检查点是否严格位于三角形内 [英] Check whether Point lies strictly inside the triangle

问题描述

给出三角形 ABC 的顶点的3个积分坐标和另一个 P 的积分坐标，如何检查 P 是否严格位于三角形内还是不?

Given 3 integral coordinates of vertices of Triangle ABC and another integral coordinate P, how do I check if P strictly lies inside the triangle or not ?

我知道如何使用Area方法检查 P 是否在三角形内，即Area ABC = Area ABP + Area ACP +区域 BCP .
但是在这个问题上，我希望P严格位于三角形内.

I know how to check if P is inside triangle or not using Area method i.e, Area ABC = Area ABP + Area ACP + Area BCP.
But In this question, I want to P to be strictly inside the triangle.

推荐答案

有很多方法可以检查点是否位于三角形内.我认为最简单的方法是:

There is lot approaches to check whether point lies inside triangle. The simplest ones, I think:

1)检查点是否在所有边的同一侧(边向量和顶点点向量AB x AP, BC x BP, CA x CP的叉积的正负号)

1) Check whether point is on the same side of all edges (find signs of cross products for edge vectors and vertex-point vectors AB x AP, BC x BP, CA x CP)

2)用AB和AC向量表示AP向量-系数及其和应在0..1范围内.德尔福代码:

2) Represent AP vector in basis of AB and AC vectors - coefficients and their sum should be in range 0..1. Delphi code:

function PtInTriangle(ax, ay, bx, by, cx, cy, px, py: Integer): Boolean;
var
  xb, yb, xc, yc, xp, yp, d: Integer;
  bb, cc, oned: Double;
begin
  Result := False;
  xb := bx - ax;
  yb := by - ay;
  xc := cx - ax;
  yc := cy - ay;
  xp := px - ax;
  yp := py - ay;
  d := xb * yc - yb * xc;
  if d <> 0 then begin
    oned := 1 / d;
    bb := (xp * yc - xc * yp) * oned;
    cc := (xb * yp - xp * yb) * oned;
    Result := (bb > 0) and (cc > 0) and (cc + bb < 1);
  end;
end;

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