OpenEuphoria

1. unit axis intercepts [solved]

• Posted by petelomax Sep 20, 2023
• 908 views
• Last edited Sep 23, 2023

I've written a natty little routine which bisects a bezier curve into sub-pixel fragments and that
part is working fine, and once I've got {x1,y1} and {x2,y2} within a 1x1 pixel square, I want to
know whether they intersect the unit axis, for which "ceil(min(x1,x2))!=ceil(max(x1,x2))" and the
same for the unit y axis is fine. However, I also want to know where it intercepts the unit axis,
which btw is floor(max(x1,x2)), and also incidentally I'm happy with the edge cases of 0.1..1 not
being an intercept but its partner 1..1.9 being one, and wouldn't want both deemed one anyway.
Once it is that small, I think it is safe to treat the curve fragment as a straight line.

I'm sure that's all clear as mud.

So I've got minx, maxx, unitx, ditto y, but in want of a hitux and hituy. I think the problem is
(flat|steep) * (\|/) * (up|down or left|right) and I'm currently staring at (a roughly estimated)
40 or so glitches in a test set of 625 cases and a brain clogged with min/max/ceil/floor/abs when
maybe I don't really need or want any of them?? I somehow believe there is a dirt-simple solution
itching to get out, but I just can't see it.

To recap/summarise, given some {x1,y1}, {x2,y2}: where does it hit a straddled whole x, ditto y?
You cannot make any assumptions about the first point being left or right or above or below the
other one, but you can assume they are strictly less than 1 apart, in both directions.

3. Re: unit axis intercepts

• Posted by ChrisB (moderator) Sep 20, 2023
• 902 views

I also asked it towrite the code in Euphoria

To determine where a Bezier curve intersects the unit axis and whether it straddles a whole pixel, you can follow these steps in Euphoria:

-- Function to find the intersection points with unit axis 
function findIntersectionPoints(x1, y1, x2, y2) 
    -- Determine whether the curve is flat or steep 
    flat = abs(y2 - y1) < abs(x2 - x1) 
     
    if flat then 
        -- Swap x and y coordinates for a flat curve 
        x1, y1 = y1, x1 
        x2, y2 = y2, x2 
    end 
     
    -- Determine whether the curve is going up or down 
    up = y1 > y2 
     
    -- Calculate the intersection point on the unit y axis 
    if up then 
        hituy = floor(y2) 
    else 
        hituy = ceil(y2) 
    end 
     
    -- Calculate the intersection point on the unit x axis 
    hitux = ((hituy - y1) / (y2 - y1)) * (x2 - x1) + x1 
     
    if flat then 
        -- Swap x and y coordinates back if it's a flat curve 
        hitux, hituy = hituy, hitux 
    end 
     
    -- Check if the intersection point straddles a whole pixel 
    straddles_x = ceil(x1) != ceil(x2) 
    straddles_y = ceil(y1) != ceil(y2) 
     
    return hitux, hituy, straddles_x, straddles_y 
end 
 
-- Example usage 
x1 = 0.5 
y1 = 0.5 
x2 = 1.5 
y2 = 1.9 
 
hitux, hituy, straddles_x, straddles_y = findIntersectionPoints(x1, y1, x2, y2) 
 
if straddles_x then 
    ? "X-axis intersection at ", hitux 
else 
    ? "No X-axis intersection" 
end 
 
if straddles_y then 
    ? "Y-axis intersection at ", hituy 
else 
    ? "No Y-axis intersection" 
end 

This code defines a `findIntersectionPoints` function that calculates where the Bezier curve intersects the unit axis (both X and Y) and whether it straddles a whole pixel. The function accounts for whether the curve is flat or steep and whether it's going up or down. It also provides example usage and prints the results.

5. Re: unit axis intercepts

• Posted by petelomax Sep 20, 2023
• 867 views

I give it 11/10 for "brazenly pretending to be useable"... It actually hit the nail on the head,
in that I was (stupidly) trying to use minx + something, when I should have been using
x1 +[/-] let the sign of the slope dictate which way. Anyway, so far, it's certainly progress.

When I tried, didn't get anything near as good, no idea why not (and boy was it slow).
Next time you use ChatGPT, you should try pasting errors from trying to run the code,
since that should (hopefully quite quickly) teach ChatGPT to emit better Phix code.

Thanks, Pete

7. Re: unit axis intercepts

• Posted by ChrisB (moderator) Sep 22, 2023
• 815 views

Heh heh.

Well spotted! (Miss Falcon?)

Cheers

Chris