Check if point lies on a line (2D)

point_lies_on_line_2d.c

// checks whether a point lies on a line (2D)
// l1_x, l1_y -> line's first point
// l2_x, l2_y -> line's second point
// p_x, p_y -> point of interest
// w -> output indicating the weight of the point
// returns 1 if point lies on the line, 0 if not
// https://gist.github.com/felipeek/93c873395506868e50ea6f2323eb3399
int point_lies_on_line_2d(float l1_x, float l1_y, float l2_x, float l2_y, float p_x, float p_y, float* w) {
	const float EPSILON = 0.000001f;
	int vertical_line = (l1_x - l2_x) > -EPSILON && (l1_x - l2_x) < EPSILON; // vertical line
	int horizontal_line = (l1_y - l2_y) > -EPSILON && (l1_y - l2_y) < EPSILON; // horizontal line

	if (vertical_line && horizontal_line) {	// degenerate case -> line is composed of a single point
		if (((p_x - l1_x) > -EPSILON && (p_x - l1_x) < EPSILON) &&
			((p_y - l1_y) > -EPSILON && (p_y - l1_y) < EPSILON)) {
			// in this case, 'w' has no real meaning
			*w = 0.5f;
			return 1;
		}
	}

	if (vertical_line) { // vertical line
		if ((p_x - l1_x) > -EPSILON && (p_x - l1_x) < EPSILON) { // p also lies on same line?
			float alpha = (p_y - l1_y) / (l2_y - l1_y);
			if (alpha < 0.0f || alpha > 1.0f) {
				return 0;
			}
			*w = alpha;
			return 1;
		}
		
		return 0;
	}

	if (horizontal_line) { // horizontal line
		if ((p_y - l1_y) > -EPSILON && (p_y - l1_y) < EPSILON) { // p also lies on same line?
			float alpha = (p_x - l1_x) / (l2_x - l1_x);
			if (alpha < 0.0f || alpha > 1.0f) {
				return 0;;
			}
			*w = alpha;
			return 1;
		}
		
		return 0;
	}

	// general case
	float alpha_x = (p_x - l1_x) / (l2_x - l1_x);
	if (alpha_x < 0.0f || alpha_x > 1.0f) {
		return 0;
	}
	float alpha_y = (p_y - l1_y) / (l2_y - l1_y);
	if (alpha_y < 0.0f || alpha_y > 1.0f) {
		return 0;
	}

	float alpha_diff = alpha_x - alpha_y;
	if (alpha_diff > -EPSILON && alpha_diff < EPSILON) {
		*w = alpha_x;
		return 1;
	}

	return 0;
}