# Curved Lines using SVG and JavaScript

March 01, 2016

This post deals with implementing an evenly curved line using SVG and JavaScript. SVG supports quadratic and cubic bezier curves using the `C`, `S` and `Q` path commands but those leave you with the calculation of the control points.

## Calculating the control points

To obtain a consistent and even curve one needs to place the control points like the following figure illustrates. Given are the outer control points A and D, as the line starting and ending points, as well as the curviness expressed by the degree a.

``````function curvedLine(Ax, Ay, Dx, Dy, a) {
``````

d is the calculated distance between the outer control points.

``````  const d = Math.sqrt(Math.pow(Ax-Dx, 2) + Math.pow(Ay-Dy, 2));
``````

rad is the radian measure of the degree a.

``````  const rad = a / 180.0 * 2.0 * Math.PI;
``````

r is the distance from the outer to the inner control points.

``````  const r = (0.3 * d) / Math.cos(rad);
``````

theta is the calculated angle of the line passing through both outer control points in radian.

``````const theta = Math.atan2(Ay - Dy, Ax - Dx);
``````

aO and aD are two angles in radian that are required to calculate the inner control points.

``````  const aO = theta - rad + Math.PI,
aD = theta + rad;
``````

The inner control points B and C, respectively, are calculated based on the line connecting the outer control points using the angle a and r as illustrated in the figure.

``````  const Bx = Ax + r*Math.cos(aO),
By = Ay + r*Math.sin(aO),
Cx = Dx + r*Math.cos(aD),
Cy = Dy + r*Math.sin(aD);
``````

Last but not least, the SVG path is built from the control points.

``````  return `M\${Ax},\${Ay} C\${Bx},\${By} \${Cx},\${Cy} \${Dx},\${Dy}`
}
``````

## Using the function

You can use an SVG library like D3.js to use the function result in an SVG path.

``````let svg = d3.select("body").append("svg")
.attr("width", 500)
.attr("height", 200);

svg.append('path')
.attr('stroke', '#000')
.attr('fill', 'none')
.attr('d', curvedLine(30, 160, 470, 160, 20));
``````