如何找到凹陷的凹陷点和凹陷点？ [英] how to find a bitangent, point of concavity and center of gravity of concavity?

问题描述

我试图用matlab来找到凹凸不平的区域以及凹面和凹面中心的对应点。
在这里，我有区域边界坐标和位于该区域凸包上的边界坐标。
这个二次曲线将是该区域凸包的线段之一。
如果我缩小凸包，它不会与区域的内部坐标重叠，从而难以识别其他参数。

我也尝试去除该区域的边界点并创建剩余点的凸包。但是船体的形状发生了变化，所以它不能保证获得正确的结果。

请帮助我解决这个问题。

解决方案

1. 曲率中心 https://i.stack.imgur.com/WR8k1.pngalt =曲率中心>

   
   
   

   我很确定我在这里发布了一个关于但现在不能找到它:(所以这里又是这样：把网格的两条相邻线从中点投射出去，在它们相交的地方有曲率中心如果它在网格的内部或外部告诉你关于凸面或使用缠绕规则...

   
   
   

   如果这不是凹面的中心，那么请添加更多关于它的信息......




2. TBN

   
   
   

   正常蓝线（半径）从曲率中心到线连接点使用方向所在的位置。
   
   

   bitangent 垂直于一行和正常

     bitangent = normal x（line.p1- line.p0）
     

   切线垂直于正常和 binormal

     tangent = bitangent x normal 
     

   制作 TBN 矢量单位的。使用你需要的方向来反转它，只需交换矢量中的操作数乘以或乘以 -1 标量。


ol>


I am trying to find the bitangent to a irregular region and corresponding point of concavity and center of concavity using matlab. Here I have the coordinates of boundary of the region and the coordinates of boundary lying on convex hull of the region. This bitangent would be one of the line segments of convex hull of the region. If I shrink the convex hull it is not overlapping with the inner coordinates of the region, making it difficult to identify other parameters.

I have also tried removing the boundary point of the region and creating a convex hull of remaining points. But the shape of the hull changed so it cannot assure the correct result.

Please help me regarding this.

解决方案

1. center of curvature

   I am pretty sure I posted here one answer about this but cant find it now :( so here it is again. Take 2 neighboring lines of the mesh and cast normals from their mid-points. Where they intersect there is the center of curvature. If it is inside or outside the mesh tells you about convexity or use winding rule ...

   if this is not the center of concavity you want then add more info about it ...

2. TBN

   normal is the blue line (radius) it lies on line from center of curvature to line join point use direction you need.

   bitangent is perpendicular to one line and normal

   bitangent = normal x (line.p1-line.p0)
   

   tangent is perpendicular to normal and binormal

   tangent = bitangent x normal
   

   it is good idea to make TBN vector unit ones. Use the direction you need to invert it just swap the operands in vector multiply or multiply vector by -1 scalar.

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