D3js cartography: auto-focus on geographic area ?

I processed SRTM raster data to generate shapefiles -> geojson -> topojson so I may feed D3js with a suitable format.

The result look like this (the blue area is my oversized svg canvas):

Given geographic area of interest geo-borders (west border, North, East, South) and center:

// India geo-frame borders in decimal ⁰
var WNES = { "W": 67.0, "N":37.5, "E": 99.0, "S": 5.0 };
// India geo-center :
var latCenter = (WNES.S + WNES.N)/2,
    lonCenter =  (WNES.W + WNES.E)/2;

// HTML expected frame dimensions
var width  = 713,
    height = 724;   

// Projection: projection, center coord, scale(?), translate:
var projection = d3.geo.mercator()
    .center([lonCenter, latCenter])
    .scale(width)
    .translate([width/2, height/2]); // this push into the center of the html frame

// SVG injection:
var svg = d3.select("body").append("svg")
    .attr("width", width)
    .attr("height", height);

What is/are the relations between geo-dimensions, svg dimensions, and the scale ?

How to do an 'auto-focus' simplified as much as possible ?

I reused some code from Bostock & al, with some edits so you input your focus geo-area bounds (decimal coordinates):

var WNES = { "W": 67.0, "N":37.5, "E": 99.0, "S": 5.0 };

and the target svg canvas' width (px) such :

var width  = 600,

to automatically set the svg canvas' height, the zoom scale, and the translation in order to focus the display only on and fully on the target geo area.

// 1. -------------- SETTINGS ------------- //
// India geo-frame borders (decimal ⁰)
var WNES = { "W": 67.0, "N":37.5, "E": 99.0, "S": 5.0 };
// Geo values of interest :
var latCenter = (WNES.S + WNES.N)/2, // will not be used
    lonCenter = (WNES.W + WNES.E)/2, // will not be used
    geo_width = (WNES.E - WNES.W),
    geo_height= (WNES.N - WNES.S);
// HTML expected frame dimensions
var width  = 600,
    height = (geo_height / geo_width) * width ; // height function of width with ratio of geo-frame (later requires equirectangular projection!)

// Projection: projection, reset scale and reset translate
var projection = d3.geo.equirectangular()
      .scale(1)
      .translate([0, 0]);

// Normal stuff: SVG injection:
var svg = d3.select("body").append("svg")
    .attr("width", width)
    .attr("height", height);

// Normal stuff: Path
var path = d3.geo.path()
    .projection(projection)
    .pointRadius(4);

// Data (getJSON: TopoJSON)
d3.json("final.json", showData);

// 2. ---------- FUNCTION ------------- //
function showData(error, fra) {
    var Levels = topojson.feature(fra, fra.objects.levels);

// Focus area box compute to derive scale & translate.
var b = path.bounds(Levels), // get data's bounds as [[left, bottom], [right, top]]  [[W, S], [E, N]]
    s = 1 / Math.max((b[1][0] - b[0][0]) / width, (b[1][1] - b[0][1]) / height),
    t = [(width - s * (b[1][0] + b[0][0])) / 2, (height - s * (b[1][1] + b[0][1])) / 2];

// Projection update
projection
    .scale(s)
    .translate(t);

//Normal stuff: Append my topojson objects => svg layers
    svg.append("path")
        .datum(Levels)
        .attr("d", path)
    svg.selectAll(".levels")
        .data(topojson.feature(fra, fra.objects.levels).features)
      .enter().append("path")
        .attr("class", function(d) { return "Topo_" + d.properties.name; })
        .attr("data-elev", function(d) { return d.properties.name; })
        .attr("d", path)
}

Result is perfect:

See:

path.bounds(feature) -- Computes the projected bounding box (in pixels) for the specified feature.
India relief map with auto-focus (Hugo Lopez) -- Working example (with custom canvas height)
Center a map in d3 given a geoJSON object (Bostock & al.) -- critical help from there
Project to Bounding Box (Mike Bostock) -- Working example (with prefixed canvas dimensions)
D3js: How to design topographic maps? (Hugo Lopez) -- tutorial with makefile and html-d3js code.