Actually drawing some ovals – that are not ellipses (2017)

    def bezier(t, *handles):
        """Computes a single point of a bezier of any order where 0 <= t <= 1."""
        if len(handles) == 1:
            return handles[0]
        else:
            pairs = zip(handles[:-1], handles[1:])
            return bezier(t, *[_bezier_interpolate(t, a, b) for a, b in pairs])


    def _bezier_interpolate(t, a, b):
        return [a * (1-t) + b * t for a, b in zip(a, b)]


    assert bezier(0.25, [1, 1, 1], [2, 2, 2], [3, 4, 5]) == [1.5, 1.5625, 1.625]

You can see the math for computing a point (or segment) is trivial (addition and multiplication) and it can be easily parallelized. It can even be a one-liner, but that isn't very readable.

Here's a good website for visualizing the math: https://www.summbit.com/blog/bezier-curve-guide/

I grew up in an area with a lot of corn field subdivisions and McMansions. They tend to have a lot of volume/floor space and incredibly poor detailing. On the one hand, I find it hard to believe that anyone building such a big, cheap (at least in the details sense) home on spec would include an elliptical arch. On the other hand, the kinds of contractors that put them up would likely be the kind that struggled to execute such a design element.

I say this having just been very humbled putting up crown in a bathroom. People tell me it looks great, and I reply that it had sure better considering the two weeks of evenings that went into putting it up!

I've shopped for houses a lot, and after "training" mostly on typical '80s+ suburban houses, noticed that when looking at older houses with saner, calmer designs, I'd have to add 500-1,000(!)sqft to my first-impression guesses at their size to get close, while I'd gotten pretty good at guessing the "McMansion" and mini-McMansion style. The older designs don't look as big, at the same size.