2d algorithm used to determine whether a vertex is in a certain triangle

Given A point of p (x0, y0) on the plane, determine whether the point is in the Triangle ABC. The vertex coordinates of the triangle are A (xa, xb), B (xb, yb ), C (xc, yc ). You can use the area method to determine the area. The method S (A, B, C) indicates the area of the Triangle ABC.
1. If abs (S (A, B, C) = abs (S (P, B, C) + abs (S (A, P, C )) + abs (S (A, B, P), P is inside or beside the Triangle ABC; if there is abs (S (P, B, C )) abs (S (A, P, C) and abs (S (A, B, P) are all greater than 0, it means that P is inside the Triangle ABC, otherwise P is on the edge of the Triangle ABC, specifically: S (P, B, C) is 0, it means P is on the edge of BC, S (A, P, C) is 0, P is on the AC side, S (A, B, P) is 0, and P is on the AB side;
2. If abs (S (A, B, C) <abs (S (P, B, C) + abs (S (A, P, C )) + abs (S (A, B, P), P is outside the Triangle ABC;
3. for abs (S (A, B, C)> abs (S (P, B, C) + abs (S (A, P, C )) + abs (S (A, B, P) does not exist theoretically.

How can we find the area of a triangle in a plane? This can be achieved using the cross multiplication, that is, S (A, B, C) is 1/2 of the Vector Model Obtained by the vector AB cross multiplication AC, then the absolute value is the area of the Triangle ABC.

 # Include <iostream> <br/> # include <math. h> <br/> using namespace std; </p> <p> # define ABS_FLOAT_0 0.0001 </p> <p> struct point_float <br/>{< br/> float x; <br/> float y; <br/> }; </p> <p>/** <br/> * @ brief calculate the Triangle Area <br/> */<br/> float GetTriangleSquar (const point_float pt0, const point_float pt1, const point_float pt2) <br/>{< br/> point_float AB, BC; <br/> AB. x = pt1.x-pt0.x; <br/> AB. y = pt1.y-pt0.y; <br/> BC. x = pt2.x-pt1.x; <br/> BC. y = pt2.y-pt1.y; <br/> return fabs (AB. x * BC. y-AB. y * BC. x)/2.0f; <br/>}</p> <p>/** <br/> * @ brief: determines whether a given point is within or on the triangle. <br/> */<br/> bool IsInTriangle (const point_float, const point_float B, const point_float C, const point_float D) <br/>{< br/> float SABC, SADB, SBDC, SADC; <br/> SABC = GetTriangleSquar (, b, C); <br/> SADB = GetTriangleSquar (A, D, B); <br/> SBDC = Ge TTriangleSquar (B, D, C); <br/> SADC = GetTriangleSquar (A, D, C); </p> <p> float SumSuqar = SADB + SBDC + SADC; </p> <p> if (-ABS_FLOAT_0 <(SABC-SumSuqar) & (SABC-SumSuqar) <ABS_FLOAT_0 )) <br/>{< br/> return true; <br/>}< br/> else <br/>{< br/> return false; <br/>}</p> <p> void main (void) <br/>{< br/> point_float A, B, C, P; <br/>. x =. y = 1.0; <br/> B. x = 4.0; <br/> B. y = 1.0; <br/> C. x = 2.0; <Br/> C. y = 5.0; <br/> P. x = 3.0; <br/> P. y = 2.0; </p> <p> if (IsInTriangle (A, B, C, P )) <br/>{< br/> cout <"P is in ABC! "<Endl; <br/>}< br/> else <br/> {<br/> cout <" P is not in ABC! "<Endl; <br/>}< br/>}