三维线路交叉口代码无法正常工作 [英] 3d line-intersection code not working properly

问题描述

我创建了这段代码来获得两个3d线段的交集。

不幸的是，这段代码的结果是不准确的，交叉点并不总是在两条线上。

这是我的代码：

   -  dir =方向
 --p1，p2 =表示行
函数GetIntersection（dirStart，dirEnd，p1，p2）
本地s1_x，s1_y，s2_x， s2_y = dirEnd.x  -  dirStart.x，dirEnd.z  -  dirStart.z，p2.x  -  p1.x，p2.z  -  p1.z 
 local div =（ -  s2_x * s1_y）+（s1_x * s2_y）
 
 if div == 0 then return nil end 
 local s =（-s1_y *（dirStart.x  -  p1.x）+ s1_x *（dirStart.z  -  p1.z ））/ div 
 local t =（s2_x *（dirStart.z  -  p1.z） -  s2_y *（dirStart.x  -  p1.x））/ div 
 
 if（s> （t）= 0且s≤1且t≥0且t≤1）和（向量（dirStart.x +（t * s1_x），0，dirStart.z +（t * s1_y））或零）then 
 local v = Vector（dirStart.x +（t * s1_x），0，dirStart.z +（t * s1_y））
 return v 
 end 
结束
  

解决方案

3D中的两条倾斜线之间。出于您的目的，如果足够小的值（交叉点确实存在）检查结果，检查s和t参数在范围0..1中，然后
使用参数s计算点

这种方法的数学描述在最短的一行...部分Paul Bourke页面

VecDiff如果向量差分函数，Dot id标量乘积函数

 函数LineLineDistance（const L0，L1：TLine3D; var s，t：Double）：Double; 
 var 
 u：TPoint3D; 
 a，b，c，d，e，det，invdet：Double; 
 begin 
 u：= VecDiff（L1.Base，L0.Base）; 
 a：=点（L0.Direction，L0.Direction）; 
 b：=点（L0.Direction，L1.Direction）; 
 c：= Dot（L1.Direction，L1.Direction）; 
 d：= Dot（L0.Direction，u）; 
 e：= Dot（L1.Direction，u）; 
 det：= a * c  -  b * b; 
如果det< eps然后
结果：= -1 
 else begin 
 invdet：= 1 / det; 
 s：= invdet *（b * e  -  c * d）; 
 t：= invdet *（a * e  -  b * d）; 
 
结果：=距离（PointAtParam（L0，s），PointAtParam（L1，t））; 
 end; 
 end; 
  

I created this piece of code to get the intersection of two 3d line-segments.

Unfortunately the result of this code is inaccurate, the intersection-point is not always on both lines.

I am confused and unsure what I'm doing wrong.

Here is my code:

--dir = direction
--p1,p2 = represents the line
function GetIntersection(dirStart, dirEnd, p1, p2)
   local s1_x, s1_y, s2_x, s2_y =  dirEnd.x - dirStart.x, dirEnd.z - dirStart.z, p2.x - p1.x, p2.z - p1.z
   local div = (-s2_x * s1_y) + (s1_x * s2_y)

   if div == 0 then return nil end
   local s = (-s1_y * (dirStart.x - p1.x) + s1_x * (dirStart.z - p1.z)) / div
   local t = ( s2_x * (dirStart.z - p1.z) - s2_y * (dirStart.x - p1.x)) / div

   if (s >= 0 and s <= 1 and t >= 0 and t <= 1) and (Vector(dirStart.x + (t * s1_x), 0, dirStart.z + (t * s1_y)) or nil) then
      local v = Vector(dirStart.x + (t * s1_x),0,dirStart.z + (t * s1_y))
      return v
   end
end

解决方案

This is example of Delphi code to find a distance between two skew lines in 3D. For your purposes it is necessary to check that result if small enough value (intersection does exist), check that s and t parameters are in range 0..1, then calculate point using parameter s

Math of this approach is described in 'the shortest line...' section of Paul Bourke page

VecDiff if vector difference function, Dot id scalar product function

function LineLineDistance(const L0, L1: TLine3D; var s, t: Double): Double;
var
  u: TPoint3D;
  a, b, c, d, e, det, invdet:Double;
begin
  u := VecDiff(L1.Base, L0.Base);
  a := Dot(L0.Direction, L0.Direction);
  b := Dot(L0.Direction, L1.Direction);
  c := Dot(L1.Direction, L1.Direction);
  d := Dot(L0.Direction, u);
  e := Dot(L1.Direction, u);
  det := a * c - b * b;
  if det < eps then   
    Result := -1
  else begin
    invdet := 1 / det;
    s := invdet * (b * e - c * d);
    t := invdet * (a * e - b * d);

    Result := Distance(PointAtParam(L0, s), PointAtParam(L1, t));
  end;
end;

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