C# 给定 3 分，我如何计算法向量？
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Given 3 points, how do I calculate the normal vector?
提问by DenaliHardtail
Given three 3D points (A,B, & C) how do I calculate the normal vector? The three points define a plane and I want the vector perpendicular to this plane.
给定三个 3D 点（A、B 和 C），我如何计算法向量？这三个点定义了一个平面，我希望向量垂直于这个平面。
Can I get sample C# code that demonstrates this?
我可以获得演示这一点的示例 C# 代码吗？
采纳答案by Frank Krueger
It depends on the order of the points. If the points are specified in a counter-clockwise order as seen from a direction opposingthe normal, then it's simple to calculate:
这取决于点的顺序。如果从与法线相反的方向看，以逆时针顺序指定点，那么计算起来很简单：
Dir = (B - A) x (C - A)
Norm = Dir / len(Dir)
where xis the cross product.
哪里x是叉积。
If you're using OpenTK or XNA (have access to the Vector3 class), then it's simply a matter of:
如果您使用的是 OpenTK 或 XNA（可以访问 Vector3 类），那么这只是一个问题：
class Triangle {
Vector3 a, b, c;
public Vector3 Normal {
get {
var dir = Vector3.Cross(b - a, c - a);
var norm = Vector3.Normalize(dir);
return norm;
}
}
}
回答by Steve Emmerson
Form the cross-product of vectors BA and BC. See http://mathworld.wolfram.com/CrossProduct.html.
形成向量 BA 和 BC 的叉积。请参阅http://mathworld.wolfram.com/CrossProduct.html。
回答by Todd Gamblin
You need to calculate the cross productof any two non-parallel vectors on the surface. Since you have three points, you can figure this out by taking the cross product of, say, vectors AB and AC.
您需要计算表面上任意两个非平行向量的叉积。由于您有三个点，因此您可以通过对向量 AB 和 AC 进行叉积来计算。
When you do this, you're calculating a surface normal, of which Wikipedia has a pretty extensive explanation.
当你这样做时，你正在计算一个表面法线，维基百科有一个非常广泛的解释。
