how to get the point in ellipse?

Question

I have ellipse and one point. I know the cener (x,y) and the point (x1,y1) how to get the point of S?

Answer 1

Hi, @mc
Use ellipse

and line.
point 1 and point c are known points. In question, it is x1,y1 x,y

So:

#include <iostream>
#include <cmath>
#include <vector>

struct Point {
    double x, y;
};


Point findIntersection(double ellipseX, double ellipseY, double MajorAxis, double MinorAxis, double x1, double y1) {
    std::vector<Point> intersections;

    // cal delta_x , delta_y
    double dx = x1 - ellipseX;
    double dy = y1 - ellipseY;

    
    double A = (dx * dx) / (MajorAxis * MajorAxis) + (dy * dy) / (MinorAxis * MinorAxis);

    if (A <= 1) {
        
        std::cout << "the point is inside or on an ellipse\n";
        return Point(x1, y1);
    }

    
    double t1 = std::sqrt(1.0 / A);
    double t2 = -t1;

    //two intersections
    intersections.push_back({ ellipseX + t1 * dx, ellipseY + t1 * dy });
    intersections.push_back({ ellipseX + t2 * dx, ellipseY + t2 * dy });

    for (const auto& intersection : intersections) {
      
        if ((intersection.x - x1) * (ellipseX - intersection.x) >= 0 &&
            (intersection.y - y1) * (ellipseY - intersection.y) >= 0) {
            std::cout << "Intersection: (" << intersection.x << ", " << intersection.y << ")\n";
            return   intersection;
        }
    }
    
}

int main() {
  
    double ellipseX = 0.0, ellipseY = 0.0; // center
    double MajorAxis = 5.0, MinorAxis = 3.0;   
    double pX = 6.0, pY = 0.0; // point

   
    Point intersection = findIntersection(ellipseX, ellipseY, MajorAxis, MinorAxis, pX, pY);
    
    return 0;
}

Best regards,

Minxin Yu

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