Curves decides how a path passes through a point: turning a sharp corner, or sweeping smoothly around. Click an anchor to make it a corner; drag from it to pull out a pair of handles and round it; drag the end of a single handle to bend one side on its own.
What it does
Press C, or choose ‘Curves’ on the rail. Hover over a shape and every one of its anchors is shown, with every handle it has, not only the handles of selected points as in Points.
- Click an anchor and its handles are taken away. It becomes a bare corner, and the lines on either side meet it at an angle. An anchor that is already a corner is left alone, and the click is not recorded in the history.
- Drag from an anchor and a new pair of handles comes out along the drag, equal in length and pointing opposite ways: the point is now smooth. The first movement decides which handle you are holding, the one on the side your pointer set off toward, so the first drag always rounds the corner rather than tying the line in a knot. Carry the pointer across to the other side of the anchor and the handle swings over with it; the curve then crosses itself in a loop, which is sometimes exactly what you want.
- Drag the end of a handle and that handle moves by itself, breaking the pair. The point becomes a corner between two curves, a cusp, like the tip of a leaf or the crest of a wave. If an anchor is nearer the pointer than the handle’s end, the anchor wins.
After each gesture the shape stays on show with all its handles, so on a touch screen, where there is no hover to call them back, you can still pick one up. Curves works wherever Points does: on shapes waiting for a flip direction, on cuts, and on flipped pieces outside the sheet. Each drag is one step of undo.
Hold Option (Alt) and Points is lent to you until you let go, since Curves has no Option behavior of its own; hold Command for Move. Going the other way, from the Pen between paths, from Draw and from the four shapes, holding Shift lends you Curves. The Pen can also do this work in the middle of a path: Option-click or Option-drag an anchor of a shape already on the canvas and it converts that anchor just as Curves would.
Why it works this way
This is Photoshop’s Convert Point tool and Illustrator’s Anchor Point tool. Points can switch an anchor with an Option-click too. Curves exists because corner or smooth is the most consequential thing you can decide about a point, and that decision deserves a tool that does nothing else and shows every handle while it does it.
The two tools treat a handle differently, on purpose. Drag a handle with Points and its partner swings to stay in line: the point stays smooth. Drag it with Curves and it moves alone: the point breaks. One tool keeps smoothness; the other takes it apart.
The rule for the first drag was learned the hard way. An earlier version always treated the drag as the outgoing handle. Start a drag back toward the previous anchor and that handle pointed backwards, folding the curve over itself. Anyone pulling out of a corner expects a curve, so the tool now watches which way you set off.
The metaphor
A draftsman drawing a curve through plotted points reached for a French curve: a flat template of wood, and later of clear plastic, whose edge runs through a whole family of bends. You find the stretch of edge that touches three or four points, draw along it, then slide on to the next stretch with a little overlap. One widely used set is known as the Burmester set, after the German geometer Ludwig Burmester. A French curve can only make smooth lines. Where the drawing turned a corner, the draftsman lifted the template and began again at a new angle.
A knife tells the same story in paper. A curve is cut in one unbroken motion, the blade kept moving while the paper turns under it. A corner is where the blade stops, comes out, and goes back in facing a new way. Curves is the choice between those two motions, made after the cut.
Where the metaphor breaks: a French curve offers only the bends it was made with, while handles make any bend at all. And no physical tool has anything like a handle, a lever standing off the line that shapes it and never appears in the finished work.
A history
In art
In 1753 William Hogarth published The Analysis of Beauty, arguing that the most beautiful line is a gently twisting S, which he called the line of beauty; a serpentine line leads the eye on, where a straight one is taken in at a glance. He had already painted it: in his self-portrait with his pug, of 1745, a painter’s palette in the corner carries a curving line and an inscription naming it. Hogarth’s S is a lesson in smooth points. At its middle the bend changes from one side to the other, and the line passes through perfectly smoothly while turning the other way: the kind of point a Curves drag makes.
