def test_edge_curves(self):
# create an arrow-like 2D geometry with the pointy end at (-1,1) towards up and left
# mixes rational and non-rational curves with different parametrization spaces
c1 = CurveFactory.circle_segment(pi / 2)
c2 = Curve(BSplineBasis(2, [0, 0, 1, 2, 2]), [[0, 1], [-1, 1], [-1, 0]])
c3 = CurveFactory.circle_segment(pi / 2)
c3.rotate(pi)
c4 = Curve(BSplineBasis(2), [[0, -1], [1, 0]])
surf = SurfaceFactory.edge_curves(c1, c2, c3, c4)
# srf spits out parametric space (0,1)^2, so we sync these up to input curves
c3.reverse()
c4.reverse()
c1.reparam()
c2.reparam()
c3.reparam()
c4.reparam()
for u in np.linspace(0, 1, 7):
self.assertAlmostEqual(surf(u, 0)[0], c1(u)[0]) # x-coord, bottom crv
self.assertAlmostEqual(surf(u, 0)[1], c1(u)[1]) # y-coord, bottom crv
for u in np.linspace(0, 1, 7):
self.assertAlmostEqual(surf(u, 1)[0], c3(u)[0]) # x-coord, top crv
self.assertAlmostEqual(surf(u, 1)[1], c3(u)[1]) # y-coord, top crv
for v in np.linspace(0, 1, 7):
self.assertAlmostEqual(surf(0, v)[0], c4(v)[0]) # x-coord, left crv
self.assertAlmostEqual(surf(0, v)[1], c4(v)[1]) # y-coord, left crv
for v in np.linspace(0, 1, 7):
self.assertAlmostEqual(surf(1, v)[0], c2(v)[0]) # x-coord, right crv
self.assertAlmostEqual(surf(1, v)[1], c2(v)[1]) # y-coord, right crv
def test_edge_curves(self):
# create an arrow-like 2D geometry with the pointy end at (-1,1) towards up and left
# mixes rational and non-rational curves with different parametrization spaces
c1 = cf.circle_segment(pi / 2)
c2 = Curve(BSplineBasis(2, [0, 0, 1, 2, 2]),
[[0, 1], [-1, 1], [-1, 0]])
c3 = cf.circle_segment(pi / 2)
c3.rotate(pi)
c4 = Curve(BSplineBasis(2), [[0, -1], [1, 0]])
surf = sf.edge_curves(c1, c2, c3, c4)
# srf spits out parametric space (0,1)^2, so we sync these up to input curves
c3.reverse()
c4.reverse()
c1.reparam()
c2.reparam()
c3.reparam()
c4.reparam()
for u in np.linspace(0, 1, 7):
self.assertAlmostEqual(surf(u, 0)[0],
c1(u)[0]) # x-coord, bottom crv
self.assertAlmostEqual(surf(u, 0)[1],
c1(u)[1]) # y-coord, bottom crv
for u in np.linspace(0, 1, 7):
self.assertAlmostEqual(surf(u, 1)[0], c3(u)[0]) # x-coord, top crv
self.assertAlmostEqual(surf(u, 1)[1], c3(u)[1]) # y-coord, top crv
for v in np.linspace(0, 1, 7):
self.assertAlmostEqual(surf(0, v)[0],
c4(v)[0]) # x-coord, left crv
self.assertAlmostEqual(surf(0, v)[1],
c4(v)[1]) # y-coord, left crv
for v in np.linspace(0, 1, 7):
self.assertAlmostEqual(surf(1, v)[0],
c2(v)[0]) # x-coord, right crv
self.assertAlmostEqual(surf(1, v)[1],
c2(v)[1]) # y-coord, right crv
# add a case where opposing sites have mis-matching rationality
crvs = Surface().edges() # returned in order umin, umax, vmin, vmax
crvs[0].force_rational()
crvs[1].reverse()
crvs[2].reverse()
# input curves should be clockwise oriented closed loop
srf = sf.edge_curves(crvs[0], crvs[3], crvs[1], crvs[2])
crvs[1].reverse()
u = np.linspace(0, 1, 7)
self.assertTrue(np.allclose(srf(u, 0).reshape((7, 2)), crvs[0](u)))
self.assertTrue(np.allclose(srf(u, 1).reshape((7, 2)), crvs[1](u)))
# test self-organizing curve ordering when they are not sequential
srf = sf.edge_curves(crvs[0], crvs[2].reverse(), crvs[3], crvs[1])
u = np.linspace(0, 1, 7)
self.assertTrue(np.allclose(srf(u, 0).reshape((7, 2)), crvs[0](u)))
self.assertTrue(np.allclose(srf(u, 1).reshape((7, 2)), crvs[1](u)))
# test error handling
with self.assertRaises(ValueError):
srf = sf.edge_curves(crvs + (Curve(), )) # 5 input curves
def test_edge_curves_elasticity(self):
# create an arrow-like 2D geometry with the pointy end at (-1,1) towards up and left
# rebuild to avoid rational representations
c1 = CurveFactory.circle_segment(pi / 2).rebuild(3,11)
c2 = Curve(BSplineBasis(2, [0, 0, 1, 2, 2]), [[0, 1], [-1, 1], [-1, 0]])
c3 = CurveFactory.circle_segment(pi / 2).rebuild(3,11)
c3.rotate(pi)
c4 = Curve(BSplineBasis(2), [[0, -1], [1, 0]]).rebuild(3,10)
c4 = c4.rebuild(4,11)
surf = SurfaceFactory.edge_curves([c1, c2, c3, c4], type='elasticity')
# check right dimensions of output
self.assertEqual(surf.shape[0], 11) # 11 controlpoints in the circle segment
