#7: Introduction to Scales

One of D3's most important and useful concepts is the scale, which is a function that maps an input domain to an output range.1

We've changed our slider so instead of sliding between values of 0 and width it now slides between 0 and 100. We'd still like our circle to move all the way across, so we need a way to define that a value of 50 is equal to a x position that's 50% across.

In graphics libraries like p5.js, there usually a map() function for this. D3 goes beyond that to provide a sophisticated system for generating map functions. Calling var x = d3.scaleLinear()2, doesn't return a value, it returns a function that you can call as x().3

Calling the domain() and range() functions on x will set the input domain and output range for x.4 This is useful since attr() takes functions as a parameter, so we can write .attr("cx", x). This is equivalent to .attr("cx", function(d){return x(d);}) but much more concise.

For x, we are using a linear scale, which maps values linearly from the domain to the range. 0 is mapped to 0, 50 is mapped to 50% of width, and 100 is mapped to width.

For y, we're using d3.scalePow(), a power scale. If we set the exponent() to 2, interpolates between 0 and 1 with exponential growth.

We've added a c scale for color, which is a d3.scaleSequential. These scales map from a domain to a specific range defined by a provided interpolator function. We're using the d3.interpolateInferno interpolator, which returns specific CSS colors as the range.

  1. For more information on the rationales behind D3 scales, see Mike Bostock's article introducing D3 Scale.

  2. In D3 v.4, Many of the method names have been changed as part of an effort to break the D3 library into reusable parts. Many of the examples that you see online will use d3.scale.linear instead of d3.scaleLinear. For information on this and other changes in D3 v.4, see this amazing postmortem by Mike Bostock: What Makes Software Good.

  3. In Javascript, all functions are first class objects, so they can be stored in variables, manipulated, have properties assigned to them, and everything else that you can do with a standard object. D3 uses this capability constantly—it's one of the things that makes D3 so powerful, but also so confusing to people coming from languages like C. For a useful overview of functions as first class objects, see this article.

  4. Yes, this is calling a function property assigned to a function object that sets properties on itself. Javascript is a powerful, strange language, and D3 takes full advantage of it.

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