Is a point inside a triangle? Ported in C from http://totologic.blogspot.com/2014/01/accurate-point-in-triangle-test.html

isintriangle.c

#include <stdio.h>
#include <math.h>

// ported in C from http://totologic.blogspot.com/2014/01/accurate-point-in-triangle-test.html?m=1
// really really really thank you!
// compile with -lm (math library)

#define EPSILON 0.00001

const static float epsilon = EPSILON;
const static float epsilon2 = EPSILON*EPSILON;

float side(float x1, float y1, float x2, float y2, float x, float y) {
	return (y2-y1)*(x-x1)+(-x2+x1)*(y-y1);
}

int naivePointInTriangle(float x1, float y1, float x2, float y2, float x3, float y3, float x, float y) {
	if((side(x1, y1, x2, y2, x, y) >= 0) && (side(x2, y2, x3, y3, x, y) >= 0) && (side(x3, y3, x1, y1, x, y) >= 0)) return 1;
	
	return 0;
}

int pointInTriangleBoundingBox(float x1, float y1, float x2, float y2, float x3, float y3, float x, float y) {
	float xMin, xMax, yMin, yMax;
	
	xMin = fminf(x1, fminf(x2, x3)) - epsilon;
	xMax = fmaxf(x1, fmaxf(x2, x3)) + epsilon;
	yMin = fminf(y1, fminf(y2, y3)) - epsilon;
	yMax = fmaxf(y1, fmaxf(y2, y3)) + epsilon;
	
	if(x < xMin || xMax < x || y < yMin || yMax < y ) return 0;
	
	return 1;
}

float distanceSquarePointToSegment(float x1, float y1, float x2, float y2, float x, float y) {
	float p1_p2_squareLength, dotProduct, p_p1_squareLength;
	
	p1_p2_squareLength = (x2 - x1) * (x2 - x1) + (y2 - y1)*(y2 - y1);
	dotProduct = ((x - x1)*(x2 - x1) + (y - y1)*(y2 - y1)) / p1_p2_squareLength;
	
	if(dotProduct < 0) {
		return (x - x1) * (x - x1) + (y - y1) * (y - y1);
	}
	if (dotProduct <= 1) {
		p_p1_squareLength = (x1 - x) * (x1 - x) + (y1 - y) * (y1 - y);
		return p_p1_squareLength - dotProduct * dotProduct * p1_p2_squareLength;
	}
	return (x - x2) * (x - x2) + (y - y2) * (y - y2);
}

int accuratePointInTriangle(float x1, float y1, float x2, float y2, float x3, float y3, float x, float y) {
	if(!pointInTriangleBoundingBox(x1, y1, x2, y2, x3, y3, x, y)) return 0;
	if(naivePointInTriangle(x1, y1, x2, y2, x3, y3, x, y)) return 1;
	if(distanceSquarePointToSegment(x1, y1, x2, y2, x, y) <= epsilon2) return 1;
	if(distanceSquarePointToSegment(x2, y2, x3, y3, x, y) <= epsilon2) return 1;
	if(distanceSquarePointToSegment(x3, y3, x1, y1, x, y) <= epsilon2) return 1;
	
	return 0;
}

int main() {
	float x1, y1, x2, y2, x3, y3, x, y;
	
	// testo un triangolo rettangolo
	x1=100; y1=100; x2=100; y2=200; x3=200; y3=100;
	x=150; y=150;
	//x=150; y=150.00001;
	
	printf("XY point is into the triangle with vertex x1.y1, x2.y2, x3.y3? Response: %s\n", accuratePointInTriangle(x1,y1,x2,y2,x3,y3,x,y) ? "yes" : "no");
	
	return 0;
}