Points

Points changes the shape of a path rather than its place. Every outline here is a chain of anchor points, the places the line passes through, and each anchor can carry two handles that steer the line into it and out of it. Points lets you take hold of any of them.

What it does

Press A, or choose ‘Points’ on the rail. Move the pointer over a shape and its outline is drawn dashed, with a small hollow square at every anchor. Selected anchors fill in, and their handles appear as thin stems ending in round knobs.

It reaches everything: a shape still waiting for its flip direction, a cut on the sheet, and a cut’s flipped piece out beyond the sheet. Reshape the piece and the cut changes to match, mirrored back across the fold.

What a press does depends on what is under it, checked in this order: a handle of a selected anchor, then an anchor, then the outline, then the inside of a shape, then empty canvas.

• An anchor. Click to select it; Shift-click to add it to the selection or take it out. Drag it and every selected anchor moves by the same amount, with Shift keeping the move to a 45° line from where it began. The arrow keys nudge the selected anchors one unit, ten with Shift, a tenth with Command. Delete or Backspace removes them. Option-click (Alt) switches an anchor between smooth and corner.
• A handle. Drag it to aim it. On a smooth point the handle opposite swings around to stay in line, keeping its own length, so the point stays smooth. Option-drag moves the one handle alone and breaks the pair. Shift holds a handle to 45° steps around its anchor.
• The outline. Click it to add an anchor there. Drag it to bend that stretch of line: only the two handles either side move, by the least they can while keeping the line under your pointer. Option-press the outline to add an anchor and drag it in one motion.
• Inside a shape. Drag to move the whole shape.
• Empty canvas. Drag a marquee to select every anchor inside it, across as many shapes as it covers; Shift adds to the selection. A plain click deselects.

With Points in hand, the ‘Controls’ tab shows ‘Path editing’. ‘Add points on click’, on at first, lets a click on the outline add an anchor. ‘Smooth while reshaping’, off at first, smooths the whole curve again after an anchor is moved; it starts off so that handles you set carefully with the Pen survive a nudge. See Path editing.

You rarely need to go to the rail for it. From the Pen between paths, from Draw and from the four shapes, hold Option and Points is in your hand until you let go; from Curves, Option does the same. When Option has fetched the tool it does not also do Option’s own jobs, so a press picks a point up instead of converting it. From Points, Command fetches Move. Every finished gesture is one step of undo.

Why it works this way

Points is Illustrator’s Direct Selection tool, the white arrow, and keeps its manners. A few choices are particular to this app.

A press inside a shape always belongs to that shape, so a marquee has to begin outside every shape. That is a price, and it was paid on purpose: dragging a shape by its inside was here first, and it is the gesture people use most.

Bending the outline is solved as a small sum. A point on a cubic curve is a weighted mix of the curve’s four control points; move the two inner ones and the point moves by a predictable amount. The tool asks for the smallest pair of handle movements that carries the curve to your pointer, so the line follows your hand and nothing on it moves more than it must.

A path is never left with fewer than three anchors, so a cut cannot collapse into a line or a dot by accident. Deleting several anchors at once is all or nothing: if it would leave any path too thin, none are removed.

The metaphor

Before computers, long fair curves, the hulls of ships and later the skins of aircraft, were drawn full size on the floor of a loft with a spline: a long, thin, springy strip of wood held in place by lead weights. The weights were called ducks, for their shape, and were painted and felted underneath so they would not mark the drawing. Move a duck and the strip finds a new curve through it. An anchor point is a duck. The handles say how steeply the strip leaves it, and how far it keeps that heading.

The metaphor breaks usefully. A real spline decides its own curve: the wood bends as little as it can, so the line between two ducks is whatever physics makes it, and it is always fair. A Bézier curve has no physics, only instructions. Its handles say exactly where it goes, and it will go there even if the result is ugly. That is more power, and more responsibility. And no duck on a lofting floor could sit on a reflection and move the thing it reflects.

A history

In art

Renaissance painters moved drawings from paper to wall as rows of points. A full-size drawing, the cartoon, was pricked with holes along its lines, held against the plaster or the panel, and patted with a bag of charcoal dust, so that the drawing arrived as a dotted line to be joined up again by hand. Pouncing, as it is called, is a drawing reduced to its anchor points, with the curve between them left to the painter’s judgment. Look closely at some frescoes and the dots are still there.

In printing

Letters were among the first things to be turned into points. From 1972 Peter Karow developed a system called Ikarus at URW in Hamburg. Drawings of letters about ten centimeters high were traced on a digitizing tablet, the operator marking points around each outline and saying what kind each one was, a start, a corner, a tangent or a curve point, recorded to a hundredth of a millimeter. Karow’s insight was that what served for the smooth outer skin of ships would serve for letters too. A type designer editing a font today is still moving those same kinds of points.

In technology

The word spline comes from an East Anglian dialect word, first recorded in English in the eighteenth century. In the early 1960s aircraft makers, J. C. Ferguson at Boeing among them, began to replace the lofting floor with mathematics, and the spline moved into the computer. In the same decade Pierre Bézier at Renault published the curves now named after him, steered not only by the points the curve passes through but by control points that pull it without being touched.

That is the model under every shape here. The drawing library the app is built on stores a path as a list of segments, and each segment is exactly three things: an anchor point, a handle in and a handle out. Points is a way to put your hand on those three things directly.

In professional software

What Studio Notan calls Points, most programs call direct selection or node editing: a tool that takes hold of a path’s anchors and handles rather than the whole object. The model underneath, an anchor with a handle in and a handle out, is the same in every program below.

• Adobe Illustrator. The Direct Selection tool (A), the white arrow, selects anchors and handles, and dragging a curved segment reshapes it as dragging the outline does here. Beware: Delete on a selected anchor also deletes the segments either side, which opens a closed path and splits an open one, while the Delete Anchor Point tool (-) removes the anchor and keeps the shape closed.
• Adobe Photoshop. Paths and shape layers are edited with the Direct Selection tool, which shares the key A with the Path Selection tool. The first takes anchors and segments; the second takes the whole path.
• Inkscape. Anchors are called nodes, and the Node tool (N) edits them. Double-click a segment to add a node. Delete removes the selected nodes and, in most cases, adjusts the curve either side to keep the shape.
• Autodesk AutoCAD. Select a polyline and grips appear at its vertices and the middle of each segment; drag one to move it, or hover over it for a menu that adds or removes a vertex or turns a straight segment into an arc. A spline’s small triangular grip switches between its fit points, which the curve passes through, and its control vertices, which pull it from outside.
• Autodesk Fusion (formerly Fusion 360). In a sketch you drag points directly, but only as far as the sketch’s constraints and dimensions allow: geometry that is fully constrained turns black and will not move. On a fit point spline, select a point to show a handle that sets the curve’s direction there.

What carries over. Selecting points rather than objects, a marquee around several anchors, and handles that stay in line on a smooth point behave much the same everywhere. Two things vary. What Delete does to an anchor differs from program to program, so try it once on a spare shape first. And Shift-click adds to a selection in the design programs, while in AutoCAD a plain click adds and Shift-click takes away.

Try this

1. Draw a rectangle, take Points, and click the middle of its top side to add an anchor. Drag the new anchor upwards: a house.
2. Drag the outline of an ellipse halfway between two anchors, and watch only the two nearby handles move.
3. With the Pen in hand and no path started, hold Option, drag a point of a shape you drew earlier, let go of Option, and carry on with the Pen.

Going further

• Path editing, Curves and Pen
• Peter Karow, Digital Typefaces
• Gerald Farin, Curves and Surfaces for Computer Aided Geometric Design