Basic Graphics - Circle Corrections

I have been doing a lot of work

trying to get the next shape

in the graphics sequence,

and discovered an aberration 

in my version of Python 3.8  32-bit.

I don't know if this is the case 

for everyone downloading this version.

But I discovered,

that when drawing the circle,

this program doesn't produce

a balanced shape.

For a circle of -

   Pt.forward(1)

   Pt.right(1)

the four equidistant points on the circle are -

    (0.00, 0.00)

    (57.79, -56.79) 

    (1.00, -114.59)

    (-56.79, -57.79)

    (-0.00, 0.00)

They should be balanced, something like -

    (0.00, 0.00)

    (57.29, -57.29)

    (0.00, -114.58)

    (-57.29, -57.29)

    (0.00, 0.00)

On closer inspection of the 4 points,

I found them to all be 

one pixel to the left of where they should be.

With some trial and error, I discovered,

that if I correct the initial orientation of the arrow, by

       Pt.right(0.5)            degrees

Then, the 4 equidistant points on the new circle are -

    (0.00, 0.00)

    (57.30, -57.30)

    (-0.00, -114.59)

    (-57.30, -57.30)

    (-0.00, 0.00)

Which can be seen to be balanced.

So I advise, if you have this problem 

when drawing a circle on this program, 

then make the adjustment of -

     Pt.right(0.5)

at the beginning of the sequence.

N

Also, I had been using -

    n  =  radius / 57.35

This seems to be a little inaccurate, from observing above, that -

    2  x  radius  =  114.59

    Thus,

    radius  =  114.59 / 2

                =  57.295

    when the program is moving at the base level of -

       Pt.forward(1)

   Pt.right(1) 

   

    and,

    n    =    the chord subtended by a    1 degree    turn of the circle

Hence, to get a circle of the desired radius here, using -

       Pt.forward(1)

   Pt.right(1)

n    needs to be adjusted to -

    n  =  radius / 57.295

For example, if a circle is required, of -

    radius  =  50

in this program, the adjustment needed is -

    n  =  50 / 57.295

which gives you a chord that is slightly shorter, 

and the circle drawn will end up with -

    radius  =  50

not,

    radius  =  57.295

I have tested this,

and it is accurate enough up to -

 

    radius  = 400

which is a circle that is a bit larger 

than an approx. 39cm (diagonal) computer screen.

:)

text (c) Katherine Stuart 2021

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