螺旋中心轴角 [英] helix central axis angle

问题描述

我在 [x,y,z] 中有 N 个点，这种形状呈螺旋状.是否有可能找到这样一个螺旋的中心轴.这不是以全局X、Y和Z轴

I have N points in [x,y,z] and this kind of takes a helix shape. Is it possible to find the central axis of such a helix. This is not a regular helix with the central axis as either of global X, Y and Z axis

当我绘制曲线时，会以与全局 Z 轴 的特定角度观察.

When I plot the curve looks at a particular angle to the global Z axis.

我的目标是知道中心轴与全局 z 轴的夹角?

My aim is to know the angle the central axis is making with the global z axis?

推荐答案

如果你的 N 个点足够密集(或等距)，切向向量(连续点的 diff 向量)将形成一个圆锥，其中心方向轴与螺旋轴的方向重合，并且其基平面与该轴方向正交.将螺旋线投影到该法线平面将得到一个以螺旋轴为中心的圆.

If your N points are dense enough (or equi-distant), the tangential vectors (diff vectors of consecutive points) will form a cone whose direction of the center axis coincides with direction of the helix axis and whose base plane is orthogonal to this axis direction. A projection of the helix into this normal plane will give a circle with a center on the helix axis.

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