def Geometry(self):
pas = 2 * npy.pi / self.Z
O = vm.Point2D((self.Ox, self.Oy))
A = O.Translation(vm.Point2D((0, self.DE / 2.)))
Bp = O.Translation(vm.Point2D((0, self.DI / 2.)))
B = Bp.Rotation(O, -self.alpha1, copy=True)
Bi = B.Rotation(O, -self.alpha2 / 2., copy=True)
C = B.Rotation(O, -self.alpha2, copy=True)
D = A.Rotation(O, -self.alpha1 - self.alpha2 - self.alpha3, copy=True)
Di = D.Rotation(O,
(-pas + self.alpha1 + self.alpha2 + self.alpha3) / 2.,
copy=True)
Ap = A.Rotation(O, -pas, copy=True)
dir1 = (B[1] - A[1]) / (B[0] - A[0])
ord1 = B[1] - dir1 * B[0]
def fonct(x, *data):
Ox, Oy, R, coeff_dir, ord_origine = data
f = (ord_origine + coeff_dir * x - Oy)**2 + (x - Ox)**2 - R**2
return f
x1 = fsolve(fonct,
0,
args=(self.Ox, self.Oy, self.DF / 2., dir1, ord1))
R1 = vm.Point2D((x1, ord1 + x1 * dir1))
dir2 = (D[1] - C[1]) / (D[0] - C[0])
ord2 = C[1] - dir2 * C[0]
x2 = fsolve(fonct,
1,
args=(self.Ox, self.Oy, self.DF / 2., dir2, ord2))
R2 = vm.Point2D((x2, ord2 + x2 * dir2))
li = [B, Bi, C, D, Di, Ap]
AB = vm.LineSegment2D(A, B)
BC = vm.Arc2D(B, Bi, C)
CD = vm.LineSegment2D(C, D)
list_seg = []
Am = A
for z in range(self.Z):
li_point = []
for pt in li:
li_point.append(pt.Rotation(O, -pas * z, copy=True))
AB = vm.LineSegment2D(Am, li_point[0])
BC = vm.Arc2D(li_point[0], li_point[1], li_point[2])
CD = vm.LineSegment2D(li_point[2], li_point[3])
DA = vm.Arc2D(li_point[3], li_point[4], li_point[5])
list_seg.extend([AB, BC, CD, DA])
Am = li_point[5]
c = vm.CompositePrimitive2D(list_seg)
return c
def update(self, new_height, new_side):
return Component(self.center, new_side, self.vectors[0],
self.vectors[1], new_height, self.plane)
self.points = self.compo_points()
self.primitives = [
vm.LineSegment2D(self.points[0], self.points[1]),
vm.LineSegment2D(self.points[1], self.points[2]),
vm.LineSegment2D(self.points[2], self.points[3]),
vm.LineSegment2D(self.points[3], self.points[0])
]
self.contour = vm.Contour2D(self.primitives)
self.solid = self.compo_solid()
return
def __init__(self, center, compo_side, vector1, vector2, height, plane):
self.center = center
self.compo_side = compo_side
self.vectors = [vector1, vector2]
self.height = height
self.plane = plane
self.points = self.compo_points()
self.primitives = [
vm.LineSegment2D(self.points[0], self.points[1]),
vm.LineSegment2D(self.points[1], self.points[2]),
vm.LineSegment2D(self.points[2], self.points[3]),
vm.LineSegment2D(self.points[3], self.points[0])
]
self.contour = vm.Contour2D(self.primitives)
self.solid = self.compo_solid()
def Draw(self, x3D=vm.X3D, y3D=vm.Y3D, ax=None):
if ax is None:
fig = plt.figure()
ax = fig.add_subplot(111)
for point in self.active_points:
vm.LineSegment2D(point, self.central_point).MPLPlot(ax)
def Geometry(self):
O = vm.Point2D((self.Ox, self.Oy))
A = O.Translation(vm.Point2D((self.LA*npy.cos(self.alpha0), self.LA*npy.sin(self.alpha0))))
alpha = self.alpha0 - self.alphaA
B = A.Translation(vm.Point2D((self.L1*npy.cos(alpha), self.L1*npy.sin(alpha))))
alpha = alpha - self.alphaB