self.assertEqual(surf.shape[1], 13) # 11 controlpoints in c4, +2 for C0-knot in c1
self.assertEqual(surf.order(0), 3)
self.assertEqual(surf.order(1), 4)
# check that c1 edge conforms to surface edge
u = np.linspace(0,1,7)
c1.reparam()
pts_surf = surf(u,0.0)
pts_c1 = c1(u)
for (xs,xc) in zip(pts_surf[:,0,:], pts_c1):
self.assertTrue(np.allclose(xs, xc))
# check that c2 edge conforms to surface edge
v = np.linspace(0,1,7)
c2.reparam()
pts_surf = surf(1.0,v)
pts_c2 = c2(v)
for (xs,xc) in zip(pts_surf[:,0,:], pts_c2):
self.assertTrue(np.allclose(xs, xc))
def test_edge_curves(self):
# create an arrow-like 2D geometry with the pointy end at (-1,1) towards up and left
# mixes rational and non-rational curves with different parametrization spaces
c1 = CurveFactory.circle_segment(pi / 2)
c2 = Curve(BSplineBasis(2, [0, 0, 1, 2, 2]), [[0, 1], [-1, 1], [-1, 0]])
c3 = CurveFactory.circle_segment(pi / 2)
c3.rotate(pi)
c4 = Curve(BSplineBasis(2), [[0, -1], [1, 0]])
surf = SurfaceFactory.edge_curves(c1, c2, c3, c4)
# srf spits out parametric space (0,1)^2, so we sync these up to input curves
c3.reverse()
c4.reverse()
c1.reparam()
c2.reparam()
c3.reparam()
c4.reparam()
for u in np.linspace(0, 1, 7):
self.assertAlmostEqual(surf(u, 0)[0], c1(u)[0]) # x-coord, bottom crv
self.assertAlmostEqual(surf(u, 0)[1], c1(u)[1]) # y-coord, bottom crv
for u in np.linspace(0, 1, 7):
self.assertAlmostEqual(surf(u, 1)[0], c3(u)[0]) # x-coord, top crv
self.assertAlmostEqual(surf(u, 1)[1], c3(u)[1]) # y-coord, top crv
for v in np.linspace(0, 1, 7):
self.assertAlmostEqual(surf(0, v)[0], c4(v)[0]) # x-coord, left crv
self.assertAlmostEqual(surf(0, v)[1], c4(v)[1]) # y-coord, left crv
for v in np.linspace(0, 1, 7):
self.assertAlmostEqual(surf(1, v)[0], c2(v)[0]) # x-coord, right crv
self.assertAlmostEqual(surf(1, v)[1], c2(v)[1]) # y-coord, right crv
# add a case where opposing sites have mis-matching rationality
crvs = Surface().edges() # returned in order umin, umax, vmin, vmax
crvs[0].force_rational()
crvs[1].reverse()
crvs[2].reverse()
# input curves should be clockwise oriented closed loop
srf = SurfaceFactory.edge_curves(crvs[0], crvs[3], crvs[1], crvs[2])
crvs[1].reverse()
u = np.linspace(0,1,7)
self.assertTrue(np.allclose(srf(u,0).reshape((7,2)), crvs[0](u)))
self.assertTrue(np.allclose(srf(u,1).reshape((7,2)), crvs[1](u)))
# test self-organizing curve ordering when they are not sequential
srf = SurfaceFactory.edge_curves(crvs[0], crvs[2].reverse(), crvs[3], crvs[1])
u = np.linspace(0,1,7)
self.assertTrue(np.allclose(srf(u,0).reshape((7,2)), crvs[0](u)))
self.assertTrue(np.allclose(srf(u,1).reshape((7,2)), crvs[1](u)))
# test error handling
with self.assertRaises(ValueError):
srf = SurfaceFactory.edge_curves(crvs + (Curve(),)) # 5 input curves
def test_circle_segment(self):
# basic circle segment
c = cf.circle_segment(pi * 0.9)
self.assertEqual(c.dimension, 2)
self.assertEqual(c.rational, True)
# test evaluation at 25 points for radius=1
t = np.linspace(c.start(0), c.end(0), 25)
x = c.evaluate(t)
for pt in np.array(x):
self.assertAlmostEqual(norm(pt, 2), 1.0) # check radius=1
# radius 7 circle segment
c = cf.circle_segment(pi * 1.87, 7)
self.assertEqual(c.dimension, 2)
self.assertEqual(c.rational, True)
# test evaluation at 25 points for radius=7
t = np.linspace(c.start(0), c.end(0), 25)
x = c.evaluate(t)
for pt in np.array(x):
self.assertAlmostEqual(norm(pt, 2), 7.0) # check radius=7
# negative theta
c = cf.circle_segment(-pi / 2)
self.assertEqual(c.rational, True)
self.assertTrue(np.allclose(c(0), [1, 0]))
self.assertTrue(np.allclose(c(-pi / 4), [1 / sqrt(2), -1 / sqrt(2)]))
self.assertTrue(np.allclose(c(-pi / 2), [0, -1]))
# boundary case with one knot span circle segment
c = cf.circle_segment(2 * pi / 3)
self.assertEqual(c.dimension, 2)
self.assertEqual(c.rational, True)
self.assertEqual(len(c.knots(0)), 2)
self.assertFalse(c.periodic(0))
# test evaluation at 25 points for radius=1
t = np.linspace(c.start(0), c.end(0), 25)
x = c.evaluate(t)
for pt in np.array(x):
self.assertAlmostEqual(norm(pt, 2), 1.0) # check radius=1
# boundary case with full circle
c = cf.circle_segment(2 * pi)
