def nikeLogo(x):
if x < 0.25:
return bezier((9, 8), (0, 2), (-4, 0), (-6, 0), x, 0.25)
elif x < 0.5:
return bezier((-6, 0), (-9, 0), (-10, 3), (-6, 7), x - (0.25), 0.25)
elif x < 0.75:
return bezier((-6, 7), (-7, 4), (-6, 3), (-5, 3), x - (0.5), 0.25)
else:
return bezier((-5, 3), (-3, 3), (0, 4), (9, 8), x - (0.75), 0.25)
def paint_canvas(x, y, colors):
"""creates the png file and colors colors it
"""
sys.setrecursionlimit(15000)
padding = 1
point1hat = math.atan((y[3] - y[0])/(x[3] - x[0])) + math.pi
if x[75] - x[0] < 0:
point1hat = math.pi + point1hat
point2hat = math.atan((y[-1] - y[-3])/(x[-1] - x[-3]))
if x[-1] - x[-75] < 0:
point2hat = math.pi + point2hat
closeIt = bezier((x[0],y[0]), point1hat, (x[-1],y[-1]), point2hat) #calls bezier function in order to close the open loop
xnew = x + closeIt[0]
ynew = y + closeIt[1]
canvas = Image.new("RGB",(int(round(max(xnew)- min(xnew)))+2*padding, int(round((max(ynew) - min(ynew))))+2*padding))
pixels = canvas.load()
for i in range(len(xnew)):
pixels[xnew[i]+padding+0, ynew[i]+padding+0] = (255, 255, 255)
imagepath = "images/techtest.png"
canvas.save(imagepath)
centers = findZones(imagepath)
for i in range(len(centers)):
flood(pixels,centers[i], color = colors[i%len(colors)], visited = [])
canvas = canvas.resize((1000,1000), Image.NEAREST)
canvas.save(imagepath)
def test_derivative_multidimensional(self):
np.random.seed(123)
w = np.random.rand(4, 3)
f = lambda t: bezier.bezier(w, t)
g = numdifftools.Jacobian(f)
np.testing.assert_array_almost_equal(np.squeeze(g(.9)),
bezier.bezier_deriv(w, .9))
def test_second_derivative_multidimensional(self):
np.random.seed(123)
w = np.random.rand(4, 3)
f = lambda t: bezier.bezier(w, t)
g2 = [numdifftools.Derivative((lambda t: f(t)[i]), n=2)(.9)
for i in range(len(w[0]))]
g2 = np.squeeze(g2)
np.testing.assert_array_almost_equal(g2,
bezier.bezier_second_deriv(w, .9))
def plot_bezier_curve(control_points, **kwargs):
colors = default_style_colors()
x, y = list(zip(*control_points))
times = np.linspace(0, 1, num=1000)
curve = [bezier(control_points, t) for t in times]
curve_x, curve_y = zip(*curve)
plot_kwargs = {"color": colors[1], "marker": "o"} # set default style
plot_kwargs.update(kwargs)
plt.plot(x, y, **plot_kwargs)
plt.plot(curve_x, curve_y, color=colors[0])
plt.axis(axis_bounds(x, y))
plt.show()
def run_furgale():
bezier_order = 4
bezier_params = np.random.rand(bezier_order, 3)
bezier_params *= 10
bez = lambda t: bezier(bezier_params, t)
bezderiv = lambda t: np.squeeze(numdifftools.Jacobian(lambda tt: bez(tt))(t))
t0 = 1.23
r0 = cayley(bez(t0))
w0 = angular_velocity_from_cayley_deriv(bez(t0), bezderiv(t0))
print 'Params:'
print bezier_params
print 'Rotation'
print r0
print 'Numeric right:', angular_velocity_right(lambda t: cayley(bez(t)), t0)
print 'Analytic global:', w0
print 'Numeric left:', angular_velocity_left(lambda t: cayley(bez(t)), t0)
