循环表示二维三角形中的点

Question

我在Python中有一个函数，可以查找点是否在二维三角形中，如下所示：

def isInsideTriangle(P,p1,p2,p3): #is P inside triangle made by p1,p2,p3?
    x,x1,x2,x3 = P[0],p1[0],p2[0],p3[0]
    y,y1,y2,y3 = P[1],p1[1],p2[1],p3[1]
    full = abs (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))
    first = abs (x1 * (y2 - y) + x2 * (y - y1) + x * (y1 - y2))
    second = abs (x1 * (y - y3) + x * (y3 - y1) + x3 * (y1 - y))
    third = abs (x * (y2 - y3) + x2 * (y3 - y) + x3 * (y - y2))
    return abs(first + second + third - full) < .0000000001

我的"p"是一堆（大约15个）点，它们来自这个（部分）文件：

PointXY
[387.9385, 200.0]
PointXY
[200.0, 387.9385]
PointXY
[200.0, 387.9385]
PointXY
[200.0, 353.2089]
PointXY

我的p1、p2和p3是三角形中的角坐标。它们来自这个（部分）文件：

TriangleXY
[193.0371, 0.1218346]
[193.0244, 0.1218346]
[186.0572, 0.4871899]
TriangleXY
[206.9799, 0.1218346]
[206.9756, 0.1218346]
[213.9428, 0.4871899]
TriangleXY
[193.0244, 0.1218346]
[193.0371, 0.1218346]
[200.0, 0.0]
TriangleXY
[206.9756, 0.1218346]

我想让我的脚本做的是，如果任何一个点在任何一个三角形中（或边上），返回三角形p1、p2和p3的（3）个特定坐标，以及其中的特定点p。它现在只适用于一个p和一组p1、p2、p3，我希望它适用于所有的点p和所有的三角形角p1、p2以及p3。有人知道如何在我的脚本中相应地调整这个吗？我的P和p1、p2和p3由以下脚本调用：

# triangle coordinates p1 p2 p3
g = open("spheretop1.stl", "r")
m = open("TriangleXYcoordinates.gcode", "w")
searchlines = g.readlines()
file = ""
for i, line in enumerate(searchlines):
    if "outer loop" in line:
        p1 = map(float, searchlines[i+1].split()[1:3])
        p2 = map(float, searchlines[i+2].split()[1:3])
        p3 = map(float, searchlines[i+3].split()[1:3])
        m.write("TriangleXY" + "n" + str(p1) + "n" + str(p2) + "n" + str(p3) + "n")
# Point coordinates P
import json
h = open("PointXYcoordinates.gcode", "r")
searchlines = h.readlines()
file = ""
for i, line in enumerate(searchlines):
    if "PointXY" in line:
        P = json.loads(searchlines[i+1].strip())

Answer 1

也许你想要这样的东西：

def pointsInsideTriangles(points,triangles):
    for (P in points):
        for (t in triangles):
            if isInsideTriangle(P,t[0],t[1],t[2]):
                print("Point " + str(P) + " is inside traingle " + str(t))

总之，你会得到这样的东西：

def isInsideTriangle(P,p1,p2,p3): #is P inside triangle made by p1,p2,p3?
    x,x1,x2,x3 = P[0],p1[0],p2[0],p3[0]
    y,y1,y2,y3 = P[1],p1[1],p2[1],p3[1]
    full = abs (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))
    first = abs (x1 * (y2 - y) + x2 * (y - y1) + x * (y1 - y2))
    second = abs (x1 * (y - y3) + x * (y3 - y1) + x3 * (y1 - y))
    third = abs (x * (y2 - y3) + x2 * (y3 - y) + x3 * (y - y2))
    return abs(first + second + third - full) < .0000000001
def pointsInsideTriangles(points,triangles):
    for (P in points):
        for (t in triangles):
            if isInsideTriangle(P,t[0],t[1],t[2]):
                print("Point " + str(P) + " is inside triangle " + str(t))

# triangle coordinates p1 p2 p3
points = [];
triangles = [];
g = open("spheretop1.stl", "r")
m = open("TriangleXYcoordinates.gcode", "w")
searchlines = g.readlines()
file = ""
for i, line in enumerate(searchlines):
    if "outer loop" in line:
        p1 = map(float, searchlines[i+1].split()[1:3])
        p2 = map(float, searchlines[i+2].split()[1:3])
        p3 = map(float, searchlines[i+3].split()[1:3])
        m.write("TriangleXY" + "n" + str(p1) + "n" + str(p2) + "n" + str(p3) + "n")
        triangles.append([p1,p2,p3])

# Point coordinates P
import json
h = open("PointXYcoordinates.gcode", "r")
searchlines = h.readlines()
file = ""
for i, line in enumerate(searchlines):
    if "PointXY" in line:
        P = json.loads(searchlines[i+1].strip())
        points.append(P)
pointsInsideTriangles(points,triangles)