在特殊情況下，坡度為無窮大/零，但基本方法是使用插值計算某個點的坡度，然后找到垂直坡度，然后計算該距離處的點。在

我修改了來自here的示例，以添加第二個圖。它與data file you provided一起工作，但您可能需要更改另一個信封的符號計算。在

編輯根據您關于希望信封連續的評論，我在結尾處添加了一個低俗的半圓，使非常接近?；旧?#xff0c;在創建封套時，越圓越凸，效果越好。另外，你需要把開頭和結尾重疊，否則你會有一個間隙。在

而且，幾乎可以肯定的是，它可以變得更有效率我不是一個numpy專家，所以這只是純Python。在def offset(coordinates, distance):

coordinates = iter(coordinates)

x1, y1 = coordinates.next()

z = distance

points = []

for x2, y2 in coordinates:

# tangential slope approximation

try:

slope = (y2 - y1) / (x2 - x1)

# perpendicular slope

pslope = -1/slope # (might be 1/slope depending on direction of travel)

except ZeroDivisionError:

continue

mid_x = (x1 + x2) / 2

mid_y = (y1 + y2) / 2

sign = ((pslope > 0) == (x1 > x2)) * 2 - 1

# if z is the distance to your parallel curve,

# then your delta-x and delta-y calculations are:

# z**2 = x**2 + y**2

# y = pslope * x

# z**2 = x**2 + (pslope * x)**2

# z**2 = x**2 + pslope**2 * x**2

# z**2 = (1 + pslope**2) * x**2

# z**2 / (1 + pslope**2) = x**2

# z / (1 + pslope**2)**0.5 = x

delta_x = sign * z / ((1 + pslope**2)**0.5)

delta_y = pslope * delta_x

points.append((mid_x + delta_x, mid_y + delta_y))

x1, y1 = x2, y2

return points

def add_semicircle(x_origin, y_origin, radius, num_x = 50):

points = []

for index in range(num_x):

x = radius * index / num_x

y = (radius ** 2 - x ** 2) ** 0.5

points.append((x, -y))

points += [(x, -y) for x, y in reversed(points)]

return [(x + x_origin, y + y_origin) for x, y in points]

def round_data(data):

# Add infinitesimal rounding of the envelope

assert data[-1] == data[0]

x0, y0 = data[0]

x1, y1 = data[1]

xe, ye = data[-2]

x = x0 - (x0 - x1) * .01

y = y0 - (y0 - y1) * .01

yn = (x - xe) / (x0 - xe) * (y0 - ye) + ye

data[0] = x, y

data[-1] = x, yn

data.extend(add_semicircle(x, (y + yn) / 2, abs((y - yn) / 2)))

del data[-18:]

from pylab import *

with open('ah79100c.dat', 'rb') as f:

f.next()

data = [[float(x) for x in line.split()] for line in f if line.strip()]

t = [x[0] for x in data]

s = [x[1] for x in data]

round_data(data)

parallel = offset(data, 0.1)

t2 = [x[0] for x in parallel]

s2 = [x[1] for x in parallel]

plot(t, s, 'g', t2, s2, 'b', lw=1)

title('Wing with envelope')

grid(True)

axes().set_aspect('equal', 'datalim')

savefig("test.png")

show()

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