print 'Analytic local:', np.dot(r0, w0)
def desenha():
global globVector
glClear(GL_COLOR_BUFFER_BIT)
# desenho do quadrado
glBegin(GL_QUADS)
glColor3f(0.75, 0.75, 0.75)
for ponto in quadrado:
glVertex2f(ponto.coord_x, ponto.coord_y)
glEnd()
# desenho dos pontos de controle da curva
if pontos.__len__() > 0:
glPointSize(12.0)
glBegin(GL_POINTS)
glColor3f(1.0, 0.0, 0.0)
for ponto in pontos:
glVertex2f(ponto.coord_x, ponto.coord_y)
glEnd()
# desenho das linhas entre os pontos de controle
if pontos.__len__() > 1:
glBegin(GL_LINE_STRIP)
glColor3f(0.0, 1.0, 1.0)
for ponto in pontos:
glVertex2f(ponto.coord_x, ponto.coord_y)
glEnd()
# desenho da curva de bezier (linhas conectando os pontos computados pelo De Casteljau
glBegin(GL_LINE_STRIP)
glColor3f(1.0, 1.0, 1.0)
globVector = bezier.bezier(pontos, fator)
glEnd()
glPointSize(6.0)
# desenho dos pontos
glBegin(GL_POINTS)
glColor3f(0.0, 1.0, 0.0)
globVector.append(pontos[-1])
for p in globVector:
glVertex2d(p.coord_x, p.coord_y)
glEnd()
# pintura da area delimitada pela curva
poligono = [ponto_b] + [ponto_a] + globVector
glEnable(GL_BLEND)
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA)
# pintura da area delimitada pela curva
glBegin(GL_POLYGON)
glColor4f(0.0,0.0,0.3,0.7)
for p in poligono:
glVertex2d(p.coord_x, p.coord_y)
glEnd()
else:
aux = pontos[0]
glVertex2d(aux.coord_x, aux.coord_y)
glFlush()
Tu_b_mean[1] = 0.1570
Tv_b_mean[1] = 0.0668
Tw_b_mean[1] = 0.0935
#%% test2 (first optimization step) -------------------------------------------
it = 1
# compute input points
[vv_P, ww_P] = multiObjGrad_Rij(uu_b, uu_exp, vv_b, vv_exp, ww_b, ww_exp, vv_P,
ww_P, index_probes, it)
[Tv_0, Tw_0] = multiObjGrad_Ti(Tu_b_mean, 0.1482, Tv_b_mean, 0.0337, Tw_b_mean,
0.0469, Tv_0, Tw_0, it)
# Bezier curves
[uu_0, zuu_0] = bezier(uu_P[:, :, 2], Nsample)
[vv_0, zvv_0] = bezier(vv_P[:, :, 2], Nsample)
[ww_0, zww_0] = bezier(ww_P[:, :, 2], Nsample)
# Write input for test2
numpy.savetxt(os.path.join(test2, 'constant/vvBarInlet'),
numpy.array([zvv_0, vv_0]).T,
header='(',
footer=')',
comments='')
numpy.savetxt(os.path.join(test2, 'constant/wwBarInlet'),
numpy.array([zww_0, ww_0]).T,
header='(',
footer=')',
comments='')
def fit_bezier_1d(ts, ys, bezier_order):
jacobian = np.array([bezier_coefs(t, bezier_order) for t in ts])
residual = np.array([bezier(np.zeros(bezier_order), t) - y for t, y in zip(ts, ys)])
return np.linalg.lstsq(jacobian, -residual)[0]
def evaluate(self, t):
return bezier.bezier(self._controls, t)
def test_derivative(self):
w = np.array([1.7, 2.8, 1.4, -3.6])
f = lambda t: bezier.bezier(w, t)
g = numdifftools.Gradient(f)
np.testing.assert_array_almost_equal(g(.9),
bezier.bezier_deriv(w, .9))
def test_second_derivative(self):
w = np.array([1.7, 2.8, 1.4, -3.6])
f = lambda t: bezier.bezier(w, t)
g2 = numdifftools.Hessdiag(f)
np.testing.assert_array_almost_equal(g2(.9),
bezier.bezier_second_deriv(w, .9))