def get_rotation_matrix_axis_angle(rot_axis, rot_angle, use_radians=True):
""" calculate rotation matrix for a normalized vector and an angle
see http://mathworld.wolfram.com/RotationMatrix.html
@type rot_axis: tuple(float)
@value rot_axis: the vector describes the rotation axis. Its length should
be 1.0 (normalized).
@type rot_angle: float
@value rot_angle: rotation angle (radiant)
@rtype: tuple(tuple(float))
@return: the rotation matrix (3x3)
"""
if not use_radians:
rot_angle *= math.pi / 180
sin = number(math.sin(rot_angle))
cos = number(math.cos(rot_angle))
return ((cos + rot_axis[0] * rot_axis[0] * (1 - cos),
rot_axis[0] * rot_axis[1] * (1 - cos) - rot_axis[2] * sin,
rot_axis[0] * rot_axis[2] * (1 - cos) + rot_axis[1] * sin),
(rot_axis[1] * rot_axis[0] * (1 - cos) + rot_axis[2] * sin,
cos + rot_axis[1] * rot_axis[1] * (1 - cos),
rot_axis[1] * rot_axis[2] * (1 - cos) - rot_axis[0] * sin),
(rot_axis[2] * rot_axis[0] * (1 - cos) - rot_axis[1] * sin,
rot_axis[2] * rot_axis[1] * (1 - cos) + rot_axis[0] * sin,
cos + rot_axis[2] * rot_axis[2] * (1 - cos)))
def move_camera_by_screen(self, x_move, y_move, max_model_shift):
""" move the camera acoording to a mouse movement
@type x_move: int
@value x_move: movement of the mouse along the x axis
@type y_move: int
@value y_move: movement of the mouse along the y axis
@type max_model_shift: float
@value max_model_shift: maximum shifting of the model view (e.g. for
x_move == screen width)
"""
factors_x, factors_y = self._get_axes_vectors()
width, height = self._get_screen_dimensions()
# relation of x/y movement to the respective screen dimension
win_x_rel = (-2 * x_move) / float(width) / math.sin(self.view["fovy"])
win_y_rel = (-2 * y_move) / float(height) / math.sin(self.view["fovy"])
# This code is completely arbitrarily based on trial-and-error for
# finding a nice movement speed for all distances.
# Anyone with a better approach should just fix this.
distance_vector = self.get("distance")
distance = float(sqrt(sum([dim**2 for dim in distance_vector])))
win_x_rel *= math.cos(win_x_rel / distance)**20
win_y_rel *= math.cos(win_y_rel / distance)**20
# update the model position that should be centered on the screen
old_center = self.view["center"]
new_center = []
for i in range(3):
new_center.append(old_center[i] + max_model_shift *
(number(win_x_rel) * factors_x[i] +
number(win_y_rel) * factors_y[i]))
self.view["center"] = tuple(new_center)
def get_support_grid_locations(minx,
maxx,
miny,
maxy,
dist_x,
dist_y,
offset_x=0.0,
offset_y=0.0,
adjustments_x=None,
adjustments_y=None):
""" calculate positions of a orthogonal grid of support bridges
@param minx: minimum x value of the target area
@param maxx: maximum x value of the target area
@param miny: minimum y value of the target area
@param maxy: maximum y value of the target area
@param dist_x: distance between two lines parallel to the y axis
@param dist_y: distance between two lines parallel to the x axis
@param adjustments_x: iterable of offsets to be added to each x position
@param adjustments_y: iterable of offsets to be added to each y position
"""
def get_lines(center, dist, min_value, max_value):
""" generate a list of positions starting from the middle going up and
and down
"""
if dist > 0:
lines = [center]
current = center
while current - dist > min_value:
current -= dist
lines.insert(0, current)
current = center
while current + dist < max_value:
current += dist
lines.append(current)
else:
lines = []
# remove lines that are out of range (e.g. due to a huge offset)
lines = [line for line in lines if min_value < line < max_value]
return lines
# convert all inputs to the type defined in "number"
dist_x = number(dist_x)
dist_y = number(dist_y)
offset_x = number(offset_x)
offset_y = number(offset_y)
center_x = (maxx + minx) / 2 + offset_x
center_y = (maxy + miny) / 2 + offset_y
lines_x = get_lines(center_x, dist_x, minx, maxx)
lines_y = get_lines(center_y, dist_y, miny, maxy)
# apply as many offsets from adjustments_x and adjustments_y as available
for value_list, adjustments in ((lines_x, adjustments_x), (lines_y,
adjustments_y)):
if adjustments:
for index, (current_value,
adjustment) in enumerate(zip(value_list, adjustments)):
value_list[index] = current_value + number(adjustment)
return lines_x, lines_y
def _get_axes_vectors(self):
"""calculate the model vectors along the screen's x and y axes"""
