d3js Redistributing labels around a pie chart

Question

I'm using d3.js to create a donut chart with labels on the outside. Using some trigonometry based on the centroids of each slice of the pie, I position the labels.

g.append("g")
        .attr("class", "percentage")
        .append("text")
            .attr("transform", function(d)
                { 
                    var c = arc.centroid(d);
                    var x = c[0];
                    var y = c[1];
                    var h = Math.sqrt(x*x + y*y);
                    return "translate(" + (x/h * obj.labelRadius) +  ',' + (y/h * obj.labelRadius) +  ")"; 
                }
            ) 
            .attr("dy", ".4em")
            .attr("text-anchor", function(d) 
                {
                    return (d.endAngle + d.startAngle)/2 > Math.PI ? "end" : "start";
                }
            )
            .text(function(d) { return d.data.percentage+"%"; });

What I'm ultimately trying to accomplish is to rearrange labels that are outside the edges of the pie chart, to prevent overlaps.

One of the ways I have tried to solve the problem is to define set "anchor points", where labels can be positioned, guaranteeing that they will no overlap. Problem is mapping the centroids to the anchors and preserving some sense of visual correspondence between the slices and the labels (Specially difficult when slices are slim).

Image above shows the possible location of the anchors (centroids of the slices shown). With these positions it is impossible to have an overlap.

Adding complexity to the problem is the fact that when labels (they're horizontal) are close to the top or bottom of the pie, they are more easily overlapped, than when they are on the right or left of the pie.

Any ideas on how to approach this problem?

[EDIT] Following the suggestion of meetamit, I implemented the following:

.attr("dy", function(d)
{
    var c = arc.centroid(d);
        var x = c[0];
        var y = c[1];
        var h = Math.sqrt(x*x + y*y);
        var dy = y/h * obj.labelRadius; 
    dy=dy*fontSizeParam*.14/heightParam);
    return (dy)+"em";
})

It helps a bit, and gives some room to the labels, still looking for a solution that will cover all cases though...

Answer 1

Can't you create two arcs? one for the chart, and one for the labels?

// first arc used for drawing the pie chart
var arc = d3.svg.arc()
  .outerRadius(radius - 10)
  .innerRadius(0);

// label attached to first arc
g.append("text")
  .attr("transform", function(d) { return "translate(" + arc.centroid(d) + ")"; })
  .attr("dy", ".35em")
  .style("text-anchor", "middle")
  .text(function(d) { return d.data.age; });

// second arc for labels
var arc2 = d3.svg.arc()
  .outerRadius(radius + 20)
  .innerRadius(radius + 20);

// label attached to second arc
g.append("text")
  .attr("transform", function(d) { return "translate(" + arc2.centroid(d) + ")"; })
  .attr("dy", ".35em")
  .style("text-anchor", "middle")
  .text(function(d) { return d.data.age; });

Answer 2

There is a good, pragmatic d3.js-based solution by programmer John Williams presented here:

https://www.safaribooksonline.com/blog/2014/03/11/solving-d3-label-placement-constraint-relaxing/

It should work well for cases with reasonable restrictions, e.g. a maximum of 12 labels as discussed above. There are also pointers in the article to more advanced algorithms, but this simple approach may actually, when used with sufficient label-content constraints, give results that have a more orderly visual appearance than other methods would yield.