[Tutor] Button 1 Motion Event

[Luke Paireepinart]

Johnston Jiaa wrote:
>
>> Just don't distinguish between quick and slow drags.  Just keep a 
>> temporary variable that has the previous mouse position, and draw 
>> ovals from there to the current mouse position every time your 
>> function is called.
>
> I now have the variable with the previous mouse position.  How would I 
> draw ovals from the current mouse position to that previous mouse 
> position?  I tried reasoning it out with a for-loop, but I couldn't 
> figure out how to do it.
Well, try reasoning it out with mathematics.
Suppose we have the points (0,0) and (100,100).
What's the slope between these two points?
well, delta-Y is 100 and delta-X is 100, and 100/100 == 1.
This is also the same as 1/1.
Therefore, for every new point we want to get, we'll add 1 to the x 
value and 1 to the y value.

Now assume we have the points (23, 45) and (45, 80).
This slope would be:
80 - 45
---------
45 - 23
or  35 / 22.
So as you can see, the number on the top is larger than the number on 
the bottom, so our Y-value is increasing more quickly.
But it doesn't really matter which value is bigger, the numerator or the 
denominator.
All we care about is the slope.  Because slope tells us: this is the 
change in Y for every change in X.
The reason slope tells us this is because slope is the ratio between the 
change in Y between our 2 points
and the change in X between our 2 points.
Because it's a ratio, it can be applied to any measure, even to 
deltaX=1, which gives us what deltaY is.
Since we don't care about any X-coordinates between integers, we don't 
care about any other deltaX measurement.

So you'd do something like this:
x = 23.0 # our first points
y = 45.0 # they're float so we can add partial amounts to them.
slope = 35/22.0 # this is float to force float division.
for deltax in range(23, 45):
    x += deltax
    y += slope

So in this case, each time through the loop, X will move 1 over, and Y 
will move slightly more than 1 up.

This still has a problem if the slope is very great in the Y-direction.
Given the case of the points (0,0) and (1,100),
we get a slope of 100.  Thus, we will draw points at 0,0 and at 1,100 
and none in-between,
when realistically we'd like at least a vertical line between them, or 
preferably one that shifts one pixel over halfway-up.

Note that the poitns (0,0) and (100, 1) would not create a problem.  
This is because our delta-x is changing at a set rate,
and our deltay is a smaller number.  It would work in this case.

What's creating the problem is that our slope is greater than 1, and 
we're using delta-x as a fixed amount.
If we add the condition that we affix delta-x to the value 1 for slopes 
less than 1, and delta-y to 1 when slopes are greater than 1,
then everything should work out perfectly.  The case of slope == 1 will 
be correctly handled in either case, just make sure to include it in one 
of them.

Thusly, our code would look something like this:

point1x, point1y = raw_input("please input the first pair of coordinates 
separated by a space: ").split(' ')
point2x, point2y = raw_input("please input the second pair of 
coordinates separated by a space: ").split(' ')

slope = (point2y - point1y) / (float(point2x - point1x))
if slope > 1:
    deltax = 1 / slope # i assume we invert slope here?
    deltay = 1
else:
    deltax = 1
    deltay = slope

currentx = float(point1x)
currenty = float(point1y)
for x in range(max((point2y - point1y), (point2x - point1x)) ):
    #we choose our range as the larger of the two lengths.
    #thus if delta-x is only 1px and delta-y is 100px, we'll
    #still draw all those points in between.

    # ..........
    #  draw the currentx, currenty point here
    # .........
    currentx += deltax
    currenty += deltay

# and draw the point one more time here, to get your ending point.




Note that I don't profess that either my code or my math is correct; I 
didn't test any of this, it's more to give you an idea of how to 
approach Computer Science problems.

>
> Also, I need to be able to save the canvas drawing.  Would it be 
> possible to write some sort of data to a file that could be used to 
> load the previously saved drawing back onto the canvas?
You can just keep a cache of all points and redraw them on load, or you 
can dump it out to an image file.  I believe TKInter supports that, but 
I haven't used that library in a long time.

Again, _please reply on-list_ unless you want a discussion to be 
private, in which case specify in the e-mail so we know it wasn't an 
accident.
-Luke