf1[fkey]
vector2 = vf2[fkey]
# compute delta between reference vector and principal bending vector
# TODO: will take m1 as reference. does this always hold?
delta = angle1 - angle_vectors(vector_ps, ref_vector)
# add delta to angles of the vector field to transform
theta = delta + angle_vectors(vector1, ref_vector)
# transform stresses - this becomes the scale of the vectors
s1, s2, _ = transformed_stresses(sx, sy, sxy, theta)
vf1_transf.add_vector(fkey, scale_vector(normalize_vector(vector1),
s1))
vf2_transf.add_vector(fkey, scale_vector(normalize_vector(vector2),
s2))
return vf1_transf, vf2_transf
def from_basis_vectors(cls, xaxis, yaxis):
"""Create rotation matrix from basis vectors (= orthonormal vectors).
"""
xaxis = normalize_vector(list(xaxis))
yaxis = normalize_vector(list(yaxis))
zaxis = cross_vectors(xaxis, yaxis)
yaxis = cross_vectors(zaxis, xaxis) # slight correction
rotation = cls()
rotation.matrix[0][0], rotation.matrix[1][0], rotation.matrix[2][0] = xaxis
rotation.matrix[0][1], rotation.matrix[1][1], rotation.matrix[2][1] = yaxis
rotation.matrix[0][2], rotation.matrix[1][2], rotation.matrix[2][2] = zaxis
return rotation
def get_normal_of_path_on_xy_plane(k, point, path, mesh):
"""
Finds the normal of the curve that lies on the xy plane at the point with index k
Parameters
----------
k: int, index of the point
point: :class: 'compas.geometry.Point'
path: :class: 'compas_slicer.geometry.Path'
mesh: :class: 'compas.datastructures.Mesh'
Returns
----------
:class: 'compas.geometry.Vector'
"""
# find mesh normal is not really needed in the 2D case of planar slicer
# instead we only need the normal of the curve based on the neighboring pts
if (0 < k < len(path.points) - 1) or path.is_closed:
prev_pt = path.points[k - 1]
next_pt = path.points[(k + 1) % len(path.points)]
v1 = np.array(normalize_vector(Vector.from_start_end(prev_pt, point)))
v2 = np.array(normalize_vector(Vector.from_start_end(point, next_pt)))
v = (v1 + v2) * 0.5
normal = [-v[1], v[0],
v[2]] # rotate 90 degrees COUNTER-clockwise on the xy plane
else:
if k == 0:
next_pt = path.points[k + 1]
v = normalize_vector(Vector.from_start_end(point, next_pt))
normal = [-v[1], v[0], v[2]
] # rotate 90 degrees COUNTER-clockwise on the xy plane
else: # k == len(path.points)-1:
prev_pt = path.points[k - 1]
v = normalize_vector(Vector.from_start_end(point, prev_pt))
normal = [v[1], -v[0],
v[2]] # rotate 90 degrees clockwise on the xy plane
if length_vector(normal) == 0:
# When the neighboring elements happen to cancel out, then search for the true normal,
# and project it on the xy plane for consistency
normal = get_closest_mesh_normal_to_pt(mesh, point)
normal = [normal[0], normal[1], 0]
normal = normalize_vector(normal)
normal = Vector(*list(normal))
return normal
def random_vector():
return scale_vector(
normalize_vector([
random.choice([-1, +1]) * random.random(),
random.choice([-1, +1]) * random.random(),
random.choice([-1, +1]) * random.random(),
]), random.random())
def vertex_normal(self, vertex):
"""Return the normal vector at the vertex as the weighted average of the
normals of the neighboring faces.
Parameters
----------
key : int
The identifier of the vertex.
Returns
-------
list
The components of the normal vector.
"""
if not self.is_vertex_on_boundary(vertex):
return
halffaces = []
for halfface in self.vertex_halffaces(vertex):
if self.is_halfface_on_boundary(halfface):
halffaces.append(halfface)
vectors = [
self.face_normal(halfface, False) for halfface in halffaces
if halfface is not None
]
return normalize_vector(centroid_points(vectors))
def matrix_from_parallel_projection(point, normal, direction):
"""Returns an parallel projection matrix to project onto a plane defined by
point, normal and direction.
Parameters
----------
point : list of float
Base point of the plane.
normal : list of float
Normal vector of the plane.
direction : list of float
Direction of the projection.