self.assertEqual(c.dimension, 2)
self.assertEqual(c.rational, True)
self.assertEqual(len(c.knots(0)), 5)
self.assertTrue(c.periodic(0))
# test evaluation at 25 points for radius=1
t = np.linspace(c.start(0), c.end(0), 25)
x = c.evaluate(t)
for pt in np.array(x):
self.assertAlmostEqual(norm(pt, 2), 1.0) # check radius=1
# test errors and exceptions
with self.assertRaises(ValueError):
c = cf.circle_segment(3 * pi) # outside domain
with self.assertRaises(ValueError):
c = cf.circle_segment(-3 * pi) # outside domain
with self.assertRaises(ValueError):
c = cf.circle_segment(pi, -2) # negative radius
def test_circle_segment(self):
# basic circle segment
c = CurveFactory.circle_segment(pi * 0.9)
self.assertEqual(c.dimension, 2)
self.assertEqual(c.rational, True)
# test evaluation at 25 points for radius=1
t = np.linspace(c.start(0), c.end(0), 25)
x = c.evaluate(t)
for pt in np.array(x):
self.assertAlmostEqual(norm(pt, 2), 1.0) # check radius=1
# radius 7 circle segment
c = CurveFactory.circle_segment(pi * 1.87, 7)
self.assertEqual(c.dimension, 2)
self.assertEqual(c.rational, True)
# test evaluation at 25 points for radius=7
t = np.linspace(c.start(0), c.end(0), 25)
x = c.evaluate(t)
for pt in np.array(x):
self.assertAlmostEqual(norm(pt, 2), 7.0) # check radius=7
# negative theta
c = CurveFactory.circle_segment(-pi/2)
self.assertEqual(c.rational, True)
self.assertTrue(np.allclose(c(0), [1,0]))
self.assertTrue(np.allclose(c(-pi/4), [1/sqrt(2),-1/sqrt(2)]))
self.assertTrue(np.allclose(c(-pi/2), [0,-1]))
# boundary case with one knot span circle segment
c = CurveFactory.circle_segment(2 * pi / 3)
self.assertEqual(c.dimension, 2)
self.assertEqual(c.rational, True)
self.assertEqual(len(c.knots(0)), 2)
self.assertFalse(c.periodic(0))
# test evaluation at 25 points for radius=1
t = np.linspace(c.start(0), c.end(0), 25)
x = c.evaluate(t)
for pt in np.array(x):
self.assertAlmostEqual(norm(pt, 2), 1.0) # check radius=1
# boundary case with full circle
c = CurveFactory.circle_segment(2 * pi)
self.assertEqual(c.dimension, 2)
self.assertEqual(c.rational, True)
self.assertEqual(len(c.knots(0)), 5)
self.assertTrue(c.periodic(0))
# test evaluation at 25 points for radius=1
t = np.linspace(c.start(0), c.end(0), 25)
x = c.evaluate(t)
for pt in np.array(x):
self.assertAlmostEqual(norm(pt, 2), 1.0) # check radius=1
# test errors and exceptions
with self.assertRaises(ValueError):
c = CurveFactory.circle_segment(3 * pi) # outside domain
with self.assertRaises(ValueError):
c = CurveFactory.circle_segment(-3 * pi) # outside domain
with self.assertRaises(ValueError):
c = CurveFactory.circle_segment(pi, -2) # negative radius
def thingy(radius, elements, out):
right = cf.circle_segment(np.pi / 2)
right.rotate(-np.pi / 4).translate((radius - 1, 0, 0))
left = right.clone().rotate(np.pi)
right.reverse()
thingy = sf.edge_curves(left, right)
thingy.raise_order(0, 1)
thingy.refine(*[e - 1 for e in elements])
with G2(out + '.g2') as f:
f.write([thingy])
def sphere(r=1, center=(0,0,0)):
"""sphere([r=1])
Create a spherical shell.
:param float r: Radius
:param point-like center: Local origin of the sphere
:return: The spherical shell
:rtype: Surface
"""
circle = CurveFactory.circle_segment(pi, r)
circle.rotate(-pi / 2)
circle.rotate(pi / 2, (1, 0, 0)) # flip up into xz-plane
return revolve(circle) + center
def sphere(r=1, center=(0, 0, 0), zaxis=(0, 0, 1), xaxis=(1, 0, 0)):
""" Create a spherical shell.
:param float r: Radius
:param array-like center: Local origin of the sphere
:param array-like zaxis: direction of the north/south pole of the parametrization
:param array-like xaxis: direction of the longitudal sem
:return: The spherical shell
:rtype: Surface
"""
circle = CurveFactory.circle_segment(pi, r)
circle.rotate(-pi / 2)
circle.rotate(pi / 2, (1, 0, 0)) # flip up into xz-plane
result = revolve(circle)
result.rotate(rotate_local_x_axis(xaxis, zaxis))
return flip_and_move_plane_geometry(result, center, zaxis)
def revolve(curve, theta=2 * pi, axis=[0,0,1]):
"""revolve(curve, [theta=2pi], [axis=[0,0,1]])
Revolve a surface by sweeping a curve in a rotational fashion around the
*z* axis.
