多个二维截面的三角测量
我有多个由 y 和 z 方向上的点构建的二维多边形，每个“面”都位于坐标 x 处。我想将其显示为实体模型，因此需要对各部分之间的点进行三角测量。
如果点分布均匀并且每个部分上的点数量相等，那么这会很容易。但事实并非如此。 一个部分可以有 4 个点，下一个部分可以有 32 个点。有谁知道有什么算法或方法可以做到这一点吗？ 我附上了一张图片，显示了横截面的外观。
I have multiple 2d polygons built up from points in y and z direction, each of these "faces" are located at a cordinate x. I want to show this as a solid model and therefor need to triangulate the points between the sections.
This would be easy if the points were evenly distributed and there were equal amounts of points on each section. But that is not the case.
One section can have 4 points, and the next can have 32. Does anyone know of any algorithms or methods to do this?
I attached a picture that shows how the cross sections can look.
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对于平行切片的情况，您可以查看 Boissonnat, Geiger 1993 对于一般情况，本文参考了其他作品 Boissonnat，Memari。 2007 年。
For the case of parallel slices, you can have a look at Boissonnat, Geiger 1993 and for the general case, this paper with references to other works Boissonnat, Memari. 2007.
一种解决方案是创建一个将截面点展开到平面上的变换，使用 Delaunay 三角剖分对这些点进行三角剖分，然后将三角形包络回坐标系中。在给定的示例中，您可以通过取每个截面上的重心或平均坐标，并使用到该点的距离和到该点的方位作为开发坐标来径向开发点。这是我以前见过的一种对隧道内部进行三角测量的方法。
One solution is to create a transformation that develops the section points onto a plane, use a Delaunay triangulation to triangulate these points, and then envelop the triangles back into your co-ordinate system. In the sample given, you could develop the points radially by taking the centre of gravity or mean coordinate on each section, and using the distance to this point and bearing to this point as your developed coordinates. This is a method I've seen before to triangulate the inside of tunnels.