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24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
January 4, 2022
Question

Oval or Ellipse? It is a question!

  • January 4, 2022
  • 1 reply
  • 3802 views

My students and me decided to check which oval Paint draws. It seems to be an ellipse. See pictures below and Prime 6 in attachment.
But there was a suspicion that these are arcs of two pairs of circles - see Oval - Wikipedia.

Problem. There are the coordinates of the four vertices of the "horizontal" oval. It is necessary to draw an ellipse through these points (this problem is solved) and an oval made up of arcs of two pairs of circles. What oval does Paint build? Maybe there is a third way?

1-Paint-Oval.png2-MXY.png3-Solver.png4-Plot.png

1 reply

W
Werner_E25-Diamond I
25-Diamond I
January 4, 2022

Don't be afraid of using vectors in the solve block (and vectorization when making the check(!

Werner_E_1-1641278870386.pngWerner_E_2-1641278881392.png

 

And as its much easier to apply different vertical and horizontal scaling to a circle as opposed to calculating the approximation circle arcs, I would strongly guess that Paint is drawing an ellips and not four approximating circle arcs.

Of course actually its drawing polygons 😉

And given that it cannot create infinite thin line segments and that there is the resolution to be taken in account it actually creates some kind of komplex, filled polygons ‌.

 

V
24-Ruby IV
ValeryOchkov24-Ruby IVAuthor
24-Ruby IV
January 4, 2022

Thanks, Wener!

@Werner_E wrote:

Don't be afraid of using vectors in the solve block (and vectorization when making the check(!

 

 

I have used at first only 4 points and add new and new!

 

And what about the promlem with 4 circle? I an waiting for the solution!

W
Werner_E25-Diamond I
25-Diamond I
January 4, 2022

I have used at first only 4 points and add new and new!

One more reason to use the vector equation so you simply can add values in the vectors and the rest remains untouched - no need for a cop and past orgy.

 

 

And what about the promlem with 4 circle? I an waiting for the solution!

What will this be good for? It may be a good way to approximate an ellipse when you have to draw it by hand, armed only with ruler and compass. But how would implementing it in a math program make sense??

Of course you could determine center and axis length of the underlying ellipse in a first step (like you already did) and then use appropriate functins to draw the four circle arcs. But again, I can see no reason for doing so.

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