:param Curve curve: Curve to revolve
:param float theta: Angle to revolve, in radians
:param vector-like axis: Axis of rotation
:return: The revolved surface
:rtype: Surface
"""
curve = curve.clone() # clone input curve, throw away input reference
curve.set_dimension(3) # add z-components (if not already present)
curve.force_rational() # add weight (if not already present)
# align axis with the z-axis
normal_theta = atan2(axis[1], axis[0])
normal_phi = atan2(sqrt(axis[0]**2 + axis[1]**2), axis[2])
curve.rotate(-normal_theta, [0,0,1])
curve.rotate(-normal_phi, [0,1,0])
circle_seg = CurveFactory.circle_segment(theta)
n = len(curve) # number of control points of the curve
m = len(circle_seg) # number of control points of the sweep
cp = np.zeros((m * n, 4))
# loop around the circle and set control points by the traditional 9-point
# circle curve with weights 1/sqrt(2), only here C0-periodic, so 8 points
dt = 0
t = 0
for i in range(m):
x,y,w = circle_seg[i]
dt = atan2(y,x) - t
t += dt
curve.rotate(dt)
cp[i * n:(i + 1) * n, :] = curve[:]
cp[i * n:(i + 1) * n, 2] *= w
cp[i * n:(i + 1) * n, 3] *= w
result = Surface(curve.bases[0], circle_seg.bases[0], cp, True)
# rotate it back again
result.rotate(normal_phi, [0,1,0])
result.rotate(normal_theta, [0,0,1])
return result
def revolve(curve, theta=2 * pi, axis=(0, 0, 1)):
""" Revolve a surface by sweeping a curve in a rotational fashion around
the *z* axis.
:param Curve curve: Curve to revolve
:param float theta: Angle to revolve, in radians
:param array-like axis: Axis of rotation
:return: The revolved surface
:rtype: Surface
"""
curve = curve.clone() # clone input curve, throw away input reference
curve.set_dimension(3) # add z-components (if not already present)
curve.force_rational() # add weight (if not already present)
# align axis with the z-axis
normal_theta = atan2(axis[1], axis[0])
normal_phi = atan2(sqrt(axis[0]**2 + axis[1]**2), axis[2])
curve.rotate(-normal_theta, [0, 0, 1])
curve.rotate(-normal_phi, [0, 1, 0])
circle_seg = CurveFactory.circle_segment(theta)
n = len(curve) # number of control points of the curve
m = len(circle_seg) # number of control points of the sweep
cp = np.zeros((m * n, 4))
# loop around the circle and set control points by the traditional 9-point
# circle curve with weights 1/sqrt(2), only here C0-periodic, so 8 points
dt = 0
t = 0
for i in range(m):
x, y, w = circle_seg[i]
dt = atan2(y, x) - t
t += dt
curve.rotate(dt)
cp[i * n:(i + 1) * n, :] = curve[:]
cp[i * n:(i + 1) * n, 2] *= w
cp[i * n:(i + 1) * n, 3] *= w
result = Surface(curve.bases[0], circle_seg.bases[0], cp, True)
# rotate it back again
result.rotate(normal_phi, [0, 1, 0])
result.rotate(normal_theta, [0, 0, 1])
return result
def revolve(surf, theta=2 * pi, axis=(0, 0, 1)):
""" Revolve a volume by sweeping a surface in a rotational fashion around
an axis.
:param Surface surf: Surface to revolve
:param float theta: Angle to revolve, in radians
:param array-like axis: Axis of rotation
:return: The revolved surface
:rtype: Volume
"""
surf = surf.clone() # clone input surface, throw away old reference
surf.set_dimension(3) # add z-components (if not already present)
surf.force_rational() # add weight (if not already present)
# align axis with the z-axis
normal_theta = atan2(axis[1], axis[0])
normal_phi = atan2(sqrt(axis[0]**2 + axis[1]**2), axis[2])
surf.rotate(-normal_theta, [0, 0, 1])
surf.rotate(-normal_phi, [0, 1, 0])
path = CurveFactory.circle_segment(theta=theta)
n = len(surf) # number of control points of the surface
m = len(path) # number of control points of the sweep
cp = np.zeros((m * n, 4))
dt = np.sign(theta) * (path.knots(0)[1] - path.knots(0)[0]) / 2.0
for i in range(m):
weight = path[i, -1]
cp[i * n:(i + 1) * n, :] = np.reshape(
surf.controlpoints.transpose(1, 0, 2), (n, 4))
cp[i * n:(i + 1) * n, 2] *= weight
cp[i * n:(i + 1) * n, 3] *= weight
surf.rotate(dt)
result = Volume(surf.bases[0], surf.bases[1], path.bases[0], cp, True)
# rotate it back again
result.rotate(normal_phi, [0, 1, 0])
result.rotate(normal_theta, [0, 0, 1])
return result
def revolve(surf, theta=2 * pi, axis=(0,0,1)):
""" Revolve a volume by sweeping a surface in a rotational fashion around
an axis.