P = B.Translation(vm.Point2D((self.L2*npy.cos(alpha), self.L2*npy.sin(alpha))))
alpha = alpha + self.alphaP
M = P.Translation(vm.Point2D((self.L5*npy.cos(alpha), self.L5*npy.sin(alpha))))
alpha = self.alpha0 - self.alphaE
E = O.Translation(vm.Point2D((self.LE*npy.cos(alpha), self.LE*npy.sin(alpha))))
alphap = alpha - self.alpha1
C = E.Translation(vm.Point2D((self.L4*npy.cos(alphap), self.L4*npy.sin(alphap))))
D = E.Translation(vm.Point2D((-self.L3*npy.cos(alphap), -self.L3*npy.sin(alphap))))
alpha = alphap + npy.pi/2. - self.alphaC
F = C.Translation(vm.Point2D((self.L7*npy.cos(alpha), self.L7*npy.sin(alpha))))
alpha = alphap + npy.pi/2. + self.alphaD
G = D.Translation(vm.Point2D((self.L6*npy.cos(alpha), self.L6*npy.sin(alpha))))
AB=vm.LineSegment2D(A, B)
BP=vm.LineSegment2D(B, P)
PM=vm.LineSegment2D(P, M)
DE=vm.LineSegment2D(D, E)
EC=vm.LineSegment2D(E, C)
DG=vm.LineSegment2D(D, G)
CF=vm.LineSegment2D(C, F)
alpha = alphap - npy.pi/2.
R = E.Translation(vm.Point2D((self.DI/2.*npy.cos(alpha), self.DI/2.*npy.sin(alpha))))
# recherche du point F1 et F2
def fonct(alpha, *data):
line, d = data
x = R.Translation(vm.Point2D((d/2.*npy.cos(alpha + npy.pi/2.), d/2.*npy.sin(alpha + npy.pi/2.))))
p = line.PointProjection(x)
return p.PointDistance(x)
sol1 = fsolve(fonct, 0, args=(DG, self.DF))
F1 = R.Translation(vm.Point2D((self.DF/2.*npy.cos(npy.pi/2. + sol1), self.DF/2.*npy.sin(npy.pi/2. + sol1))))
sol2 = fsolve(fonct, 0, args=(CF, self.DF))
F2 = R.Translation(vm.Point2D((self.DF/2.*npy.cos(npy.pi/2. + sol2), self.DF/2.*npy.sin(npy.pi/2. + sol2))))
Cr = vm.Circle2D(R, self.DF/2.)
c=vm.CompositePrimitive2D([O, AB, BP, PM, DE, EC, DG, CF, R, Cr, F1, F2])
c.MPLPlot(style='--ob')
#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Tue Feb 12 19:23:27 2019 @author: steven """ import volmdlr as vm import math r = 0.23 p1 = vm.Point2D((0, 0)) p2 = vm.Point2D((r, r)) p3 = vm.Point2D((2 * r, 0)) a = vm.Arc2D(p1, p2, p3) l = vm.LineSegment2D(p3, p1) c = vm.Contour2D([a, l]) f, ax = c.MPLPlot() cog = c.CenterOfMass() cog.MPLPlot(ax) assert math.isclose(a.radius, r) assert math.isclose(c.Area(), math.pi * r**2 / 2.) assert math.isclose(cog[0], r) print(cog[1], 4 * r / 3. * math.pi) assert math.isclose(cog[1], 4 * r / 3. / math.pi)
offset_theta1 = random.randrange(
angle_min, angle_max,
20) / 100 #Theta's offset if you want to turn it with normal's reference
offset_phi1 = random.randrange(angle_min, angle_max,
20) / 100 #Idem but with circle's normal
print('param1', phi1, theta1, offset_phi1, offset_theta1)
#You have to create a cutting pattern in 2D
pt1, pt2, pt3, pt4 = volmdlr.Point2D(
(offset_theta1, offset_phi1)), volmdlr.Point2D(
(offset_theta1, offset_phi1 + phi1)), volmdlr.Point2D(
(offset_theta1 + theta1, offset_phi1 + phi1)), volmdlr.Point2D(
(offset_theta1 + theta1, offset_phi1))
seg1, seg2, seg3, seg4 = volmdlr.LineSegment2D(
pt1, pt2), volmdlr.LineSegment2D(pt2, pt3), volmdlr.LineSegment2D(
pt3, pt4), volmdlr.LineSegment2D(pt4, pt1)
edges = [seg1, seg2, seg3, seg4]
contours2d = [volmdlr.Contour2D(edges)]
points = [theta1, phi1]
#Cylinder