A notan sharpens the question, because every edge is shared. The boundary of a cut is the outline of the hole and, mirrored, of the piece. Make a point sharp and it is sharp twice.
In printing
Type designers have lived with this distinction for as long as letters have been digital. Karow’s Ikarus system of the early 1970s asked the operator to say, for every point, whether it was a corner, a tangent or a curve point. The UFO format that many type designers work in today still records, for each point, whether it is smooth. The PostScript language, on the other hand, has no such flag. Its curveto command simply takes control points, and a point is smooth only because its two handles happen to lie on one straight line through it. TrueType, the other great font format, uses simpler quadratic curves and goes further still: where two off-curve control points follow each other, a smooth point is understood to sit exactly halfway between them without ever being written down.
In technology
Engineers have exact words for what Curves changes. Two curves that merely meet at a point are joined with positional continuity, called G0: a corner. If they leave the point in the same direction, handles on one straight line, the join is tangent-continuous, G1. If the handles are also equal in length, the curve flows through without a jolt in its speed as well, C1. Beyond that is curvature continuity, G2, where the tightness of the bend also matches on both sides.
The difference between G1 and G2 is invisible in a line drawing and obvious on a car. Light reflected along a glossy body panel shows every change in curvature as a kink in the reflection, which is why car designers study surfaces under bands of light, and why design software imitates those bands on screen. Car design is the trade in which Pierre Bézier and Paul de Casteljau developed these curves. In this app, a Curves drag makes a C1 point, Points keeps G1 while you aim a handle, and a Curves handle drag makes a G0 cusp.
In professional software
Every path editor can switch an anchor between corner and smooth, with a tool of its own or a key held with the Pen. CAD programs describe the same choice as continuity: whether two curves meet at an angle, share a direction, or share their bend as well.
- Adobe Illustrator. The Anchor Point tool (Shift-C) behaves like Curves: click a smooth anchor to make it a corner, drag from a corner to pull out a pair of handles, and drag one handle to move it alone. The Curvature tool draws smooth curves through the points you click, and a double-click on an anchor switches it between smooth and corner.
- Adobe Photoshop. The Convert Point tool, grouped with the Pen, does the same three jobs on paths and shape layers, and holding Option (Alt) with the Pen borrows it. The Curvature Pen tool works like Illustrator’s Curvature tool, double-click included.
- Figma. In vector edit mode (press Enter, or double-click a shape), the Bend tool adds handles to a point. The right sidebar sets how the two handles of a selected point behave: ‘No mirroring’, ‘Mirror angle’ or ‘Mirror angle and length’, which match the cusp, the G1 point and the C1 point described above.
- Inkscape. The Node tool (
N) has four node types, each with a key: cusp (Shift-C), smooth (Shift-S), symmetric (Shift-Y), and auto-smooth (Shift-A), whose handles adjust themselves as neighboring nodes move. - Autodesk Fusion (formerly Fusion 360). Sketch curves are joined by constraints as well as handles: the Tangent constraint makes a G1 join and the Curvature constraint a G2 one. To judge a surface, ‘Inspect › Zebra Analysis’ lays stripes over a body, and a join that is only G1 shows as a sharp bend in the stripes.
What carries over. The three gestures of Curves, click to sharpen, drag to round, drag a handle to break, are those of Illustrator’s Anchor Point tool and Photoshop’s Convert Point tool. The words change more than the idea: corner, cusp and G0 name one kind of point; smooth, tangent and G1 another. Watch what a program’s handles do and you will know which it means.
Try this
- Draw a hexagon, take Curves, and drag outwards from one corner. Click the same anchor again to make it sharp once more.
- Drag from a corner, then carry the pointer across to the other side of the anchor and watch the loop form.
- Click the left and right anchors of a circle: it becomes a lens, pointed at both ends. Then drag one handle end at the top to push the curve to one side.
Going further
- Points, Pen and Path editing
- William Hogarth, The Analysis of Beauty
- Pierre Bézier, The Mathematical Basis of the UNISURF CAD System