:param Surface surf: Surface to revolve
:param float theta: Angle to revolve, in radians
:param array-like axis: Axis of rotation
:return: The revolved surface
:rtype: Volume
"""
surf = surf.clone() # clone input surface, throw away old reference
surf.set_dimension(3) # add z-components (if not already present)
surf.force_rational() # add weight (if not already present)
# align axis with the z-axis
normal_theta = atan2(axis[1], axis[0])
normal_phi = atan2(sqrt(axis[0]**2 + axis[1]**2), axis[2])
surf.rotate(-normal_theta, [0,0,1])
surf.rotate(-normal_phi, [0,1,0])
path = CurveFactory.circle_segment(theta=theta)
n = len(surf) # number of control points of the surface
m = len(path) # number of control points of the sweep
cp = np.zeros((m * n, 4))
dt = np.sign(theta)*(path.knots(0)[1] - path.knots(0)[0]) / 2.0
for i in range(m):
weight = path[i,-1]
cp[i * n:(i + 1) * n, :] = np.reshape(surf.controlpoints.transpose(1, 0, 2), (n, 4))
cp[i * n:(i + 1) * n, 2] *= weight
cp[i * n:(i + 1) * n, 3] *= weight
surf.rotate(dt)
result = Volume(surf.bases[0], surf.bases[1], path.bases[0], cp, True)
# rotate it back again
result.rotate(normal_phi, [0,1,0])
result.rotate(normal_theta, [0,0,1])
return result
def curves_from_path(self, path):
# see https://www.w3schools.com/graphics/svg_path.asp for documentation
# and also https://www.w3.org/TR/SVG/paths.html
# figure out the largest polynomial order of this path
if re.search('[cCsS]', path):
order = 4
elif re.search('[qQtTaA]', path):
order = 3
else:
order = 2
last_curve = None
result = []
# each 'piece' is an operator (M,C,Q,L etc) and accomponying list of argument points
for piece in re.findall('[a-zA-Z][^a-zA-Z]*', path):
# if not single-letter command (i.e. 'z')
if len(piece) > 1:
# points is a (string-)list of (x,y)-coordinates for the given operator
points = re.findall('-?\d+\.?\d*', piece[1:])
if piece[0].lower() != 'a' and piece[0].lower(
) != 'v' and piece[0].lower() != 'h':
# convert string-list to a list of numpy arrays (of size 2)
np_pts = np.reshape(
np.array(points).astype('float'),
(int(len(points) / 2), 2))
if piece[0] == 'm' or piece[0] == 'M':
# I really hope it always start with a move command (think it does)
startpoint = np_pts[0]
if len(np_pts) > 1:
if piece[0] == 'M':
knot = [0] + list(range(
len(np_pts))) + [len(np_pts) - 1]
curve_piece = Curve(BSplineBasis(2, knot), np_pts)
elif piece[0] == 'm':
knot = [0] + list(range(
len(np_pts))) + [len(np_pts) - 1]
controlpoints = [startpoint]
for cp in np_pts[1:]:
controlpoints.append(cp + controlpoints[-1])
curve_piece = Curve(BSplineBasis(2, knot),
controlpoints)
else:
continue
elif piece[0] == 'c':
# cubic spline, relatively positioned
controlpoints = [startpoint]
knot = list(range(int(len(np_pts) / 3) + 1)) * 3
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
startpoint = controlpoints[int(
(len(controlpoints) - 1) / 3) * 3]
controlpoints.append(cp + startpoint)
curve_piece = Curve(BSplineBasis(4, knot), controlpoints)
elif piece[0] == 'C':
# cubic spline, absolute position
controlpoints = [startpoint]
knot = list(range(int(len(np_pts) / 3) + 1)) * 3
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
controlpoints.append(cp)
curve_piece = Curve(BSplineBasis(4, knot), controlpoints)
elif piece[0] == 's':
# smooth cubic spline, relative position
controlpoints = [startpoint]
knot = list(range(int(len(np_pts) / 2) + 1)) * 3
knot += [knot[0], knot[-1]]
knot.sort()
x0 = np.array(last_curve[-1])
xn1 = np.array(last_curve[-2])
controlpoints.append(2 * x0 - xn1)
startpoint = controlpoints[-1]
for i, cp in enumerate(np_pts):
if i % 2 == 0 and i > 0:
startpoint = controlpoints[-1]
controlpoints.append(2 * controlpoints[-1] -
controlpoints[-2])
controlpoints.append(cp + startpoint)
curve_piece = Curve(BSplineBasis(4, knot), controlpoints)
elif piece[0] == 'S':
# smooth cubic spline, absolute position
controlpoints = [startpoint]
knot = list(range(int(len(np_pts) / 2) + 1)) * 3
knot += [knot[0], knot[-1]]
knot.sort()
x0 = np.array(last_curve[-1])
xn1 = np.array(last_curve[-2])
controlpoints.append(2 * x0 - xn1)
for i, cp in enumerate(np_pts):
if i % 2 == 0 and i > 0:
controlpoints.append(2 * controlpoints[-1] -
controlpoints[-2])
controlpoints.append(cp)
curve_piece = Curve(BSplineBasis(4, knot), controlpoints)
elif piece[0] == 'q':
# quadratic spline, relatively positioned
controlpoints = [startpoint]
knot = list(range(int(len(np_pts) / 2) + 1)) * 2
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
startpoint = controlpoints[int(
(len(controlpoints) - 1) / 2) * 2]
controlpoints.append(cp + startpoint)
curve_piece = Curve(BSplineBasis(3, knot), controlpoints)
elif piece[0] == 'Q':
# quadratic spline, absolute position
controlpoints = [startpoint]