Examples
--------
>>> point = [0, 0, 0]
>>> normal = [0, 0, 1]
>>> direction = [1, 1, 1]
>>> P = matrix_from_parallel_projection(point, normal, direction)
"""
T = identity_matrix(4)
normal = normalize_vector(normal)
scale = dot_vectors(direction, normal)
for j in range(3):
for i in range(3):
T[i][j] -= direction[i] * normal[j] / scale
T[0][3], T[1][3], T[2][3] = scale_vector(
direction,
dot_vectors(point, normal) / scale)
return T
def test_axis_and_angle():
axis1 = normalize_vector([-0.043, -0.254, 0.617])
angle1 = 0.1
R = Rotation.from_axis_and_angle(axis1, angle1)
axis2, angle2 = R.axis_and_angle
assert allclose(axis1, axis2)
assert allclose([angle1], [angle2])
def matrix_from_orthogonal_projection(point, normal):
"""Returns an orthogonal projection matrix to project onto a plane defined
by point and normal.
Parameters
----------
point : list of float
Base point of the plane.
normal : list of float
Normal vector of the plane.
Examples
--------
>>> point = [0, 0, 0]
>>> normal = [0, 0, 1]
>>> P = matrix_from_orthogonal_projection(point, normal)
"""
T = identity_matrix(4)
normal = normalize_vector(normal)
for j in range(3):
for i in range(3):
T[i][j] -= normal[i] * normal[j] # outer_product
T[0][3], T[1][3], T[2][3] = scale_vector(normal,
dot_vectors(point, normal))
return T
def _draw_arc(normal_1, normal_2, origin):
mid_pt = normalize_vector(add_vectors(normal_1, normal_2))
arc = Arc(Point3d(*[sum(axis) for axis in zip(normal_1, origin)]),
Point3d(*[sum(axis) for axis in zip(mid_pt, origin)]),
Point3d(*[sum(axis) for axis in zip(normal_2, origin)]))
arc_as_curve = ArcCurve(arc)
return arc_as_curve
def matrix_from_orthogonal_projection(plane):
"""Returns an orthogonal projection matrix to project onto a plane.
Parameters
----------
plane : [point, normal] | :class:`compas.geometry.Plane`
The plane to project onto.
Returns
-------
list[list[float]]
The 4x4 transformation matrix representing an orthogonal projection.
Examples
--------
>>> point = [0, 0, 0]
>>> normal = [0, 0, 1]
>>> plane = (point, normal)
>>> P = matrix_from_orthogonal_projection(plane)
"""
point, normal = plane
T = identity_matrix(4)
normal = normalize_vector(normal)
for j in range(3):
for i in range(3):
T[i][j] -= normal[i] * normal[j] # outer_product
T[0][3], T[1][3], T[2][3] = scale_vector(normal,
dot_vectors(point, normal))
return T
def test_axis_and_angle_from_matrix():
axis1 = normalize_vector([-0.043, -0.254, 0.617])
angle1 = 0.1
R = matrix_from_axis_and_angle(axis1, angle1)
axis2, angle2 = axis_and_angle_from_matrix(R)
assert allclose(axis1, axis2)
assert allclose([angle1], [angle2])
def polygon_normal_oriented(polygon, unitized=True):
"""Compute the oriented normal of any closed polygon (can be convex, concave or complex).
Parameters
----------
polygon : sequence
The XYZ coordinates of the vertices/corners of the polygon.
The vertices are assumed to be in order.
The polygon is assumed to be closed:
the first and last vertex in the sequence should not be the same.
Returns
-------
list
The weighted or unitized normal vector of the polygon.
"""
p = len(polygon)
assert p > 2, "At least three points required"
w = centroid_points(polygon)
normal_sum = (0, 0, 0)
for i in range(-1, len(polygon) - 1):
u = polygon[i]
v = polygon[i + 1]
uv = subtract_vectors(v, u)
vw = subtract_vectors(w, v)
normal = scale_vector(cross_vectors(uv, vw), 0.5)
normal_sum = add_vectors(normal_sum, normal)
if not unitized:
return normal_sum
return normalize_vector(normal_sum)
def edge_vector(self, u, v, unitized=True):
u_xyz = self.vertex_coordinates(u)
v_xyz = self.vertex_coordinates(v)
vector = subtract_vectors(v_xyz, u_xyz)
if unitized:
return normalize_vector(vector)
return vector
def matrix_from_parallel_projection(plane, direction):
"""Returns an parallel projection matrix to project onto a plane.
Parameters
----------
plane : compas.geometry.Plane or (point, normal)
The plane to project onto.
direction : list of float
Direction of the projection.
Examples
--------
>>> point = [0, 0, 0]
>>> normal = [0, 0, 1]
>>> plane = (point, normal)
>>> direction = [1, 1, 1]
>>> P = matrix_from_parallel_projection(plane, direction)
"""
point, normal = plane
T = identity_matrix(4)
normal = normalize_vector(normal)
scale = dot_vectors(direction, normal)
for j in range(3):
for i in range(3):
T[i][j] -= direction[i] * normal[j] / scale
T[0][3], T[1][3], T[2][3] = scale_vector(
direction,
dot_vectors(point, normal) / scale)
return T