hmin, hmax = -50, 50
h2 = random.randrange(hmin, hmax, 5) / 100 #Height of cylinder
angle_cyl = random.randrange(angle_min, angle_max, 20) / 100
center2d2 = c2.To2D(c2, plane2.vectors[0], plane2.vectors[1])
segbh2 = volmdlr.LineSegment2D(center2d2, center2d2 + volmdlr.Point2D(
(0, h2)) + volmdlr.Point2D(
(angle_cyl / 3, 0))) #### Minus Pt2D because of Step adaptation
offset_theta1 = random.randrange(
angle_min, angle_max,
20) / 100 #Theta's offset if you want to turn it with normal's reference
offset_phi1 = random.randrange(angle_min, angle_max,
20) / 100 #Idem but with circle's normal
print('param1', phi1, theta1, offset_phi1, offset_theta1)
#You have to create a cutting pattern in 2D
pt1, pt2, pt3, pt4 = volmdlr.Point2D(
(offset_theta1, offset_phi1)), volmdlr.Point2D(
(offset_theta1, offset_phi1 + phi1)), volmdlr.Point2D(
(offset_theta1 + theta1, offset_phi1 + phi1)), volmdlr.Point2D(
(offset_theta1 + theta1, offset_phi1))
seg1, seg2, seg3, seg4 = volmdlr.LineSegment2D(
pt1, pt2), volmdlr.LineSegment2D(pt2, pt3), volmdlr.LineSegment2D(
pt3, pt4), volmdlr.LineSegment2D(pt4, pt1)
edges = [seg1, seg2, seg3, seg4]
contours2d = [volmdlr.Contour2D(edges)]
points = [theta1, phi1]
theta2 = random.randrange(angle_min, angle_max, 20) / 100 #Tore's length
phi2 = random.randrange(angle_min, angle_max, 20) / 100 #angle of circle
offset_theta2 = random.randrange(
angle_min, angle_max,
20) / 100 #Theta's offset if you want to turn it with normal's reference
offset_phi2 = random.randrange(angle_min, angle_max,
20) / 100 #Idem but with circle's normal
print('param2', phi2, theta2, offset_phi2, offset_theta2)
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Fri May 12 10:04:09 2017
@author: steven
"""
import volmdlr as vm
l = 0.1
p1 = vm.Point2D((0, 0))
p2 = vm.Point2D((l, 0))
p3 = vm.Point2D((l, l))
p4 = vm.Point2D((0, l))
l1 = vm.LineSegment2D(p1, p2)
l2 = vm.LineSegment2D(p2, p3)
l3 = vm.LineSegment2D(p3, p4)
l4 = vm.LineSegment2D(p4, p1)
p5 = vm.Point2D((l / 2, l / 2))
c1 = vm.Circle2D(p5, l / 5)
ct1 = vm.Contour2D([l4, l3, l2, l1])
ct2 = vm.Contour2D([c1])
mesh = vm.Mesh2D([ct1, ct2], {}, 0.01)
print(mesh.GeoScript('mesh2D.geo'))
center = vm.Point3D([0, 0, 0]) #Choose the coordinate of the center
normal1 = vm.Vector3D([0, 0, 1]) #Choose the normal of the generative
normal1.Normalize() #Normalize the normal if it is not the case
vec1 = normal1.deterministic_unit_normal_vector()
frame = vm.Frame3D(center, vec1, normal1.Cross(vec1),
normal1) #Frame in the center of the generative arc3D
toroidalsurface3d = vm.ToroidalSurface3D(frame, r1, r2)
theta = 4 * math.pi / 3 #Tore's length
phi = 2 * math.pi #angle of circle
offset_theta = math.pi / 4 #Theta's offset if you want to turn it with normal's reference
offset_phi = math.pi #Idem but with circle's normal
#You have to create a cutting pattern in 2D
pt1, pt2, pt3, pt4 = vm.Point2D((offset_theta, offset_phi)), vm.Point2D(
(offset_theta, offset_phi + phi)), vm.Point2D(
(offset_theta + theta, offset_phi + phi)), vm.Point2D(
(offset_theta + theta, offset_phi))