knot = list(range(len(np_pts) / 2 + 1)) * 2
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
controlpoints.append(cp)
curve_piece = Curve(BSplineBasis(3, knot), controlpoints)
elif piece[0] == 'l':
# linear spline, relatively positioned
controlpoints = [startpoint]
knot = list(range(len(np_pts) + 1))
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
startpoint = controlpoints[-1]
controlpoints.append(cp + startpoint)
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
elif piece[0] == 'L':
# linear spline, absolute position
controlpoints = [startpoint]
knot = list(range(len(np_pts) + 1))
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
controlpoints.append(cp)
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
elif piece[0] == 'h':
# horizontal piece, relatively positioned
np_pts = np.array(points).astype('float')
controlpoints = [startpoint]
knot = list(range(len(np_pts) + 1))
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
startpoint = controlpoints[-1]
controlpoints.append(np.array([cp, 0]) + startpoint)
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
elif piece[0] == 'H':
# horizontal piece, absolute position
np_pts = np.array(points).astype('float')
controlpoints = [startpoint]
knot = list(range(len(np_pts) + 1))
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
controlpoints.append([cp, startpoint[1]])
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
elif piece[0] == 'v':
# vertical piece, relatively positioned
np_pts = np.array(points).astype('float')
controlpoints = [startpoint]
knot = list(range(len(np_pts) + 1))
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
startpoint = controlpoints[-1]
controlpoints.append(np.array([0, cp]) + startpoint)
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
elif piece[0] == 'V':
# vertical piece, absolute position
np_pts = np.array(points).astype('float')
controlpoints = [startpoint]
knot = list(range(len(np_pts) + 1))
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
controlpoints.append([startpoint[0], cp])
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
elif piece[0] == 'A' or piece[0] == 'a':
np_pts = np.reshape(
np.array(points).astype('float'), (int(len(points))))
rx = float(points[0])
ry = float(points[1])
x_axis_rotation = float(points[2])
large_arc_flag = (points[3] != '0')
sweep_flag = (points[4] != '0')
xend = np.array([float(points[5]), float(points[6])])
if piece[0] == 'a':
xend += startpoint
R = np.array(
[[np.cos(x_axis_rotation),
np.sin(x_axis_rotation)],
[-np.sin(x_axis_rotation),
np.cos(x_axis_rotation)]])
xp = np.linalg.solve(R, (startpoint - xend) / 2)
if sweep_flag == large_arc_flag:
cprime = -(np.sqrt(
abs(rx**2 * ry**2 - rx**2 * xp[1]**2 -
ry**2 * xp[0]**2) /
(rx**2 * xp[1]**2 + ry**2 * xp[0]**2)) *
np.array([rx * xp[1] / ry, -ry * xp[0] / rx]))
else:
cprime = +(np.sqrt(
abs(rx**2 * ry**2 - rx**2 * xp[1]**2 -
ry**2 * xp[0]**2) /
(rx**2 * xp[1]**2 + ry**2 * xp[0]**2)) *
np.array([rx * xp[1] / ry, -ry * xp[0] / rx]))
center = np.linalg.solve(R.T, cprime) + (startpoint + xend) / 2
def arccos(vec1, vec2):
return (np.sign(vec1[0] * vec2[1] - vec1[1] * vec2[0]) *
np.arccos(
vec1.dot(vec2) / np.linalg.norm(vec1) /
np.linalg.norm(vec2)))
tmp1 = np.divide(xp - cprime, [rx, ry])
tmp2 = np.divide(-xp - cprime, [rx, ry])
theta1 = arccos(np.array([1, 0]), tmp1)
delta_t = arccos(tmp1, tmp2) % (2 * np.pi)
if not sweep_flag and delta_t > 0:
delta_t -= 2 * np.pi
elif sweep_flag and delta_t < 0:
delta_t += 2 * np.pi
curve_piece = (curve_factory.circle_segment(delta_t) *
[rx, ry]).rotate(theta1) + center
# curve_piece = curve_factory.circle_segment(delta_t)
elif piece[0] == 'z' or piece[0] == 'Z':
# periodic curve
# curve_piece = Curve(BSplineBasis(2), [startpoint, last_curve[0]])
# curve_piece.reparam([0, curve_piece.length()])
# last_curve.append(curve_piece).make_periodic(0)
last_curve.make_periodic(0)
result.append(last_curve)
last_curve = None
continue
else:
raise RuntimeError('Unknown path parameter:' + piece)
if (curve_piece.length() > state.controlpoint_absolute_tolerance):
curve_piece.reparam([0, curve_piece.length()])
if last_curve is None:
last_curve = curve_piece
else:
last_curve.append(curve_piece)
startpoint = last_curve[-1, :
2] # disregard rational weight (if any)
if last_curve is not None:
result.append(last_curve)
return result
# Institute: Norwegian University of Science and Technology (NTNU)
# Date: March 2016
#
from sys import path
path.append('../')
from splipy import *
import splipy.curve_factory as curves
import splipy.surface_factory as surfaces
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from math import pi, cos, sin
# create the three sides of the triangle, each consisting of a circle segment
c1 = curves.circle_segment(pi/3)
