Modify a formula from calculating around a circle to around an oval?

Question

I have this formula in a function below. It's a fairly simple concept, yet this formula took me almost 2 weeks to get perfect. What it does is calculates what point to place an object at a given degree around and distance from a central point. It's useful for manually drawing circles, and also I primarily use it for a needle gauge component of mine. It calculates where to draw the needle.

Now I'm trying to figure out how to modify this formula to take ovals or ellipses into account. I did think of the idea of drawing a component a round shape first, and then stretching it after everything's drawn, but this is not a clean solution, as the drawing which I'm doing will already be in the shape of an oval.

I need to add just one parameter to this function to tell it the ratio between the width/height so it knows how to off-set this point. By default, this parameter should be 1, meaning Width=Height, meaning no ovalish drawing or offset. But suppose I put 2, which means width is twice the size of the height, or 1.5 would mean the width is 1.5 times the height.

Here's the original function:

function NewPosition(Center: TPoint; Distance: Integer; Degrees: Single): TPoint;
var
  Radians: Real;
begin
  //Convert angle from degrees to radians; Subtract 135 to bring position to 0 Degrees
  Radians:= (Degrees - 135) * Pi / 180;
  Result.X:= Trunc(Distance*Cos(Radians)-Distance*Sin(Radians))+Center.X;
  Result.Y:= Trunc(Distance*Sin(Radians)+Distance*Cos(Radians))+Center.Y;
end;

Here it is with the added parameter I need:

function NewPosition(Center: TPoint; Distance: Integer; Degrees: Single;
  OvalOffset: Single = 1): TPoint;
var
  Radians: Real;
begin
  //Convert angle from degrees to radians; Subtract 135 to bring position to 0 Degrees
  Radians:= (Degrees - 135) * Pi / 180;
  Result.X:= Trunc(Distance*Cos(Radians)-Distance*Sin(Radians))+Center.X;
  Result.Y:= Trunc(Distance*Sin(Radians)+Distance*Cos(Radians))+Center.Y;
end;

DEFINITIONS:

• Center = Central point where to base calculations from (center of ellipse)
• Distance = How far from Center in any direction, regardless of Degrees
• Degrees = How many degrees around central point, starting from up-right
• OvalOffset = Ratio of difference between Width and Height

Duggins

Are the ellipse axes of symmetry horizontal and vertical? – Belgian

Yes, I don't care about rotation of the oval, just width differing from height. – Duggins

Just to clarify: the result from NewPosition shall have the given Distance from the center and be on the angle given by Degrees? At least that is what I read from your DEFINITIONS. – Excursionist

Exactly. I already have this working, no more help needed, unless you want to do something even fancier with it? Such as, add ability to rotate this oval to a certain degree? Not important though, thanks. – Duggins

In that case your question is somewhat unclear. Given a fixed distance and varying degrees to the function, most of the resulting points will have a different distance to the center as specified. For an elliptic curve the values for Distance and Degree usually don't match the measured distance and degree of each point. – Excursionist

I added a picture to show an example of how it works now and what I want it to do (even though my question has already been answered) – Duggins

Actually, when looking at the picture, it's very reasonable to say that what I call Distance is actually considered the Radius of this circle, while Degrees is of course the Angle. I should have paid more attention in my Math classes :P – Duggins

oval or ellipse? – Belike

Other than the reference to 'Oval' instead of 'Ellipse', I don't see any reason for this question to deserve a down-vote - I swear, there are really some haters here. – Duggins

Without being the down-voter: The fact is, that if you enter the values labeled 2 and 3 from the elliptic drawing into the function, you won't get the point labeled 4 as the result. To get the desired result labeled 4 you have to enter different values for distance and degrees than those shown in the drawing. – Excursionist

Sorry I still don't understand what you're trying to say. This function has always worked just fine, even after adding this new parameter (as answered below) I am getting the results I am wanting. If you mean Distance will be altered due to a NEW sizing of the ellipse, then yes, this I know. But keeping all the same parameters and changing just the new OvalOffset parameter basically turns the circle into an ellipse. – Duggins

Your definition for degree is not valid. Simply because you used the term degree in the definition – Battologize

Answer 1

Add a division by OvalOffset to just the Result.Y formula...

Result.Y:= Trunc((Distance*Sin(Radians)+Distance*Cos(Radians))/OvalOffset)
           +Center.Y;

Darrin

Perhaps I got it wrong, but with your code won't the distance between Result and Center be different to the given value Distance? – Excursionist

Distance = how far away from center regardless of degrees, Degrees = degrees around center point starting from up-right – Duggins

And yes I tried your formula and instead of making an oval, it made just a smaller circle (I used exact formula on Result.X too) – Duggins

@Jerry How could a linear scaling of the Y offset result in a circle? – Belgian

Ah ha, I misunderstood the answer because it wasn't thoroughly explained. I tried to copy this formula over to Result.X as well, which resulted in just a smaller circle. Changed Result.X back to original code, and it works now :D – Duggins