Flyinghearts book notes serialized in the beauty of programming (18)

4.4 Is in the Triangle

Geometric questions are often used as vectors. If the P point is inside the triangle, vector PA rotates Three times in a certain direction of the clock after petabytes, PCs, and then returns to Pa. The rotation angle does not exceed 180 degrees each time. That is to say, the Three Vector products of PA × Pb, Pb × PC and PC × PA should be both positive or negative. If P is on the edge of the triangle, one of the three Vector products should be 0, and the other two are both positive and negative. If a vertex is in a triangle, there must be two of the three Vector products, which are 0 and one is not 0. If ABC three-point is collocated and P is in this line, all the Vector products are 0. If P is not in this line, it is two positive, one negative, or two negative and one positive.

 

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Struct point {
Double X;
Double Y;
};

Int direction (const point & A, const point & B, const point & P)
{
Const double zero = 1e-6;
Double TMP = (P. x-a.x) * (p. y-b.y)-(P. x-b.x) * (p. y-a.y );
If (TMP> zero) return 1;
If (TMP <-1 * zero) return 4;
Return 0;
}

Bool is_in_triangle (const point & A, const point & B, const point & C, const point & P)
{
Int T = direction (A, B, P) + direction (B, c, p) + direction (C, A, P );
/*
If (t = 3 | T = 12) return true; // within the Triangle ABC
If (t = 1 | T = 4) return true; // coincides with one of the points A B C
If (t = 2 | T = 8) return true; // It is on the edge of the Triangle ABC.
*/
If (T> = 1 & T <= 4) return true;
If (t = 8 | T = 12) return true;
Return false;

// Within the triangle a [3] = A [12] = 1 on the edge a [2] = A [8] = 1 on the vertex A [1] = A [4] = 1;
// Int A [] = {0, 0, 1, 0, 0, 1 };
// Return a [direction (A, B, P) + direction (B, c, p) + direction (C, A, P)];
}

 

From: http://blog.csdn.net/flyinghearts/archive/2010/05/19/5605993.aspx