Drawing

Drawing sets how much of your hand a freehand line keeps. One slider runs from Accurate, which follows every wobble and keeps gentle corners, to Smooth, which tidies curves and straightens runs that are nearly straight. It is the question every inker and engraver has faced: in this line, what is the drawing and what is only the tremor?

What it does

The DRAWING section is always on the Controls tab, whichever tool is in hand, and it applies to the next shape you draw freehand with the Draw tool. Shapes already drawn keep the points they have. The Pen and the ready-made shapes are not affected.

The slider has five stops: Accurate, Fairly accurate, Balanced, Fairly smooth and Smooth. It starts on Balanced, in the middle.

When you lift the pen, the app turns the stream of positions it recorded into a clean outline. First it trims the overshoot, where your hand ran on past the start as it closed the shape. Then it fits:

1. It respaces the samples evenly along the line and drops the tiny hooks where the pen touched down and lifted off.
2. It finds the corners. A bend counts as a corner if it turns sharply when measured over both a short and a longer stretch of line: a wobble turns over a short stretch and not a long one, a generous curve the other way around. Where the pen slowed down at a turn, a borderline bend is more readily taken as a corner.
3. It cuts the line at the corners, averages the shake out of each piece, turns any piece that is close enough to straight into a true straight line, and fits the rest with smooth curves that must stay close to what you drew.

The slider moves four numbers together. From Accurate to Smooth, the distance the curve may stray from your line grows from 0.35 to 2 screen pixels; the turn needed to make a corner grows from 32° to 65°; the tolerance for straightening grows from 0.75 to 3 pixels; and the stretch of line averaged to steady it grows from 1.5 to 8 pixels. So Accurate keeps more corners, more curves and more of the texture of your hand, and Smooth keeps fewer, straighter, calmer ones.

Those distances are measured on the screen, not on the paper. Zoom in and the same tolerance is a smaller distance on the sheet, so drawing a small, intricate shape zoomed in keeps finer detail.

Why it works this way

One slider rather than four, because it is one judgment. Nobody drawing a leaf wants to think about fit tolerances and corner thresholds; they want to say how tidy the line should come out. Illustrator reached the same conclusion: in 2014 it replaced its Pencil tool’s separate Fidelity and Smoothness settings with a single Fidelity slider running from Accurate to Smooth. This slider borrows the words.

The corners are found first because in a notan corners matter. A cut edge is crisp. An earlier version of the app fitted each stroke in a single pass, and that kind of fit cannot tell a corner from a bend: a hand-drawn square came out as a lozenge. Finding the corners first lets a square come back as four points and four straight sides.

The tolerances live on the glass because that is where the tremor lives. A hand shakes by roughly the same amount on the screen whatever the zoom, so the allowance for it should be the same on the screen too.

The metaphor

The metaphor is the clean-up artist. In hand-drawn animation, rough pencil drawings were passed to artists who traced them into a single clean line, deciding which wobbles were intention and which were accident; comic-book inkers do the same over a penciler’s drawing. Accurate is a faithful inker who keeps every quirk. Smooth is a confident one who straightens as they go.

Where it breaks: a human clean-up artist knows what is being drawn, a hand or a hat. The fit knows only geometry – distance, angle and the speed of the pen. It cannot tell that the little bump was the point of the drawing. When it matters, draw at Accurate, or add the bump back with the Points tool.

A history

In art

Art has always argued about the living line and the clean one. Calligraphy prizes the trace of the hand – speed, pressure, hesitation – while technical drawing works to remove it. Cut paper sits between the two. Matisse, in the cut-outs of his last years, cut shapes with scissors from sheets of paper painted with gouache by his assistants, and the edges keep the movement of the blade. A notan made in this app inherits both traditions: you draw like a draftsman, and the edge comes out like a cut.

In printing

For centuries an artist’s drawing reached print through another pair of hands. A block-cutter or an engraver re-cut every line, and in doing so decided what to keep – a Fidelity slider made of a person. Photomechanical line blocks, which spread in the later nineteenth century, removed that middle hand: the drawing was photographed onto a metal plate and etched, and every tremor was printed exactly as drawn. Much of the history of reproduction swings between those two poles, interpretation and fidelity.

In technology

Drawing into a computer by hand began with the RAND Tablet, available to research laboratories in 1964. RAND’s GRAIL system, described in 1969, went further and recognized hand-drawn letters, symbols and shapes. The problem of throwing away points without losing shape was attacked from cartography: David Douglas and Thomas Peucker’s method of 1973 keeps the point farthest from a straight line and drops the rest if they are close enough, and it is still among the most widely used ways to simplify a coastline.

The curve fit most drawing software uses descends from Philip Schneider’s ‘An Algorithm for Automatically Fitting Digitized Curves’, published in Graphics Gems in 1990. It fits a smooth curve to a run of points and, if the fit is poor, splits the run at its worst point and tries again. Paper.js, the drawing library under this app, fits curves that way. The corner-finding step is modeled, loosely, on corner finders from the sketch-recognition research of 2008 and 2009, known as ShortStraw and IStraw.

In professional software

Every freehand tool trades fidelity against smoothness, and the words at the ends of this slider come from Illustrator. There are two approaches: vector programs fit curves after you lift the pen, as this app does, while painting programs steady the stroke as you draw.

• Adobe Illustrator. Double-click the Pencil tool (N) for its options: the ‘Fidelity’ slider runs from Accurate to Smooth, as here. The Smooth tool calms a stretch of a path already drawn, and the Shaper tool (Shift+N) turns a rough rectangle, ellipse or triangle into a crisp one.
• Adobe Photoshop. The brush options bar has a ‘Smoothing’ percentage that steadies the stroke while you paint. Its settings include ‘Adjust for Zoom’, which lowers the smoothing as you zoom in: the same reasoning that measures this app’s tolerances on the screen.
• Procreate. StreamLine, in the Stabilization section of the Brush Studio, smooths out wobbles as you draw. QuickShape tidies whole shapes: finish a stroke and hold the pencil still, and a rough line, ellipse or rectangle snaps to a clean one.
• Inkscape. The Pencil tool (P) has a ‘Smoothing’ setting in its controls bar, and ‘Path › Simplify’ thins out the points of a line already drawn.
• Autodesk AutoCAD. The SKETCH command draws freehand and records the line as lines, a polyline or a spline. Its Increment sets how far the pointer must travel before a new segment starts, and for a spline its Tolerance sets how closely the curve must follow your hand.

What carries over. Set the slider before you draw, because in most programs it shapes the next stroke, not the ones already made. Then judge the result by its points: a clean freehand path has few anchors, with corners only where you meant them. Where a program smooths while you paint, expect the line to trail a little behind the pen; that lag is the smoothing at work.

Try this

• Draw the same freehand star at Accurate and at Smooth, then look at each with the Points tool and count the points.
• Draw a square slowly, pausing at each corner, at Smooth. It should come back with four corners and four straight sides.
• Zoom in, draw a small shape with fine wiggles, then zoom out and draw the same shape at the same size on the sheet. Compare the detail each one kept.

Going further

Reshape what the fit made with Path editing. Tracing a photo has its own settings for the outline; see Smoothness and Corner angle and span.

• Kimon Nicolaïdes, The Natural Way to Draw
• Andrew S. Glassner (editor), Graphics Gems