# The "up" vector defines, in what proportion each axis of the model is
# in line with the screen's y axis.
v_up = self.view["up"]
factors_y = (number(v_up[0]), number(v_up[1]), number(v_up[2]))
# Calculate the proportion of each model axis according to the x axis of
# the screen.
distv = self.view["distance"]
distv = pnormalized((distv[0], distv[1], distv[2]))
factors_x = pnormalized(pcross(distv, (v_up[0], v_up[1], v_up[2])))
return (factors_x, factors_y)
def get_absolute_limits(self, reference=None):
""" calculate the current absolute limits of the Bounds instance
@value reference: a reference object described by a tuple (or list) of
three item. These three values describe only the lower boundary of
this object (for the x, y and z axes). Each item must be a float
value. This argument is ignored for the boundary type "TYPE_CUSTOM".
@type reference: (tuple|list) of float
@returns: a tuple of two lists containg the low and high limits
@rvalue: tuple(list)
"""
# use the default reference if none was given
if reference is None:
reference = self.reference
# check if a reference is given (if necessary)
if self.bounds_type \
in (Bounds.TYPE_RELATIVE_MARGIN, Bounds.TYPE_FIXED_MARGIN):
if reference is None:
raise ValueError(
"any non-custom boundary definition requires a reference "
"object for calculating absolute limits")
else:
ref_low, ref_high = reference.get_absolute_limits()
low = [None] * 3
high = [None] * 3
# calculate the absolute limits
if self.bounds_type == Bounds.TYPE_RELATIVE_MARGIN:
for index in range(3):
dim_width = ref_high[index] - ref_low[index]
low[index] = ref_low[index] - self.bounds_low[index] * dim_width
high[index] = ref_high[
index] + self.bounds_high[index] * dim_width
elif self.bounds_type == Bounds.TYPE_FIXED_MARGIN:
for index in range(3):
low[index] = ref_low[index] - self.bounds_low[index]
high[index] = ref_high[index] + self.bounds_high[index]
elif self.bounds_type == Bounds.TYPE_CUSTOM:
for index in range(3):
low[index] = number(self.bounds_low[index])
high[index] = number(self.bounds_high[index])
else:
# this should not happen
raise NotImplementedError(
"the function 'get_absolute_limits' is currently not "
"implemented for the bounds_type '%s'" % str(self.bounds_type))
return Box3D(Point3D(low), Point3D(high))
def __init__(self, radius, location=None, height=None):
super().__init__()
if location is None:
location = (0, 0, 0)
if height is None:
height = 10
radius = number(radius)
self.height = number(height)
self.radius = radius
self.radiussq = radius**2
self.required_distance = 0
self.distance_radius = self.radius
self.distance_radiussq = self.distance_radius**2
self.shape = {}
self.location = location
self.moveto(self.location)
self.uuid = None
self.update_uuid()
def get_offset_polygons_incremental(self, offset, depth=20):
if offset == 0:
return [self]
if offset in self._cached_offset_polygons:
return self._cached_offset_polygons[offset]
def is_better_offset(previous_offset, alternative_offset):
return (((offset < alternative_offset < 0) or
(0 < alternative_offset < offset))
and (abs(alternative_offset) > abs(previous_offset)))
# check the cache for a good starting point
best_offset = 0
best_offset_polygons = [self]
for cached_offset in self._cached_offset_polygons:
if is_better_offset(best_offset, cached_offset):
best_offset = cached_offset
best_offset_polygons = self._cached_offset_polygons[
cached_offset]
remaining_offset = offset - best_offset
result_polygons = []
for poly in best_offset_polygons:
