给定3分，我该如何计算法向矢量? [英] Given 3 points, how do I calculate the normal vector?

问题描述

给出三个3D点(A，B和C)，如何计算法向矢量?这三个点定义了一个平面，我希望向量垂直于该平面.

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.

我可以获取演示此内容的示例C#代码吗?

Can I get sample C# code that demonstrates this?

推荐答案

这取决于要点的顺序.如果从法线相反的方向按逆时针方向指定点，则计算起来很简单:

It depends on the order of the points. If the points are specified in a counter-clockwise order as seen from a direction opposing the normal, then it's simple to calculate:

Dir = (B - A) x (C - A)
Norm = Dir / len(Dir)

其中x是叉积.

如果您使用的是OpenTK或XNA(可以访问Vector3类)，则只需考虑以下问题:

If you're using OpenTK or XNA (have access to the Vector3 class), then it's simply a matter of:

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;
        }
    }
}

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