3d 线交叉代码无法正常工作 [英] 3d line-intersection code not working properly

问题描述

我创建了这段代码来获取两个 3d 线段的交集.

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

不幸的是，这段代码的结果不准确，交点并不总是在两条线上.

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

我很困惑，不确定自己做错了什么.

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

这是我的代码:

--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

推荐答案

这是 Delphi 代码示例，用于查找 3D 中两条斜线之间的距离.为了您的目的，如果值足够小(确实存在交集)，则有必要检查该结果，检查 s 和 t 参数是否在 0..1 范围内，然后使用参数 s 计算点

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

Paul Bourke 页面的最短线..."部分描述了这种方法的数学原理

VecDiff if 向量差分函数，Dot id 标量积函数

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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