result = poly.get_offset_polygons_validated(remaining_offset)
if result is not None:
result_polygons.extend(result)
else:
lower = number(0)
upper = remaining_offset
loop_limit = 90
while (loop_limit > 0):
middle = (upper + lower) / 2
result = poly.get_offset_polygons_validated(middle)
if result is None:
upper = middle
else:
if depth > 0:
# the original polygon was split or modified
print("Next level: %s" % str(middle))
shifted_sub_polygons = []
for sub_poly in result:
shifted_sub_polygons.extend(
sub_poly.get_offset_polygons(
remaining_offset - middle,
depth=depth - 1))
result_polygons.extend(shifted_sub_polygons)
break
else:
print("Maximum recursion level reached")
break
loop_limit -= 1
else:
# no split event happened -> no valid shifted polygon
pass
self._cached_offset_polygons[offset] = result_polygons
return result_polygons
def multiply_vector_matrix(v, m):
""" Multiply a 3d vector with a 3x3 matrix. The result is a 3d vector.
@type v: tuple(float) | list(float)
@value v: a 3d vector as tuple or list containing three floats
@type m: tuple(tuple(float)) | list(list(float))
@value m: a 3x3 list/tuple of floats
@rtype: tuple(float)
@return: a tuple of 3 floats as the matrix product
"""
if len(m) == 9:
m = [number(value) for value in m]
m = ((m[0], m[1], m[2]), (m[3], m[4], m[5]), (m[6], m[7], m[8]))
else:
new_m = []
for column in m:
new_m.append([number(value) for value in column])
v = [number(value) for value in v]
return (v[0] * m[0][0] + v[1] * m[0][1] + v[2] * m[0][2],
v[0] * m[1][0] + v[1] * m[1][1] + v[2] * m[1][2],
v[0] * m[2][0] + v[1] * m[2][1] + v[2] * m[2][2])
def get_support_grid(minx,
maxx,
miny,
maxy,
z_plane,
dist_x,
dist_y,
thickness,
height,
length,
offset_x=0.0,
offset_y=0.0,
adjustments_x=None,
adjustments_y=None):
lines_x, lines_y = get_support_grid_locations(minx, maxx, miny, maxy,
dist_x, dist_y, offset_x,
offset_y, adjustments_x,
adjustments_y)
# create all x grid lines
grid_model = Model()
# convert all inputs to "number"
thickness = number(thickness)
height = number(height)
# helper variables
thick_half = thickness / 2
for line_x in lines_x:
# we make the grid slightly longer (by thickness) than necessary
grid_model += _add_aligned_cuboid_to_model(line_x - thick_half,
line_x + thick_half,
miny - length,
maxy + length, z_plane,
z_plane + height)
for line_y in lines_y:
# we make the grid slightly longer (by thickness) than necessary
grid_model += _add_aligned_cuboid_to_model(minx - length,
maxx + length,
line_y - thick_half,
line_y + thick_half,
z_plane, z_plane + height)
return grid_model
def __init__(self, radius, minorradius, **kwargs):
minorradius = number(minorradius)
self.minorradius = minorradius
# we need "minorradius" for "moveto" - thus set it before parent's init
BaseCutter.__init__(self, radius, **kwargs)
self.majorradius = self.radius - minorradius
self.axis = (0, 0, 1)
self.majorradiussq = self.majorradius**2
self.minorradiussq = self.minorradius**2
self.distance_majorradius = self.majorradius + self.get_required_distance(
)
self.distance_minorradius = self.minorradius + self.get_required_distance(
)
self.distance_majorradiussq = self.distance_majorradius**2
self.distance_minorradiussq = self.distance_minorradius**2
def auto_adjust_distance(self):
v = self.view
# adjust the distance to get a view of the whole object
low_high = list(zip(*self._get_low_high_dims()))
if (None, None) in low_high:
return
max_dim = max([high - low for low, high in low_high])
distv = pnormalized((v["distance"][0], v["distance"][1], v["distance"][2]))
