[ad8e]

The ideal dimensionality of the parameter space depends on the jaggedness of the curve. Derivatives are useful when they stay constant over a stretch of time; when derivatives vary too much, it becomes more efficient to use more points of lower degree. This is the same calculation in other domains of approximation: numerical integration, DiffEq, and Taylor series.

For example, to draw rough surfaces, point-to-point lines are the most efficient way, with a ton of points. For industrial geometric shapes, lines and ellipses become efficient. As the smoothness of the curve goes up, more derivatives become valid. But sometimes those higher derivatives are not useful.

This is why the parent comment likes the Pencil tool; it's optimal for high variation, because it is a local (smoothed) control of position, the zeroth derivative. The cost is some loss of smoothness, which likely doesn't matter for her domain, since her hands move smoothly enough.

I think the Pen tool would be a more competitive alternative with a better control scheme. For example, a Pen tool with local control would unify the Pencil and Pen: letting you draw jagged curves by holding your mouse down, and letting you draw straight lines and smooth curves by clicking. There would be no interruption of flow, as you can use either method freely to continue a curve. They should inherently be the same tool anyway, just with different numbers of derivatives.

[egypturnash]

For example, to draw rough surfaces, point-to-point lines are the most efficient way, with a ton of points.

I usually just draw a quick simple line and tell Illustrator to rough it up for me. There's a lot of ways to do this; "use a custom brush" is a common one, so's "apply the Roughen effect". These will dynamically generate a buttload of virtual points in the vicinity of the basic path when it gets rendered; the editing view is still just a handful of points. Much easier to edit, much faster to draw. If I need precise, human-defined jagginess to a path, then I whip it out with the Pencil, and push it around with stuff like the Puppet Warp tool, which lets me drop a few pins into a complex set of paths, and distort it based on how I move those around.

Illustrator's Pencil tool actually performs a certain amount of smoothing on the raw positional input from the drawing tablet. There's a slider for how much it does this. I have it right in the middle of the range and it makes for a pretty nice compromise between catching every deliberate motion of my fingers/hand/arm across the tablet, and throwing away the little irregularities that I would be working hard to eliminate if I was working in pen and ink.