How to get a parabola shape according to a moved point and nearest points-CodePudding

Being not very good at math, I have a problem with my project.

The objective is boundary correction on 3D files.

In my application, the user moves a 3D point on X-axis in order to correct or modify the boundary of the object.

I want to move the nearest boundary points in the same direction but decreasingly. I mean no point should move more than the main point. The nearest points move most and, the farthest points should move less.

On the image, the red dots represent the initial status of points. And the user pulls the P0 in the x-direction. And the other points follow it. The last status of the points is represented by violet dots.

Here is what I tried.

        //On point moved event

        //Get nearest boundary Points (Uses Geometry3D to get boundary points).
        (var clothDMesh, _) = Utilities3D.BuildDMesh(baseMesh);
        CreateClothModel(clothDMesh);

        var boundryVertices = nodes.Where(ro => ro.Value.isBorder).Select(ro => ro.Value.vertex).ToList();

        var refPoint = CustomPoint.FromPoint3D(movedPoint);

        //Gets the delta X.
        var deltaX = p.X - initialX;
        
       //Gets nearest country points, so 15 points above and 15 points below to move only a given number of points (I know maybe this should be calculated according to delta).
       var nearestPoints = refPoint.GetNearesPoints(boundryVertices, 30);

        foreach (var item in nearestPoints)
        {
           //This is only one of what I tried as a function. None of them worked correctly.
           item.X  = deltaX - (deltaX * 1/ Math.Pow(item.Distance, 2));
        }

Any help will be appreciated.

Thanks in advance.

CodePudding user response：

Here's the math part: I call "a" your "deltaX". We also need a second parameter: "b", the maximum height of the red dots. I assume it is symetrical and "-b" would be the minimum height of the red dots.

So, if you look for the value X, horizontal move, in fonction of the coordinate Y of the dot:

X = a - a * Y * Y / (b * b);

You can verify that for Y = 0, you obtain X = a and for Y = b (or -b) you get X = 0. You have your parabola (X is function of Y^2).