# The multiplier "1.25" is based on experiments. 1.414 (sqrt(2)) should
# be roughly sufficient for showing the diagonal of any model.
distv = pmul(distv, (max_dim * 1.25) / number(math.sin(v["fovy"] / 2)))
self.view["distance"] = distv
# Adjust the "far" distance for the camera to make sure, that huge
# models (e.g. x=1000) are still visible.
self.view["zfar"] = 100 * max_dim
def get_support_grid_locations(minx,
maxx,
miny,
maxy,
dist_x,
dist_y,
offset_x=0.0,
offset_y=0.0,
adjustments_x=None,
adjustments_y=None):
def get_lines(center, dist, min_value, max_value):
""" generate a list of positions starting from the middle going up and
and down
"""
if dist > 0:
lines = [center]
current = center
while current - dist > min_value:
current -= dist
lines.insert(0, current)
current = center
while current + dist < max_value:
current += dist
lines.append(current)
else:
lines = []
# remove lines that are out of range (e.g. due to a huge offset)
lines = [line for line in lines if min_value < line < max_value]
return lines
# convert all inputs to the type defined in "number"
dist_x = number(dist_x)
dist_y = number(dist_y)
offset_x = number(offset_x)
offset_y = number(offset_y)
center_x = (maxx + minx) / 2 + offset_x
center_y = (maxy + miny) / 2 + offset_y
lines_x = get_lines(center_x, dist_x, minx, maxx)
lines_y = get_lines(center_y, dist_y, miny, maxy)
if adjustments_x:
for index in range(min(len(lines_x), len(adjustments_x))):
lines_x[index] += number(adjustments_x[index])
if adjustments_y:
for index in range(min(len(lines_y), len(adjustments_y))):
lines_y[index] += number(adjustments_y[index])
return lines_x, lines_y
def pdiv(a, c):
c = number(c)
return (a[0] / c, a[1] / c, a[2] / c)
def scale_distance(self, scale):
if scale != 0:
scale = number(scale)
dist = self.view["distance"]
self.view["distance"] = (scale * dist[0], scale * dist[1],
scale * dist[2])
def pmul(a, c):
c = number(c)
return (a[0] * c, a[1] * c, a[2] * c)
def pmul(a, c):
c = number(c)
if not a:
return (False, False, False)
return (a[0] * c, a[1] * c, a[2] * c)
def set_required_distance(self, value):
if value >= 0:
self.required_distance = number(value)
self.distance_radius = self.radius + self.get_required_distance()
self.distance_radiussq = self.distance_radius * self.distance_radius
self.update_uuid()
def get_offset_polygons(self, offset, callback=None):
def simplify_polygon_intersections(lines):
new_group = lines[:]
# remove all non-adjacent intersecting lines (this splits the group)
if len(new_group) > 0:
group_starts = []
index1 = 0
while index1 < len(new_group):
index2 = 0
while index2 < len(new_group):
index_distance = min(
abs(index2 - index1),
abs(len(new_group) - (index2 - index1)))
# skip neighbours
if index_distance > 1:
line1 = new_group[index1]
line2 = new_group[index2]
intersection, factor = line1.get_intersection(
line2)
if intersection and (pdist(intersection, line1.p1) > epsilon) \
and (pdist(intersection, line1.p2) > epsilon):
del new_group[index1]
new_group.insert(index1,
Line(line1.p1, intersection))
new_group.insert(index1 + 1,
Line(intersection, line1.p2))
