Question

A path may also contain curved lines. These are, unfortunately, a bit more involved to draw than straight lines.

The quadraticCurveTo method draws a curve to a given point. To determine the curvature of the line, the method is given a control point as well as a destination point. Imagine this control point as attracting the line, giving the line its curve. The line won’t go through the control point. Rather, the direction of the line at its start and end points will be such that it aligns with the line from there to the control point. The following example illustrates this:

<canvas></canvas>
<script>
  var cx = document.querySelector("canvas").getContext("2d");
  cx.beginPath();
  cx.moveTo(10, 90);
  // control=(60,10) goal=(90,90)
  cx.quadraticCurveTo(60, 10, 90, 90);
  cx.lineTo(60, 10);
  cx.closePath();
  cx.stroke();
</script>

It produces a path that looks like this:

We draw a quadratic curve from the left to the right, with (60,10) as control point, and then draw two line segments going through that control point and back to the start of the line. The result somewhat resembles a Star Trek insignia. You can see the effect of the control point: the lines leaving the lower corners start off in the direction of the control point and then curve toward their target.

The bezierCurveTo method draws a similar kind of curve. Instead of a single control point, this one has two—one for each of the line's endpoints. Here is a similar sketch to illustrate the behavior of such a curve:

<canvas></canvas>
<script>
  var cx = document.querySelector("canvas").getContext("2d");
  cx.beginPath();
  cx.moveTo(10, 90);
  // control1=(10,10) control2=(90,10) goal=(50,90)
  cx.bezierCurveTo(10, 10, 90, 10, 50, 90);
  cx.lineTo(90, 10);
  cx.lineTo(10, 10);
  cx.closePath();
  cx.stroke();
</script>

The two control points specify the direction at both ends of the curve. The further they are away from their corresponding point, the more the curve will “bulge” in that direction.

Such curves can be hard to work with—it’s not always clear how to find the control points that provide the shape you are looking for. Sometimes you can compute them, and sometimes you’ll just have to find a suitable value by trial and error.

Arcs—fragments of a circle—are easier to reason about. The arcTo method takes no less than five arguments. The first four arguments act somewhat like the arguments to quadraticCurveTo . The first pair provides a sort of control point, and the second pair gives the line’s destination. The fifth argument provides the radius of the arc. The method will conceptually project a corner—a line going to the control point and then to the destination point—and round the corner’s point so that it forms part of a circle with the given radius. The arcTo method then draws the rounded part, as well as a line from the starting position to the start of the rounded part.

<canvas></canvas>
<script>
  var cx = document.querySelector("canvas").getContext("2d");
  cx.beginPath();
  cx.moveTo(10, 10);
  // control=(90,10) goal=(90,90) radius=20
  cx.arcTo(90, 10, 90, 90, 20);
  cx.moveTo(10, 10);
  // control=(90,10) goal=(90,90) radius=80
  cx.arcTo(90, 10, 90, 90, 80);
  cx.stroke();
</script>

This produces two rounded corners with different radii.

The arcTo method won’t draw the line from the end of the rounded part to the goal position, though the word to in its name would suggest it does. You can follow up with a call to lineTo with the same goal coordinates to add that part of the line.

To draw a circle, you could use four calls to arcTo (each turning 90 degrees). But the arc method provides a simpler way. It takes a pair of coordinates for the arc’s center, a radius, and then a start and end angle.

Those last two parameters make it possible to draw only part of circle. The angles are measured in radians, not degrees. This means a full circle has an angle of 2π, or 2 * Math.PI , which is about 6.28. The angle starts counting at the point to the right of the circle’s center and goes clockwise from there. You can use a start of 0 and an end bigger than 2π (say, 7) to draw a full circle.

<canvas></canvas>
<script>
  var cx = document.querySelector("canvas").getContext("2d");
  cx.beginPath();
  // center=(50,50) radius=40 angle=0 to 7
  cx.arc(50, 50, 40, 0, 7);
  // center=(150,50) radius=40 angle=0 to ½π
  cx.arc(150, 50, 40, 0, 0.5 * Math.PI);
  cx.stroke();
</script>

The resulting picture contains a line from the right of the full circle (first call to arc ) to the right of the quarter-circle (second call). Like other path-drawing methods, a line drawn with arc is connected to the previous path segment by default. You’d have to call moveTo or start a new path if you want to avoid this.

This is a book about getting computers to do what you want them to do. Computers are about as common as screwdrivers today, but they contain a lot more hidden complexity and thus are harder to operate and understand. To many, they remain alien, slightly threatening things.