Draw arc passing in three points

1

Hello I am looking for a function with this header :
double drawArc(cv::Mat& image, const cv::Point& pointA, const cv::Point& pointB, const cv::Point& pointC, const cv::Scalar& color, int thickness);
which draw a circle arc beginning at point A, ending at point B and passing at point C
it return the arc angle in degrees
I have asking chatGPT but it fails to find a solution.
Thank you very much
Best regards

2

finally after fighting 4 hours with chatGPT 4 I obtained the following code which seems to work :

double drawArc(cv::Mat& image, const cv::Point& pointA, const cv::Point& pointB, const cv::Point& pointC, const cv::Scalar& color, int thickness) {
	// Calculer le centre du cercle passant par les trois points
	double ax = pointA.x, ay = pointA.y;
	double bx = pointB.x, by = pointB.y;
	double cx = pointC.x, cy = pointC.y;

	double d = 2.0 * (ax * (by - cy) + bx * (cy - ay) + cx * (ay - by));

	double ux = ((ax * ax + ay * ay) * (by - cy) + (bx * bx + by * by) * (cy - ay) + (cx * cx + cy * cy) * (ay - by)) / d;
	double uy = ((ax * ax + ay * ay) * (cx - bx) + (bx * bx + by * by) * (ax - cx) + (cx * cx + cy * cy) * (bx - ax)) / d;

	cv::Point center(ux, uy);

	// Calculer le rayon du cercle
	double radius = std::hypot(pointA.x - center.x, pointA.y - center.y);

	// Calculer les angles des points par rapport au centre du cercle
	double angleA = std::atan2(pointA.y - center.y, pointA.x - center.x) * 180 / CV_PI;
	double angleB = std::atan2(pointB.y - center.y, pointB.x - center.x) * 180 / CV_PI;
	double angleC = std::atan2(pointC.y - center.y, pointC.x - center.x) * 180 / CV_PI;

	// Ajuster les angles si nécessaire
	if (angleA < 0) angleA += 360;
	if (angleB < 0) angleB += 360;
	if (angleC < 0) angleC += 360;

	// Déterminer l'angle de début et de fin pour le dessin
	double startAngle, endAngle;
	// Organiser les angles dans l'ordre croissant
	std::vector<double> angles = { angleA, angleB, angleC };
	std::sort(angles.begin(), angles.end());

	// Si l'angle de C est l'angle intermédiaire, alors C est entre A et B
	if (angles[1] == angleC) {
		startAngle = angleA;
		endAngle = angleB;
	}
	else {
		// Si non, dessiner l'arc complémentaire
		if (angleA > angleB) {
			startAngle = angleA;
			endAngle = angleB + 360;
		}
		else {
			startAngle = angleA + 360;
			endAngle = angleB;
		}
	}

	// Dessiner l'arc
	cv::ellipse(image, center, cv::Size(radius, radius), 0, startAngle, endAngle, color, thickness);

	// Calculer et retourner l'angle de l'arc
	double arcAngle = endAngle - startAngle;
	if (arcAngle < 0) arcAngle += 360;

	return arcAngle;
}
3

since OpenCV does not have a "fitCircle" (only fitEllipse), this would require solving for the circle parameters manually:

4

OK thank you but what I wanted was not simply draw a circle passing by 3 points but an arc beginning at A, ending at B and passing at C

6

but the code of chatGPT works