使用Newell方法在Python中计算表面法线 [英] Calculating surface normal in Python using Newell's Method

问题描述

我正在尝试基于这里.

Begin Function CalculateSurfaceNormal (Input Polygon) Returns Vector

   Set Vertex Normal to (0, 0, 0)

   Begin Cycle for Index in [0, Polygon.vertexNumber)

      Set Vertex Current to Polygon.verts[Index]
      Set Vertex Next    to Polygon.verts[(Index plus 1) mod Polygon.vertexNumber]

      Set Normal.x to Sum of Normal.x and (multiply (Current.y minus Next.y) by (Current.z plus Next.z))
      Set Normal.y to Sum of Normal.y and (multiply (Current.z minus Next.z) by (Current.x plus Next.x))
      Set Normal.z to Sum of Normal.z and (multiply (Current.x minus Next.x) by (Current.y plus Next.y))

   End Cycle

   Returning Normalize(Normal)

End Function

这是我的代码:

Point3D = collections.namedtuple('Point3D', 'x y z')

def surface_normal(poly):
    n = [0.0, 0.0, 0.0]

    for i, v_curr in enumerate(poly):
        v_next = poly[(i+1) % len(poly)]
        n[0] += (v_curr.y - v_next.y) * (v_curr.z - v_next.z)
        n[1] += (v_curr.z - v_next.z) * (v_curr.x - v_next.x)
        n[2] += (v_curr.x - v_next.x) * (v_curr.y - v_next.y)

    normalised = [i/sum(n) for i in n]

    return normalised

def test_surface_normal():
    poly = [Point3D(0.0, 0.0, 0.0),
            Point3D(0.0, 1.0, 0.0),
            Point3D(1.0, 1.0, 0.0),
            Point3D(1.0, 0.0, 0.0)]

    assert surface_normal(poly) == [0.0, 0.0, 1.0]

这在归一化步骤中失败，因为此时的 n 为 [0.0，0.0，0.0] .如果我理解正确，则应为 [0.0，0.0，1.0] (

This fails at the normalisation step since the n at that point is [0.0, 0.0, 0.0]. If I'm understanding correctly, it should be [0.0, 0.0, 1.0] (confirmed by Wolfram Alpha).

我在这里做错了什么?还有在python中计算表面法线的更好方法吗?我的多边形将始终是平面的，因此如果有其他方法，则不一定要使用Newell的方法.

What am I doing wrong here? And is there a better way of calculating surface normals in python? My polygons will always be planar so Newell's Method isn't absolutely necessary if there's another way.

推荐答案

好，这个问题实际上是一个愚蠢的问题.

Ok, the problem was actually a stupid one.

像这样的行:

n[0] += (v_curr.y - v_next.y) * (v_curr.z - v_next.z)

应为:

n[0] += (v_curr.y - v_next.y) * (v_curr.z + v_next.z) 

第二组括号中的值应加而不是减.

The values in the second set of brackets should be added, not subtracted.

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