### Paul Cowan

Nomadic cattle rustler and inventor of the electric lasso.
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# Negative Axes and Axes positioning with d3.js

January 16, 2016

Up until now when I have been dealing with d3.js’s axes components, I have always kept the axes positive, i.e. both the x and y axes where showing values greater than 0.

I have been hacking around with this fun side project that takes the input of an algebraic expression and plots a graph for a sample range of values for x. You can checkout the source code here if you are interested.

Below is a screenshot of the end result:

It quickly became apparent that in order to show the curve of the expression properly, I would need to construct negative and positive x and y axes.

I have the following function below that constructs the data of x and y coordinates to plot the curve against which uses the excellent mathjs library to transform the string algebraic expression into a javascript function (line 2). I then create a sample range for x values ranging from -10 to 11 and evaluate the y coordinate for each item in the range by applying the function on line 5 to each item:

  getDataFromProps(expr) {
const expression = math.parse(expr);

const fn = (x) => {
return expression.eval({x: x});
};

return d3.range(-10, 11).map( (d) => {
return {x:d, y:fn(d)};
});
}

Armed with this data, I can now construct my axes.

I first create the axis against a scale that is in proportion with the viewport dimensions.

const dimensions = this.getDimensions();

xScale = d3.scale.linear()
.range([0, dimensions.width]);

yScale = d3.scale.linear()
.range([dimensions.height, 0]);

const xAxis = d3.svg.axis()
.scale(xScale);

const yAxis = d3.svg.axis()
.orient('left')
.scale(yScale);

The domain function of d3 allows you to specify a minimum and maximum value as the range of values that we can use for a particular axis.

Below I am using d3’s extent function that returns the minum and maximum values of an array and is equivalent to calling d3.min and d3.max simultaneously.

this.xScale.domain(d3.extent(data, function (d) {return d.x;}));

As I am supplying the values for the range of x values in the code above, I know that I will always have negative x values and positive x values.

The y coordinates are different depending on the function generated from the algebraic expression. Depending on the expression, there are basically 3 conditions I want to capture when displaying a curve.

The first case is when there are only positive y values:

The next case is when there are both negative and positive y values;

Lastly, only negative y values:

With this in mind, the code below creates a domain based on the minimum values of y and the maximum values of y:

const minY = d3.min(data, (d) => { return d.y; });
const maxY = d3.max(data, (d) => { return d.y; });

const nonNegativeAxis = minY >= 0 && maxY >= 0;
const positiveAndNegativeAxis = minY < 0 && maxY > 0;

let yScaleDomain, xAxisPosition;

if(nonNegativeAxis) {
yScaleDomain = [0, d3.max(data, (d) => {return d.y;})];
}  else {
yScaleDomain = d3.extent(data, (d) => {return d.y;});
}

this.yScale.domain(yScaleDomain);

this.svg.append('g')
.attr('class', 'axis')
.attr('transform', 'translate(' + dimensions.width/2 + ',0)')
.call(yAxis);

I either start my domain at 0 or use d3.extent again to get the maximum and minimum values for y like I did before for x.

The last problem to solve was to position the x axis. In the 3 code samples below, I am capturing the domain for y and the x axis position for each condition.

This is easy if I only have negative or positive values for y. I can simply place the x axis at the bottom for only positive values:

yScaleDomain = [0, d3.max(data, (d) => {return d.y;})];
xAxisPosition = dimensions.height;

When I have only negative values, then I can place the x axis at the top of the document:

yScaleDomain = d3.extent(data, (d) => {return d.y;});
xAxisPosition = 0;

The interesting case was when I have both positive and negative values for y.

What I ended up doing was selecting all the ticks or labels from the y axis and finding the label that had 0 against it and from that I could use d3 to to select its position and then use that for my x axis position.

Below is the code that does that:

xAxisPosition = this.svg.selectAll(".tick").filter((data) => {
return data === 0;
}).map((tick) => {
return d3.transform(d3.select(tick).attr('transform')).translate;
});

In the code above, I filter out all the other ticks apart from the 0 label. The zero tick is then passed into the map function which selects the transform attribute of the tick which might look something like this translate(0,280). The second value of translate, 280 in this instance gives me the position of the 0 label in the y axis. I can use this value to position my x axis.

Once I have the position of 0 in the y axis, I can position the axis to the document:

this.svg.append('g')
.attr('class', 'axis')
.attr('transform', 'translate(0,' + xAxisPosition + ')')
.call(xAxis);

When it comes to positioning the y axis, I simply divide the width by 2 and position it there:

this.svg.append('g')
.attr('class', 'axis')
.attr('transform', 'translate(' + dimensions.width/2 + ',0)')
.call(yAxis); Nomadic cattle rustler and inventor of the electric lasso.
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