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so in the previous video we create we
ended up creating this circle function

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and actually ran it and I'll just run it
again let's have a look at the output

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and there is the output there and as I mentioned the circles are a lil bit vague you can see just

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around the edges to the left and the
right their and just a little bit vague the line

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the dots don't sort of lined up
correctly the reasons for that at the moment is

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we were only plotting points for integer
values of x so we don't get many points plotted

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and we can't use decimal values in the
step for our range

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and I'm referring to the code here showing there
on line 16 which of course is our

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circle function but what we can do is
multiply the range up so that more

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values are used and scale each value back down again so doing this by a factor of a

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hundred will give the same effect as a range
and increments by 0.01 and that should therefore

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then fix up the circle so let's have a look at that

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so what we wanna do is make a change to the code on line 17

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in the way you can see for x in range g then
g + radius so let's just add the

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multiplication step to that so.....

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....but then what we

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need to do is scaled back X as well so
put.......because again we're just using

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the multiplied by a
hundred to give us a bigger range

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effectively the same as we had a range
that increments 0.01 so we then have to divide it back by a

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hundred to take it back to the original
point that it was before so they will

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plot if we now run this again

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...and their you can see it's now a lot better it's actually plotting a hundred times as many points

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as it was previously and as a result
looking at that it's a lot better but

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did you notice that it also took
significantly longer so I'll just run it again

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so I ran it and try to tab over and I can't still tab over because it is still generating it and their it is in the screen

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there now their you go did you see it pop ups
it took a quite a deal more time to actually

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create that and again the reason is why we are
plotting a hundred times as many points

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as we did previously so its doing a
hundred times more calculations but the

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end result is the circle is a much more
well defined with modifications that

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are actually made now if you're not sure
what's going on with scaling the range

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what we can do is print the value of x so
let's go ahead and do that just so we

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can sort of see what is going on so if
we add a print their...and run that that showing us

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a representation of the values that are
being plotted you can see their is quiet a

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a few their and if I tab over now and see if its finished we got our parabola their on the screen you can see everything

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at once so for the first circle we
ended up with the range running from 100 to 200 in

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steps of 0.01 you can see the 0.01 their for each one of course we
did that by scaling up the start and end

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values of the range and then scaling x back down again before actually using it so

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that it would actually plot in the
right position so although the range

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function can only use integer values it can still
be used to produce a range of decimals by

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and I'll be showing how to do that now by
multiplying it by a hundred now we are

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going to be looking at another way to do
the same thing using a generator later

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in the course which can result in much
more readable code now the disadvantage

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with this is that performances is
suffered but the result is much nicer

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and by having the circle drawing code in
a function you saw that the change has

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applied to all circles that were drawn so basically putting the code

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in one place enabled us to make the
change to every single circle

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that was actually drawn but with that said
in fact the canvas widget has a create

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oval method that can be used to draw
circles and is actually much faster than

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the method data we've come up with so the
create oval method needs the coordinates

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of the top left and bottom right of a
bounding rectangle but we're working with

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the radius and coordinates of the center we can still use our circle method we just

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change it so that it calculates the
coordinates that the create oval method

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needs so lets go ahead and do that so lets close it down and I'm making it a lot easier so comment out this code in our circle

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function and the code at the top so all we
need to do is put.....and then

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we need to calculate the coordinates for
the create oval method it needs again what it needs is

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the coordinates of the top left and bottom
right of a bounding rectangle then it is

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gonna draw it over within those parameters so put....

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.......

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.....

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and that's all we need to do and I just need to add a line

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there to keep that happy 2
lines in between each function so now if we run

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that...and bingo we already got our circles and I have made a

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mistake their what I've done is I've actually
multiplied the radius instead of adding

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it so that should have been G Plus right radius.....

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...and the other two should be fine so again the top left of the first

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2 parameters are the bottom right of the last 2 so if I run it again we should get basically results similar to what

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we had before you can see that was significantly faster and

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it's reduced a very good effect and the
advantage with that is we are using

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optimized code those built in part of
Python so always a good idea where possible

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if you could find some code that has been already written to
use that rather than reinventing the

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wheel that we did initially with our
function circle function on line 60 now

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I use the term method instead of function
when referring to the create_oval method and

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because a canvas is actually class and
class functions are called methods that's

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actually the right terminology to use so
in this case the create_oval is a method and again as

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classes methods the correct term
instead of functions but don't worry too

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much about that because we'll be looking
at classes and object-oriented

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programming in the next section and
you'll understand why they're called

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that and once we go through that it will make a lot more sense but it's probably a good idea

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to start using the correct terminology
as you can see their isn't really a great

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deal of difference between functions and
class methods when it comes down to

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actually using them

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okay so it's time for a mini challenge
and it is very much a mini challenge

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and I'm just going to type it just above the circle
method because it's ultimately where we

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are going to be using it we will modify the
circle function so that it allows

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the color of the circle to be specified
and defaults to red color is not given and just a

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note here you may want to review the previous lecture about named parameters and default values so that's basically it

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modify the circle functions so that it allows
the color of the circle to be specified

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it defaults to red if the color is not given
now you may want to review the previous

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lectures about named parameters and default values to get it working so it's now time to pause the

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video go away and make the change to the
circle function and when you made your change come back and

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you can compare the code that we've
actually about to put in ours

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so we'll see you when you get back pause the video now ok so
hopefully you figure it out all we really need

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to do is change make the change now on line 19 actually I'll put 2 spaces their keep it happy

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and we need to add an extra parameter

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and we just put....so by putting the
equals red that's defaulting that as a parameter

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if one is passed and of course we
need to change the code here where it is

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hard coded for red and make that color so once we do that that should work that should be all we need to do

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and we can test this by the

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first four lets changed those so put.....

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...and notice we are not getting any errors with
these other circle calls on line 63 through 67

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because we are not specifying a parameter its going to default to red and it doesn't come up with an error

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but the first four circle should be in green yellow black and blue so

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lets try running that and you can see it's working nicely so we got a blue yellow black and green circle

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so that's actually it that's the end of the
lecture and I'll see you in the next

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lecture where are we are going to take a
little bit of a different tack and we are going to

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start looking at creating a blackjack
card game so we'll see you in the next

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video