如何从 x,y 点列表和偏移距离获取偏移样条线的 x,y 坐标

我需要制作翼型轮廓曲线的偏移平行封闭体，但我无法弄清楚如何使所有点与主轮廓曲线上所需距离的点等距。

this is my example airfoil profile

this is my best and not good approach

EDIT @Patrick Solution for distance 0.2

您必须处理无穷大/零的特殊情况斜率，但基本方法是使用插值来计算某个点的斜率，然后找到垂直斜率，然后计算该距离处的点。

我已经修改了示例here添加第二个图表。它与您提供的数据文件，但您可能需要更改不同包络的符号计算。

EDIT根据您关于希望信封连续的评论，我在末尾添加了一个俗气的半圆，得到非常接近为你做这件事。本质上，在创建信封时，你可以把它做得越圆、越凸，效果就越好。另外，你需要重叠开头和结尾，否则就会有间隙。

而且，它几乎肯定可以变得更加高效——无论如何，我都不是 numpy 专家，所以这只是纯 Python。

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()