有限同情段的错误

Question

我正在与一个具有 12 个线段的平面相交，这些线段代表立方体的边。我遇到的问题是所有的交点都产生一个点，即使这个点不应该是线段的一部分，因为它们应该是有限的，对吧？

代码：

from sympy import Point3D, Plane, intersection, Segment3D

# Cube's vertices
v = (Point3D(500, 500, 500), Point3D(-500, 500, 500), Point3D(-500, -500, 500),
     Point3D(500, -500, 500), Point3D(500, 500, -500), Point3D(-500, 500, -500),
     Point3D(-500, -500, -500), Point3D(500, -500, -500))
# Cube´s edges
a = (Segment3D(v[0], v[1]), Segment3D(v[1], v[2]),
     Segment3D(v[2], v[3]), Segment3D(v[3], v[0]),
     Segment3D(v[0], v[4]), Segment3D(v[1], v[5]),
     Segment3D(v[2], v[6]), Segment3D(v[3], v[7]),
     Segment3D(v[4], v[5]), Segment3D(v[5], v[6]),
     Segment3D(v[6], v[7]), Segment3D(v[7], v[4]))

# Example plane which should generate 3 points
plano = Plane(Point3D(450, 400, 400), Point3D(400, 450, 400), Point3D(400, 400, 450))

bad = []
good = []
for i in range(12):
    inter = intersection(plano, a[i])
    # This should be executed when the intersection generates anything, but is always executed:
    if inter:
        bad.append(inter[0])
        # This comparation should not be necessary, checks if point is in range desired
        if abs(inter[0][0]) <= 500 and abs(inter[0][1]) <= 500 and abs(inter[0][2]) <= 500: 
            good.append(inter[0])

print(len(bad), bad)
print(len(good), good)

输出：

12 [Point3D(250, 500, 500), Point3D(-500, 1250, 500), Point3D(1250, -500, 500), Point3D(500, 250, 500), Point3D(500, 500, 250), Point3D(-500, 500, 1250), Point3D(-500, -500, 2250), Point3D(500, -500, 1250), Point3D(1250, 500, -500), Point3D(-500, 2250, -500), Point3D(2250, -500, -500), Point3D(500, 1250, -500)]
3 [Point3D(250, 500, 500), Point3D(500, 250, 500), Point3D(500, 500, 250)]

12 个点中有 9 个不属于任何线段

Answer 1

目前这是一个错误（在 sympy 1.4 或早期版本中），将在 1.5 版本中修复。 https://github.com/sympy/sympy/pull/16637

Answer 2

这已在 SymPy master 上修复，但修复尚未在发布版本中。在 master 上我得到：

3 [Point3D(250, 500, 500), Point3D(500, 250, 500), Point3D(500, 500, 250)]
3 [Point3D(250, 500, 500), Point3D(500, 250, 500), Point3D(500, 500, 250)]

（我假设这就是您所期望的）

有限同情段的错误

Bug with finite sympy segments

geometry

linear-algebra

sympy