def reflect_across_2D_pts(edgepts):
x1 = edgepts[0][0]
y1 = edgepts[0][1]
x2 = edgepts[1][0]
y2 = edgepts[1][1]
dx = (x1 - x2)
if dx == 0: #Edge is a vertical line
shift = np.array([[1, 0, 0, -x1], [0, 1, 0, 0], [0, 0, 1, 0],
[0, 0, 0, 1]])
shift2 = np.array([[1, 0, 0, x1], [0, 1, 0, 0], [0, 0, 1, 0],
[0, 0, 0, 1]])
reflect = np.array([[-1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0],
[0, 0, 0, 1]])
r = np.dot(shift2, np.dot(reflect, shift))
return r
m = (y1 - y2) / dx
n = 1 + m * m
b = y1 - (m * x1)
a = m * -1
d = 1 + (m * m)
#Product of two opposite shifts of b in the y direction and a reflection across y = mx
shift = np.array([[1, 0, 0, 0], [0, 1, 0, -b], [0, 0, 1, 0], [0, 0, 0, 1]])
shift2 = np.array([[1, 0, 0, 0], [0, 1, 0, b], [0, 0, 1, 0], [0, 0, 0, 1]])
reflec = np.array([[1 - 2 * (a * a) / n, -2 * a / n, 0, 0],
[-2 * a / n, 1 - 2 / n, 0, 0], [0, 0, 1, 0],
[0, 0, 0, 1]])
return np.dot(shift2, np.dot(reflec, shift))
def transform(self, scale=1, angle=0, origin=(0, 0)):
r = np.array([[np.cos(angle), -np.sin(angle)],
[np.sin(angle), np.cos(angle)]]) * scale
o = np.array([origin] * len(self.pts_2D))
pts = np.transpose(np.dot(r, np.transpose(np.array(self.pts_2D)))) + o
self.pts_2D = [tuple(x) for x in np.rows(pts)]
for (i, d) in enumerate(self.decorations):
o = np.array([origin] * len(d[0]))
pts = np.transpose(np.dot(r, np.transpose(np.array(d[0])))) + o
self.decorations[i] = ([tuple(x) for x in np.rows(pts)], d[1])
def get_2D_decorations(self):
if self.transform_2D is not None:
edges = []
for i, e in enumerate(self.decorations):
if e[1] == "hole":
for j in range(len(e[0])):
name = self.name + ".d%d.e%d" % (i, j)
pt1 = np.dot(self.transform_2D, np.array(list(e[0][j - 1]) + [0, 1]))[0:2]
pt2 = np.dot(self.transform_2D, np.array(list(e[0][j]) + [0, 1]))[0:2]
# XXX use EdgeType appropriately
edges.append([name, pt1, pt2, 1])
else:
name = self.name + ".d%d" % i
pt1 = np.dot(self.transform_2D, np.array(list(e[0][0]) + [0, 1]))[0:2]
pt2 = np.dot(self.transform_2D, np.array(list(e[0][1]) + [0, 1]))[0:2]
edges.append([name, pt1, pt2, e[1]])
return edges
return []
def place_faces(self, face, edge_from, transform_2D, placed=None, allow_overlap=False):
"""Recursively adds faces to the 2D drawing.
Args:
face: the current face being placed
edge_from: the edge by which to attach the current face
transform_2D: A tranformation matrix to move the face into its position in 2D space
placed: dictionary containing metadata about previously placed entities
allow_overlap: Whether or not to allow two face to be placed on top of each other
"""
if placed is not None and face in placed['faces']:
#This face has already been placed, do not place again
return
if placed is None:
#No faces have been placed yet, initialize data structures
placed = {'faces': [], 'edges': {}, 'overlapping': []}
check_for_overlap = not allow_overlap
else:
#Overlap checking is handled only in top level call
check_for_overlap = False
"""
Placing faces involves the notion of "pretransformed" and "transformed" values.
Pretransformation moves the edge a face is being connected by to the x axis,
and can be thought of as a face's relative position to its neighbor.
Transformation moves a face to its absolute position in 2D space.
