3d 宽度和横截面
您好，
我们有一个角形的 3d 体，它表示为顶点和面的列表。每个面都是一个由 3 个顶点表示的三角形。主体沿 Z 轴（高度）定位。我们想在某些高度进行多次切割。每次切割（垂直于 Z 轴的平面）可能会与主体形成一个或多个横截面（主体可能会分裂成多个分支）。问题是如何找到这些横截面。 另一个问题：如何（有效地）找到物体的最大宽度，即物体表面上具有相同 z 坐标的 2 个点（不一定来自顶点列表），以及它们之间的最大距离？
谢谢
Greetings,
We have a horn-shaped 3d body, which is represented as a list of vertices and faces. Each face is a triangle represented by 3 vertices. The body is positioned along the Z-axis (height). We would like to make several cuts at certain heights. Each cut (a plane perpendicular to the Z- axis) may create one or more cross-sections with the body (the body may split to several branches). The question is how to find those cross-sections.
Another question: how to find (efficiently) the maximum width of the body, i.e. 2 points (not necessarily from the list of vertices) on the surface of the body with the same z-coordinate, and maximum distance between them?
Thank you
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对于第一部分，Z 坐标上三角形（或更好的边）的二元空间划分可以回答哪些三角形（边）被平行于 Z 轴的平面切割。
对于第二部分，我认为只有作为切割多边形顶点的点才需要检查最大宽度。但它很复杂，因为最大宽度不必是任何 Z 坐标区间内的单调（仅升序或仅降序）函数，甚至在原始顶点的 2 个相邻不同 Z 坐标的区间中也不必是单调函数。
For the first part binary space partitioning of triangles (or better edges) on Z coordinate can answer what triangles (edges) are cut with plane parallel to Z-axis.
For second part, I think that only points that are vertices of cutting polygon has to be checked for maximum width. But it is complex since maximum width doesn't have to be monotone (only ascending or only descending) function in any interval of Z-coordinates, not even in interval of 2 adjacent different Z coordinates of original vertices.