c2 = c1.clone().rotate(2*pi/3) + [1,0]
c3 = c1.clone().rotate(4*pi/3) + [cos(pi/3), sin(pi/3)]
# merge the three circles into one, and center it at the origin
c = c1.append(c2).append(c3)
c -= c.center()
# plot the reuleaux triangle
t = np.linspace(c.start(0), c.end(0), 151) # 151 parametric evaluation points
x = c(t) # evaluate (x,y)-coordinates
plt.plot(x[:,0], x[:,1])
plt.axis('equal')
plt.show()
# split the triangle in two, and align this with the y-axis
import splipy.curve_factory as CurveFactory
import splipy.surface_factory as SurfaceFactory
from splipy.io import G2
from math import sqrt, sin, pi
beta = 0.1
R = 2540
l = 508
w = 2*R*sin(beta)
y0 = -sqrt(R*R-0.25*w*w)
arch = CurveFactory.circle_segment(2*beta,R,[0,0,1])
arch.rotate(pi/2-beta)
arch.translate([0,y0,0])
shell = SurfaceFactory.extrude(arch,[0,0,l])
print(shell)
with G2('shallow_arch.g2') as output:
output.write(shell)
# Institute: Norwegian University of Science and Technology (NTNU)
# Date: March 2016
#
from sys import path
path.append('../')
from splipy import *
import splipy.curve_factory as curves
import splipy.surface_factory as surfaces
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from math import pi, cos, sin
# create the three sides of the triangle, each consisting of a circle segment
c1 = curves.circle_segment(pi / 3)
c2 = c1.clone().rotate(2 * pi / 3) + [1, 0]
c3 = c1.clone().rotate(4 * pi / 3) + [cos(pi / 3), sin(pi / 3)]
# merge the three circles into one, and center it at the origin
c = c1.append(c2).append(c3)
c -= c.center()
# plot the reuleaux triangle
t = np.linspace(c.start(0), c.end(0), 151) # 151 parametric evaluation points
x = c(t) # evaluate (x,y)-coordinates
plt.plot(x[:, 0], x[:, 1])
plt.axis('equal')
plt.show()
# split the triangle in two, and align this with the y-axis
def curves_from_path(self, path):
# see https://www.w3schools.com/graphics/svg_path.asp for documentation
# and also https://www.w3.org/TR/SVG/paths.html
# figure out the largest polynomial order of this path
if re.search('[cCsS]', path):
order = 4
elif re.search('[qQtTaA]', path):
order = 3
else:
order = 2
last_curve = None
result = []
# each 'piece' is an operator (M,C,Q,L etc) and accomponying list of argument points
for piece in re.findall('[a-zA-Z][^a-zA-Z]*', path):
# if not single-letter command (i.e. 'z')
if len(piece)>1:
# points is a (string-)list of (x,y)-coordinates for the given operator
points = re.findall('-?\d+\.?\d*', piece[1:])
if piece[0].lower() != 'a' and piece[0].lower() != 'v' and piece[0].lower() != 'h':
# convert string-list to a list of numpy arrays (of size 2)
np_pts = np.reshape(np.array(points).astype('float'), (int(len(points)/2),2))
if piece[0] == 'm' or piece[0] == 'M':
# I really hope it always start with a move command (think it does)
startpoint = np_pts[0]
if len(np_pts) > 1:
if piece[0] == 'M':
knot = [0] + list(range(len(np_pts))) + [len(np_pts)-1]
curve_piece = Curve(BSplineBasis(2, knot), np_pts)
elif piece[0] == 'm':
knot = [0] + list(range(len(np_pts))) + [len(np_pts)-1]
controlpoints = [startpoint]
for cp in np_pts[1:]:
controlpoints.append(cp + controlpoints[-1])
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
else:
continue
elif piece[0] == 'c':
# cubic spline, relatively positioned
controlpoints = [startpoint]
knot = list(range(int(len(np_pts)/3)+1)) * 3
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
startpoint = controlpoints[int((len(controlpoints)-1)/3)*3]
controlpoints.append(cp + startpoint)
curve_piece = Curve(BSplineBasis(4, knot), controlpoints)
elif piece[0] == 'C':
# cubic spline, absolute position
controlpoints = [startpoint]
knot = list(range(int(len(np_pts)/3)+1)) * 3
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
controlpoints.append(cp)
curve_piece = Curve(BSplineBasis(4, knot), controlpoints)
elif piece[0] == 's':
# smooth cubic spline, relative position
controlpoints = [startpoint]
knot = list(range(int(len(np_pts)/2)+1)) * 3
knot += [knot[0], knot[-1]]
knot.sort()
x0 = np.array(last_curve[-1])
xn1 = np.array(last_curve[-2])
controlpoints.append(2*x0 -xn1)
startpoint = controlpoints[-1]
for i, cp in enumerate(np_pts):
if i % 2 == 0 and i>0:
startpoint = controlpoints[-1]
controlpoints.append(2*controlpoints[-1] - controlpoints[-2])
controlpoints.append(cp + startpoint)
curve_piece = Curve(BSplineBasis(4, knot), controlpoints)
elif piece[0] == 'S':
# smooth cubic spline, absolute position
controlpoints = [startpoint]
knot = list(range(int(len(np_pts)/2)+1)) * 3
knot += [knot[0], knot[-1]]
knot.sort()
x0 = np.array(last_curve[-1])
xn1 = np.array(last_curve[-2])
controlpoints.append(2*x0 -xn1)
for i,cp in enumerate(np_pts):
if i % 2 == 0 and i>0:
controlpoints.append(2*controlpoints[-1] - controlpoints[-2])
controlpoints.append(cp)