"""
if edge_from is not None:
#Align connected edges
pretransform_matrix = face.pre_transform(edge_from)
else:
#Place edge as is
pretransform_matrix = np.eye(4)
transform_matrix = np.dot(transform_2D, pretransform_matrix)
#4D pts are the homogenous coordinates of the face i.e. [x,y,z,1]
pretransformed_pts_4D = np.dot(pretransform_matrix, face.pts_4D)
transfromed_pts_4D = np.dot(transform_matrix, face.pts_4D)
pretransformed_pts_2D = pretransformed_pts_4D[0:2,:]
#Numerical values for the coordinates are required for placement
transfromed_pts_2D = eval_equation(transfromed_pts_4D[0:2, :])
if not self.add_face(transfromed_pts_2D):
#If face cannot be placed without collisions, attempt to reflect it
reflection_matrix = np.array([[1, 0, 0, 0],
[0, -1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
#Recompute pretransform and transform with rotation
pretransform_matrix = np.dot(reflection_matrix, pretransform_matrix)
transform_matrix = np.dot(transform_2D, pretransform_matrix)
pretransformed_pts_4D = np.dot(pretransform_matrix, face.pts_4D)
transfromed_pts_4D = np.dot(transform_matrix, face.pts_4D)
pretransformed_pts_2D = pretransformed_pts_4D[0:2,:]
transfromed_pts_2D = eval_equation(transfromed_pts_4D[0:2, :])
if not self.add_face(transfromed_pts_2D) and not allow_overlap:
#Face was not able to be placed connected to this edge
#Keep track of face and hope it gets placed elsewhere
#TODO: Try connecting along other edges or undoing previous placements?
placed['overlapping'].append(face)
return
#Face is being placed
placed['faces'].append(face)
if face in placed['overlapping']:
placed['overlapping'].remove(face)
face.transform_2D = transform_matrix
#Will this break if a face has to be flipped?
## find out how to transform the decoration. ##
for e in face.get_2D_decorations():
self.edges[e[0]] = DrawingEdge(e[0], [eval_equation(x) for x in e[1]],
[eval_equation(x) for x in e[2]], EdgeType(e[3]))
## edges here is a dictionary, the key is decoration edge name. e is nested list and its first element is the edge name. ##
#Place each edge
for (i, edge) in enumerate(face.edges):
#HACK: Do not place temporary edges
if edge is None or edge.name[:4] == "temp":
continue
#Get the endpoints of the edge
edge_pts_2D = (transfromed_pts_2D[:,i - 1],transfromed_pts_2D[:,i])
if edge.name in placed['edges'].keys():
edge_alias = placed['edges'][edge.name]
if diff_edge(edge_alias, edge_pts_2D,2):
#If the edge has already been placed in a different place, a cut must be made
#Create a new edge
self.edges['temp' + edge.name] = DrawingEdge('temp' + edge.name, edge_pts_2D[0], edge_pts_2D[1], Cut())
# Make old edge into a cut
self.edges[edge.name] = DrawingEdge(edge.name, edge_alias[0], edge_alias[1], Cut())
else:
#Add edge normally
if len(edge.faces) == 1:
edge_type = Cut()
else:
edge_type = Fold()
self.edges[edge.name] = DrawingEdge(edge.name, edge_pts_2D[0], edge_pts_2D[1], edge_type)
placed['edges'][edge.name] = edge_pts_2D
if len(edge.faces) <= 1:
# No other faces to be found, move on to next edge.
continue
if edge.is_tab():
# Don't follow faces off of a Tab
continue
#Compute new transform matrix for next face
rotation_matrix = rotate_x_to(pretransformed_pts_2D[:,i],pretransformed_pts_2D[:,i-1])
origin_matrix = move_origin_to(pretransformed_pts_2D[:,i-1])
next_transfrom_2D = np.dot(transform_2D,np.dot(origin_matrix,np.dot(rotation_matrix,np.eye(4))))
#Place faces connected to edge
for(f,a) in edge.faces.iteritems():
self.place_faces(f, edge, next_transfrom_2D, placed)
if check_for_overlap and len(placed['overlapping']):
#Placement has finished, but some edges are still unplaced
raise Exception('One or more faces could not be placed without overlap!')
def stl_write(faces, filename, thickness=0):
"""
Writes a graph object represented by faces to an STL file.
Args:
faces (list): list of faces that compose the object.
filename (str): filename to write STL to.
thickness (int or float): thickness of each face to draw.
