Making a pong game shaped like a octagon, need help!

I am trying to make a pong game in matlab that has an octagon shaped court to learn about the math of billiards.

At this point I have the goals working and I have the ball bouncing for every case except for the diagonals of the octagon.

The top, bottom and sides are easy because I just test if the new x and y vectors I'm creating are > or < then the values I have set for the walls. The diagonals are a bit tricky because I need to test the x and y vectors of the ball for every single point of the diagonal line.

I created the polygon using

POLY = [1 75; 1 25; 75 5; 175 5; 250 25; 250 75; 175 96; 75 96];
POLYG = [POLY; POLY(1,:) ]; %repeat first row at the end
    plot(POLYG(:,1),POLYG(:,2))
    axis equal %same scale on both axes

I need a way to create a set of points between the points that draw the diagonal line so that I can test the balls path against those points. E.g. if one diagonal is the line between (1,25) and (75,5) on my plot how do I get all of the sets of points between them into a matrix?

Thank you for your help

Answer 1

[Image Analyst]

It's not that much harder. You just have four equation of lines like

y = x + r  % Upper left quadrant
y = -x + r % Upper right quadrant
y = -x - r % Lower left quadrant
y = x + r  % Lower right quadrant

I'm sure you can figure out what r is based on your side length or whatever other parameters you're using - it's just simple math. Then you just stick in your proposed x and find out if the resulting y is greater than or less than the y from the above equations. Like if the proposed x = 4, and your proposed y = 5, but the y from the equation would be 4, and it's in the upper half plane, then your proposed y is above the lines, so you need to reflect it. Does that make sense?

[Image Analyst]

brian's response moved here since it's not an answer to the original question:

Image analyst I kind of see what you are saying...

I just used linspace to create a set of 1000 x and y values for each corner of the octagon so I'm hoping I can use these to check my balls position against them using what you just mentioned. I guess the only question left is how do I check it for every single x and every single y value I created?

[Image Analyst]

If you want, you could make a binary image with false in the corners and true inside the octagon. Then you could get the proposed next row and column and check it against your binary image

if binaryImage(nextRow, nextColumn)
    % It's inside the octagon
else
    % It's outside the octagon.
end

Not sure it's any better, but it is an alternate way of doing it if you want.

[brian grove]

I like that idea. Do I need to put this in a loop so binaryImage can use all values in the matrix? or is it simpler than that?

[Image Analyst]

You must have a loop for moving your ball don't you? How else are you going to generate new (x,y) coordinates?