curve_piece = Curve(BSplineBasis(4, knot), controlpoints)
elif piece[0] == 'q':
# quadratic spline, relatively positioned
controlpoints = [startpoint]
knot = list(range(int(len(np_pts)/2)+1)) * 2
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
startpoint = controlpoints[int((len(controlpoints)-1)/2)*2]
controlpoints.append(cp + startpoint)
curve_piece = Curve(BSplineBasis(3, knot), controlpoints)
elif piece[0] == 'Q':
# quadratic spline, absolute position
controlpoints = [startpoint]
knot = list(range(len(np_pts)/2+1)) * 2
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
controlpoints.append(cp)
curve_piece = Curve(BSplineBasis(3, knot), controlpoints)
elif piece[0] == 'l':
# linear spline, relatively positioned
controlpoints = [startpoint]
knot = list(range(len(np_pts)+1))
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
startpoint = controlpoints[-1]
controlpoints.append(cp + startpoint)
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
elif piece[0] == 'L':
# linear spline, absolute position
controlpoints = [startpoint]
knot = list(range(len(np_pts)+1))
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
controlpoints.append(cp)
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
elif piece[0] == 'h':
# horizontal piece, relatively positioned
np_pts = np.array(points).astype('float')
controlpoints = [startpoint]
knot = list(range(len(np_pts)+1))
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
startpoint = controlpoints[-1]
controlpoints.append(np.array([cp, 0]) + startpoint)
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
elif piece[0] == 'H':
# horizontal piece, absolute position
np_pts = np.array(points).astype('float')
controlpoints = [startpoint]
knot = list(range(len(np_pts)+1))
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
controlpoints.append([cp, startpoint[1]])
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
elif piece[0] == 'v':
# vertical piece, relatively positioned
np_pts = np.array(points).astype('float')
controlpoints = [startpoint]
knot = list(range(len(np_pts)+1))
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
startpoint = controlpoints[-1]
controlpoints.append(np.array([0, cp]) + startpoint)
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
elif piece[0] == 'V':
# vertical piece, absolute position
np_pts = np.array(points).astype('float')
controlpoints = [startpoint]
knot = list(range(len(np_pts)+1))
knot += [knot[0], knot[-1]]
knot.sort()
for cp in np_pts:
controlpoints.append([startpoint[0], cp])
curve_piece = Curve(BSplineBasis(2, knot), controlpoints)
elif piece[0] == 'A' or piece[0] == 'a':
np_pts = np.reshape(np.array(points).astype('float'), (int(len(points))))
rx = float(points[0])
ry = float(points[1])
x_axis_rotation = float(points[2])
large_arc_flag = (points[3] != '0')
sweep_flag = (points[4] != '0')
xend = np.array([float(points[5]), float(points[6]) ])
if piece[0] == 'a':
xend += startpoint
R = np.array([[ np.cos(x_axis_rotation), np.sin(x_axis_rotation)],
[-np.sin(x_axis_rotation), np.cos(x_axis_rotation)]])
xp = np.linalg.solve(R, (startpoint - xend)/2)
if sweep_flag == large_arc_flag:
cprime = -(np.sqrt(abs(rx**2*ry**2 - rx**2*xp[1]**2 - ry**2*xp[0]**2) /
(rx**2*xp[1]**2 + ry**2*xp[0]**2)) *
np.array([rx*xp[1]/ry, -ry*xp[0]/rx]))
else:
cprime = +(np.sqrt(abs(rx**2*ry**2 - rx**2*xp[1]**2 - ry**2*xp[0]**2) /
(rx**2*xp[1]**2 + ry**2*xp[0]**2)) *
np.array([rx*xp[1]/ry, -ry*xp[0]/rx]))
center = np.linalg.solve(R.T, cprime) + (startpoint+xend)/2
def arccos(vec1, vec2):
return (np.sign(vec1[0]*vec2[1] - vec1[1]*vec2[0]) *
np.arccos(vec1.dot(vec2)/np.linalg.norm(vec1)/np.linalg.norm(vec2)))
tmp1 = np.divide( xp - cprime, [rx,ry])
tmp2 = np.divide(-xp - cprime, [rx,ry])
theta1 = arccos(np.array([1,0]), tmp1)
delta_t= arccos(tmp1, tmp2) % (2*np.pi)
if not sweep_flag and delta_t > 0:
delta_t -= 2*np.pi
elif sweep_flag and delta_t < 0:
delta_t += 2*np.pi
curve_piece = (curve_factory.circle_segment(delta_t)*[rx,ry]).rotate(theta1) + center
# curve_piece = curve_factory.circle_segment(delta_t)
elif piece[0] == 'z' or piece[0] == 'Z':
# periodic curve
# curve_piece = Curve(BSplineBasis(2), [startpoint, last_curve[0]])
# curve_piece.reparam([0, curve_piece.length()])
# last_curve.append(curve_piece).make_periodic(0)
last_curve.make_periodic(0)
result.append(last_curve)
last_curve = None
continue
else:
raise RuntimeError('Unknown path parameter:' + piece)
if(curve_piece.length()>state.controlpoint_absolute_tolerance):
curve_piece.reparam([0, curve_piece.length()])
if last_curve is None:
last_curve = curve_piece
else:
last_curve.append(curve_piece)
startpoint = last_curve[-1,:2] # disregard rational weight (if any)
if last_curve is not None:
result.append(last_curve)
return result