"""
import triangle
shape = None
shells = []
triangles = []
for f in faces:
r = f[0]
# print ("the tramsform function is ",r)
# if r is None:
# continue
# if r is None: #No transform
# r = np.eye(4)
A = f[1]
facets = []
B = triangle.triangulate(A, opts='p')
if not 'triangles' in B:
print "No triangles in " + f[2]
continue
if thickness:
for t in [
np.transpose(
np.array([
list(B['vertices'][x]) + [0, 1]
for x in (face[0], face[1], face[2])
])) for face in B['triangles']
]:
facets.extend(
[np.dot(r, x) for x in inflate(t, thickness=thickness)])
for t in [
np.transpose(
np.array([
list(A['vertices'][x]) + [0, 1]
for x in (edge[0], edge[1])
])) for edge in A['segments']
]:
facets.extend([
np.dot(r, x)
for x in inflate(t, thickness=thickness, edges=True)
])
else:
for t in [
np.transpose(
np.array([
list(B['vertices'][x]) + [0, 1]
for x in (face[0], face[1], face[2])
])) for face in B['triangles']
]:
#print "Here",r,t
facets.append(np.dot(r, t))
triangles.extend(facets)
if thickness:
FREECADPATH = '/usr/lib64/freecad/lib'
import sys
sys.path.append(FREECADPATH)
import Part
meshes = []
for f in (np.transpose(t[0:3, :]) for t in facets):
try:
meshes.append(
Part.Face(
Part.Wire([
Part.makeLine(tuple(f[x]), tuple(f[x - 1]))
for x in range(3)
])))
except RuntimeError:
print "Skipping face: " + repr(f)
shell = Part.makeShell(meshes)
shells.append(shell)
if shape is None:
shape = shell
else:
shape = shape.fuse(shell)
if shape:
with open("freecad" + filename, 'wb') as fp:
shape.exportStl("freecad" + filename)
from stlwriter import Binary_STL_Writer
faces = triangles
with open(filename, 'wb') as fp:
writer = Binary_STL_Writer(fp)
writer.add_faces(faces)
writer.close()
def get_3D_normal(self):
if self.transform_3D is not None:
o = np.dot(self.transform_3D, np.array([0, 0, 0, 1]))
z = np.dot(self.transform_3D, np.array([0, 0, 1, 1]))
return (z - o)[0:3, :]
def get_3D_com(self):
if self.transform_3D is not None:
return np.dot(self.transform_3D, self.com_4D)[0:3, :]
def get_3D_coords(self):
if self.transform_3D is not None:
return np.dot(self.transform_3D, self.pts_4D)[0:3, :]
def get_2D_com(self):
if self.transform_2D is not None:
return np.dot(self.transform_2D, self.com_4D)[0:2, :]
def get_2D_coords(self):
if self.transform_2D is not None:
return np.dot(self.transform_2D, self.pts_4D)[0:2, :]
def place(self, edge_from, transform_2D, transform_3D, placed=None):
if self.transform_2D is not None and self.transform_3D is not None and placed is not None and self in \
placed['faces']:
# TODO : verify that it connects appropriately along alternate path
# print "Repeated face : " + self.name
return
if placed is None: # Replacing the entire component
placed = {'faces': []} ## create a dictionary: placed, the key is 'faces'.
## Face is being placed into the list of key:'faces'. placed={'faces':[face1,face2,...,facen]} ##
placed['faces'].append(self)
if edge_from is not None:
r = self.pre_transform(edge_from)
else:
r = np.eye(4) ## create a identity unit matrix. ##
self.transform_2D = np.dot(transform_2D, r)
self.transform_3D = np.dot(transform_3D, r)
pts_2D = np.dot(r, self.pts_4D)[0:2, :] ##using numpy, 0-2 rows and all columns. ##
coords_2D = self.get_2D_coords()
coords_3D = self.get_3D_coords()
for (i, e) in enumerate(self.edges):
# XXX hack: don't follow small edges
if e is None or e.is_tab(): ## do nothing to edges which is tabbed or without connection? ##
continue
el = self.edge_length(i) ##return the length of edge by edge index i. ##
try:
if el <= 0.01:
continue
except TypeError:
# print 'sympyicized variable detected - ignoring edge length check'
pass
da = e.faces[self] ## e is an edge? ##
if da[1]:
e.place((coords_2D[:, i - 1], coords_2D[:, i]), (coords_3D[:, i - 1], coords_3D[:, i]))
else:
e.place((coords_2D[:, i], coords_2D[:, i - 1]), (coords_3D[:, i], coords_3D[:, i - 1]))
if len(e.faces) <= 1: ## how !!!!! ##
# No other faces to be found, move on to next edge.
continue
pt1 = pts_2D[:, i - 1]
pt2 = pts_2D[:, i]
# TODO : Only skip self and the face that you came from to verify multi-connected edges
# XXX : Assumes both faces have opposite edge orientation
# Only works for non-hyper edges -- need to store edge orientation info for a +/- da
for (f, a) in e.faces.iteritems():
if a[1] ^ da[1]:
# opposite orientation
pta, ptb = pt1, pt2
else:
# same orientation
pta, ptb = pt2, pt1
x = rotate_x_to(ptb, pta)
r2d = np.eye(4)
r2d = np.dot(x, r2d)
r2d = np.dot(move_origin_to(pta), r2d)
r3d = rotate_x(np.deg2rad(a[0] + da[0]))
r3d = np.dot(x, r3d)
r3d = np.dot(move_origin_to(pta), r3d)
f.place(e, np.dot(transform_2D, r2d), np.dot(transform_3D, r3d), placed=placed)
def pre_transform(self, edge):
index = self.edges.index(edge)
# print edge
# print self.edgeCoords(index)
return np.dot(rotate_onto_x(*self.edge_coords(index)), move_to_origin(self.pts_2D[index]))