[abenedik]

For such general 3D graphics problems, it is best to search the internet for the anwser.

For example, I found an answer to your question on stackoverflow (https://stackoverflow.com/questions/2316...ne-segment) - on answer mentioned the code on https://bloodstrawberry.tistory.com/1037

I have updated the code to work with WPF 3D objects (Point3D and Vector3D):

Code:

public double GetDistanceTwoLine(Point3D A, Point3D B, Point3D C, Point3D D)
{
    Vector3D AB = A - B;
    Vector3D CD = C - D;
    Vector3D AC = A - C;
    Vector3D line = Vector3D.CrossProduct(AB, CD);

    return Math.Abs(Vector3D.DotProduct(AC, line)) / line.Length;
}

public Point3D GetContactPoint(Vector3D normal, Point3D planeDot, Point3D A, Point3D B)
{
    Vector3D nAB = B - A;
    nAB.Normalize();

    return A + nAB * Vector3D.DotProduct(normal, planeDot - A) / Vector3D.DotProduct(normal, nAB);
}

public (Point3D point1, Point3D point2) GetShortestPath(Point3D A, Point3D B, Point3D C, Point3D D)
{
    Vector3D AB = A - B;
    Vector3D CD = C - D;
    Vector3D line = Vector3D.CrossProduct(AB, CD);
    Vector3D crossLineAB = Vector3D.CrossProduct(line, AB);
    Vector3D crossLineCD = Vector3D.CrossProduct(line, CD);

    return (GetContactPoint(crossLineAB, A, C, D), GetContactPoint(crossLineCD, C, A, B));
}