seg1, seg2, seg3, seg4 = vm.LineSegment2D(pt1, pt2), vm.LineSegment2D(
pt2, pt3), vm.LineSegment2D(pt3, pt4), vm.LineSegment2D(pt4, pt1)
edges = [seg1, seg2, seg3, seg4]
contours2d = [vm.Contour2D(edges)]
points = [theta, phi]
toroidalface = vm.ToroidalFace3D(contours2d, toroidalsurface3d, points)
shell = vm.Shell3D([toroidalface])
m = vm.VolumeModel([shell])
m.babylonjs(debug=True)
def Draw(self, ax=None):
if ax is None:
fig = plt.figure()
ax = fig.add_subplot(111)
vm.LineSegment2D(*self.points).MPLPlot(ax)
offset_theta1 = random.randrange(
angle_min, angle_max,
20) / 100 #Theta's offset if you want to turn it with normal's reference
offset_phi1 = random.randrange(angle_min, angle_max,
20) / 100 #Idem but with circle's normal
print('param1', phi1, theta1, offset_phi1, offset_theta1)
#You have to create a cutting pattern in 2D
pt1, pt2, pt3, pt4 = volmdlr.Point2D(
(offset_theta1, offset_phi1)), volmdlr.Point2D(
(offset_theta1, offset_phi1 + phi1)), volmdlr.Point2D(
(offset_theta1 + theta1, offset_phi1 + phi1)), volmdlr.Point2D(
(offset_theta1 + theta1, offset_phi1))
seg1, seg2, seg3, seg4 = volmdlr.LineSegment2D(
pt1, pt2), volmdlr.LineSegment2D(pt2, pt3), volmdlr.LineSegment2D(
pt3, pt4), volmdlr.LineSegment2D(pt4, pt1)
edges = [seg1, seg2, seg3, seg4]
contours2d = [volmdlr.Contour2D(edges)]
points = [theta1, phi1]
toroidalface1 = volmdlr.ToroidalFace3D(contours2d, toresurface1, points)
pts1, tangle1 = toroidalface1.triangulation(resolution=10)
# number_holes = 5
# outer_circle = volmdlr.Circle2D(volmdlr.O2D, 0.06)
# circles = []
# delta_angle = 2*math.pi/number_holes
Distance to lines and projection debug
"""
import numpy as npy
import volmdlr as vm
p1 = vm.Point2D(2*npy.random.random(2)-1)
p2 = vm.Point2D(2*npy.random.random(2)-1)
line = vm.Line2D(p1, p2)
line_segment = vm.LineSegment2D(p1, p2)
for i in range(100):
point = vm.Point2D(4*npy.random.random(2)-2)
point_projection_line = line.PointProjection(point)
point_projection_line_segment = line_segment.PointProjection(point)
assert point_projection_line.PointDistance(point) == line.PointDistance(point)
assert point_projection_line_segment.PointDistance(point) == line_segment.PointDistance(point)
#fig, ax = line.MPLPlot()
#point.MPLPlot(ax=ax)
#point_projection_line.MPLPlot(ax=ax)
#point_projection_line_segment.MPLPlot(ax=ax)
def rolling_circle_in_polygon(polygon, interpoints_distance=0.001):
# discrétisation du polygon
polygon_mesh = []
# on partcourt les arrêtes
for (vertice1, vertice2) in zip(polygon.points, polygon.points[1:]+[polygon.points[0]]):
side_direction = vm.Vector2D((vertice2[0] - vertice1[0], vertice2[1] - vertice1[1]))
normalized_side_direction = vm.Vector2D((vertice2[0] - vertice1[0], vertice2[1] - vertice1[1]))
normalized_side_direction.Normalize()
pt_number = 0
# on ajoute les points un par un sans dépasser la longueur du côté
segment_mesh = []
while interpoints_distance * pt_number < side_direction.Norm():
side_point = vertice1 + interpoints_distance * pt_number * normalized_side_direction
segment_mesh.append(side_point)