# Shift all items in "group_starts" by one if
# they reference a line whose index changed.
for i in range(len(group_starts)):
if group_starts[i] > index1:
group_starts[i] += 1
if index1 + 1 not in group_starts:
group_starts.append(index1 + 1)
# don't update index2 -> maybe there are other hits
elif intersection and (pdist(
intersection, line1.p1) < epsilon):
if index1 not in group_starts:
group_starts.append(index1)
index2 += 1
else:
index2 += 1
else:
index2 += 1
index1 += 1
# The lines intersect each other
# We need to split the group.
if len(group_starts) > 0:
group_starts.sort()
groups = []
last_start = 0
for group_start in group_starts:
transfer_group = new_group[last_start:group_start]
# add only non-empty groups
if transfer_group:
groups.append(transfer_group)
last_start = group_start
# Add the remaining lines to the first group or as a new
# group.
if groups[0][0].p1 == new_group[-1].p2:
groups[0] = new_group[last_start:] + groups[0]
else:
groups.append(new_group[last_start:])
# try to find open groups that can be combined
combined_groups = []
for index, current_group in enumerate(groups):
# Check if the group is not closed: try to add it to
# other non-closed groups.
if current_group[0].p1 == current_group[-1].p2:
# a closed group
combined_groups.append(current_group)
else:
# the current group is open
for other_group in groups[index + 1:]:
if other_group[0].p1 != other_group[-1].p2:
# This group is also open - a candidate
# for merging?
if other_group[0].p1 == current_group[
-1].p2:
current_group.reverse()
for line in current_group:
other_group.insert(0, line)
break
if other_group[-1].p2 == current_group[
0].p1:
other_group.extend(current_group)
break
else:
# not suitable open group found
combined_groups.append(current_group)
return combined_groups
else:
# just return one group without intersections
return [new_group]
else:
return None
offset = number(offset)
if offset == 0:
return [self]
if self.is_outer():
inside_shifting = max(0, -offset)
else:
inside_shifting = max(0, offset)
if inside_shifting * 2 >= self.get_max_inside_distance():
# This offset will not create a valid offset polygon.
# Sadly there is currently no other way to detect a complete flip of
# something like a circle.
log.debug("Skipping offset polygon: polygon is too small")
return []
points = []
for index in range(len(self._points)):
points.append(self.get_shifted_vertex(index, offset))
new_lines = []
for index in range(len(points) - 1):
p1 = points[index]
p2 = points[(index + 1)]
new_lines.append(Line(p1, p2))
if self.is_closed and (len(points) > 1):
new_lines.append(Line(points[-1], points[0]))
if callback and callback():
return None
cleaned_line_groups = simplify_polygon_intersections(new_lines)
if cleaned_line_groups is None:
log.debug("Skipping offset polygon: intersections could not be "
"simplified")
return None
else:
if not cleaned_line_groups:
log.debug("Skipping offset polygon: no polygons left after "
"intersection simplification")
groups = []
for lines in cleaned_line_groups:
if callback and callback():
return None
group = Polygon(self.plane)
for line in lines:
group.append(line)
groups.append(group)
if not groups:
log.debug("Skipping offset polygon: toggled polygon removed")
# remove all polygons that are within other polygons
result = []
for group in groups:
inside = False
for group_test in groups:
if callback and callback():
return None
if group_test is group:
continue
if group_test.is_polygon_inside(group):
inside = True
if not inside:
result.append(group)
if not result:
log.debug(
"Skipping offset polygon: polygon is inside of another one"
)
return result