Math Is Fun Forum

You can 'solve a math problem"...

Here is what someone did elsewhere, but did not take the values from the survey and plug them into the  W, L, R, etc. (I do not know myself).  Do you understand it?

    abs(W) = L / R
    (A + W) modulo 2pi ≡ arctangent((Ey-Cy) / (Ex-Cx));

Use both equations to get the right value for W.

So it looks like you have or can calculate:

   S = starting point of the arc.
   E = ending point of the arc,
   R = radius of the arc (so it must be a section of circle)
   L = arc length.

Skia needs C, the center of the circle that the arc is part of.  From the definintion of a circle:

    distance(C, S) = R
    distance(C, E) = R

    (Cx-Sx)^2 + (Cy-Sy)^2 = R^2
    (Cx-Ex)^2 + (Cy-Ey)^2 = R^2

Solve for C = {Cx,Cy}.  Throw one answer away.

Skia also needs the start angle A and the sweep W.

    A = arctangent((Sy-Cy) / (Sx-Cx)) ;
    W = arctangent((Ey-Cy) / (Ex-Cx)) - A;

The bounding rectangle of the circle is  {Cx-R,Cy-R,Cx+R,Cy+R}

    SkPath path;

    path.arcTo({Cx-R,Cy-R,Cx+R,Cy+R}, radian2degree(A), radian2degree(W), false);

Yes...I posted in this forum because it is called "Coder's Corner', and it is Math, and I would expect that there is Geo\Gis expertise.  I would be grateful if someone could translate the survey curve information posted in the link (first posting here), into what the Skiasharp arcTo function is looking for...

https://developer.xamarin.com/api/member/SkiaSharp.SKPath.ArcTo/p/SkiaSharp.SKRect/System.Single/System.Single/System.Boolean/

public Void ArcTo (SKRect oval, Single startAngle, Single sweepAngle, Boolean forceMoveTo)

oval The bounding oval defining the shape and size of the arc.
startAngle The starting angle (in degrees) where the arc begins.
sweepAngle The sweep angle (in degrees) measured clockwise.
forceMoveToWhether to always begin a new contour with the arc.

https://www.xamarin.com/ - It used to be called Mono (using c# cross-platform, develop on Windows, Android, iOS).  Bought by Microsoft last year.  Stand alone Studio product for Android and IOS, or, now part of Visual Studio, for Windows, Android, IOS development.  You can use C# to target individual (Native) OS's, or, use Xamarin Forms and write one program that can target them all.

Lot's of views, no replies.  Should I post this elsewhere (please tell me where to go...figuratively )?