pt_number += 1
polygon_mesh.append(segment_mesh)
# prendre un point quelconque
# construire le plus grand cercle possible
min_radius = 1e+10
for index1, segment1 in enumerate(polygon_mesh):
for index2, segment2 in enumerate(polygon_mesh):
if index2-index1 >= 2 and index2-index1 < len(polygon_mesh)-1:
for point1 in segment1[1:]:
seg1 = vm.LineSegment2D(segment1[0], segment1[-1])
seg2 = vm.LineSegment2D(segment2[0], segment2[-1])
circle1, circle2 = seg2.CreateTangentCircle(point1, seg1)
polygon_mesh_modified = polygon_mesh[:]
polygon_mesh_modified.pop(index1)
polygon_mesh_modified = [p for seg in polygon_mesh_modified for p in seg]
if circle1 is not None and not points_inside_circle(polygon_mesh_modified, circle1) and circle1.radius < min_radius:# and circle1.radius != 0:
min_radius = circle1.radius
min_circle = circle1
other_circle = circle2
min_point = point1
min_seg1 = index1
min_seg2 = index2
for point2 in segment2[1:]:
seg1 = vm.LineSegment2D(segment1[0], segment1[-1])
seg2 = vm.LineSegment2D(segment2[0], segment2[-1])
circle1, circle2 = seg1.CreateTangentCircle(point2, seg2)
polygon_mesh_modified = polygon_mesh[:]
polygon_mesh_modified.pop(index2)
polygon_mesh_modified = [p for seg in polygon_mesh_modified for p in seg]
if circle1 is not None and not points_inside_circle(polygon_mesh_modified, circle1) and circle1.radius < min_radius:# and circle1.radius != 0:
min_radius = circle1.radius
min_circle = circle1
other_circle = circle2
min_point = point2
min_seg1 = index2
min_seg2 = index1
return min_radius, min_circle, other_circle, min_point, min_seg1, min_seg2
p3 = vm.Point2D((0.1, 0.2))
p4 = vm.Point2D((0.05, 0.1))
p5 = vm.Point2D((0., 0.21))
p6 = vm.Point2D((0.05, 0.05))
p7 = vm.Point2D((0.06, 0.05))
p8 = vm.Point2D((0.04, 0.07))
radius = {0: 0.01, 2: 0.01, 3: 0.015}
outer_profile = primitives2D.RoundedLineSegments2D([p1, p2, p3, p4, p5],
radius,
closed=True)
#hole = vm.Circle2D(p6, 0.01)
#inner_profile = primitives2D.RoundedLineSegments2D([p6, p7, p8], {0: }, closed = True)
l1 = vm.LineSegment2D(p6, p7)
l2 = vm.LineSegment2D(p7, p8)
l3 = vm.LineSegment2D(p8, p6)
c2 = vm.Contour2D([l1, l2, l3])
c1 = vm.Contour2D([outer_profile])
#c2 = vm.Contour2D([inner_profile])
po = vm.Point3D((0, 0, 0))
xp = vm.Vector3D((1, 0, 0))
yp = vm.Vector3D((0, 1, 0))
f, a = c1.MPLPlot()
c2.MPLPlot(a)
profile = primitives3D.ExtrudedProfile(po,
xp,
n1.Normalize() #Normalize the normal if it is not the case n2.Normalize() plane1, plane2 = volmdlr.Plane3D.from_normal(c1, n1), volmdlr.Plane3D.from_normal(c2, n2) #Create a plane to give us two others vector frame1 = volmdlr.Frame3D(c1, plane1.vectors[0], plane1.vectors[1], n1) #Frame in the center of the cylinder frame2 = volmdlr.Frame3D(c2, plane2.vectors[0], plane2.vectors[1], n2) cylsurface1 = volmdlr.CylindricalSurface3D(frame1, r1) cylsurface2 = volmdlr.CylindricalSurface3D(frame2, r2) hmin, hmax = 0, 100 h1, h2 = random.randrange(hmin, hmax, 5)/100, random.randrange(hmin, hmax, 5)/100 #Height of cylinder # center2d = c1.To2D(c1, plane1.vectors[0], plane1.vectors[1]) center2d = volmdlr.Point2D((0,0)) segbh = volmdlr.LineSegment2D(center2d, center2d + volmdlr.Point2D((0,h1))) #### Minus Pt2D because of Step adaptation circlestart = volmdlr.LineSegment2D(segbh.points[1], segbh.points[1]+volmdlr.Point2D((2*math.pi*3/4,0))) #You can change 2*pi by an other angle seghb = volmdlr.LineSegment2D(circlestart.points[1],circlestart.points[1]-segbh.points[1]) circlend = volmdlr.LineSegment2D(seghb.points[1],segbh.points[0]) edges = [segbh, circlestart, seghb, circlend] points = edges[0].points contours = [volmdlr.Contour2D(edges)] # center2d2 = c2.To2D(c2, plane2.vectors[0], plane2.vectors[1]) center2d2 = volmdlr.Point2D((0,0)) segbh2 = volmdlr.LineSegment2D(center2d2, center2d2 + volmdlr.Point2D((0,h2))) #### Minus Pt2D because of Step adaptation circlestart2 = volmdlr.LineSegment2D(segbh2.points[1], segbh2.points[1]+volmdlr.Point2D((2*math.pi,0))) #You can change 2*pi by an other angle seghb2 = volmdlr.LineSegment2D(circlestart2.points[1],circlestart2.points[1]-segbh2.points[1]) circlend2 = volmdlr.LineSegment2D(seghb2.points[1],segbh2.points[0]) edges2 = [segbh2, circlestart2, seghb2, circlend2] points2 = edges2[0].points
Created on Wed Mar 14 15:32:37 2018 @author: Steven Masfaraud [email protected] """ import volmdlr as vm import volmdlr.primitives2D as primitives2D import numpy as npy #for i in range(20): triangle_points = [vm.Point2D(npy.random.random(2)) for i in range(3)] triangle = vm.Polygon2D(triangle_points) cog_triangle = triangle.CenterOfMass() c1 = vm.CompositePrimitive2D([triangle, cog_triangle]) c1.MPLPlot() print(triangle.Area()) p0 = vm.Point2D((-1, 0)) p1 = vm.Point2D((-npy.cos(npy.pi / 4), npy.sin(npy.pi / 4))) p2 = vm.Point2D((0, 1)) a = vm.Arc2D(p2, p1, p0) l = vm.LineSegment2D(p2, a.center) list_node = a.Discretise() c = vm.Contour2D([a, l] + list_node) print(c.plot_data()) c2 = vm.CompositePrimitive2D([c]) c2.MPLPlot(style='ob') print(c.Area())
n1 = volmdlr.Vector3D([x3, y3, z3])
n1.Normalize() #Normalize the normal if it is not the case
plane1 = volmdlr.Plane3D.from_normal(c1, n1)
frame1 = volmdlr.Frame3D(c1, plane1.vectors[0], plane1.vectors[1],
n1) #Frame in the center of the cylinder
cylsurface1 = volmdlr.CylindricalSurface3D(frame1, r1)
hmin, hmax = -50, 50
h1 = random.randrange(hmin, hmax, 5) / 100
center2d = c1.To2D(c1, plane1.vectors[0], plane1.vectors[1])
#Classic Contour
segbh = volmdlr.LineSegment2D(center2d, center2d + volmdlr.Point2D(
(0, h1))) #### Minus Pt2D because of Step adaptation
circlestart = volmdlr.LineSegment2D(
segbh.points[1], segbh.points[1] + volmdlr.Point2D(
(2 * math.pi * 3 / 4, 0))) #You can change 2*pi by an other angle
seghb = volmdlr.LineSegment2D(circlestart.points[1],
circlestart.points[1] - segbh.points[1])
circlend = volmdlr.LineSegment2D(seghb.points[1], segbh.points[0])
edges = [segbh, circlestart, seghb, circlend]
points = edges[0].points
contours = [volmdlr.Contour2D(edges)]
cyl1 = volmdlr.CylindricalFace3D(contours, cylsurface1, points)
pts1, tangle1 = cyl1.triangulation(resolution=12)
fig = plt.figure()