OpenEuphoria

Re: unit axis intercepts

• Posted by ChrisB (moderator) Sep 20, 2023
• 1011 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.