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` ````
This is the math supporting the concept of [this other Pen](https://codepen.io/CrocoDillon/pen/fBJxu) of mine ;-)
On the horizontal axis you have the ratio between 0 and 4, on the vertical axis you have the text area relative to the viewport area between 0 and 120%.
The green line is the ideal situation if you could just do `font-size: calc(10 * 1vw * 1vh)` and the text area is always 100% of the viewport area. Sadly you can’t do this.
The blue lines are poor attempts to match the green line as close as possible (`font-size: calc(5vw + 5vh)` and `font-size: 10vmin`) but they only match 100% for `ratio = 1`.
The red line is a combination of the two (`font-size: calc(4vw + 4vh + 2vmin)`) and is the best approach so far. This one even allows for tweaking of the actual numbers depending of what minimum and maximum ratio you want to support.
In those examples all scalars add up to 10 and that is the magic number that depends on how much how much text you want to fit, line height and the area relative to the viewport you want to fill.
```

` ````
canvas {
display: block;
margin: 1em auto;
}
```

` ````
var Graph = (function(document, undefined) {
function Graph(width, height) {
this.canvas = document.createElement('canvas');
this.canvas.width = width;
this.canvas.height = height;
this.context = this.canvas.getContext('2d');
this.functions = [];
this.domain = {lo: -10, hi: 10, range: 20};
this.codomain = {lo: -10, hi: 10, range: 20};
}
Graph.prototype.setDomain = function(x1, x2) {
this.domain.lo = x1;
this.domain.hi = x2;
this.domain.range = x2 - x1;
}
Graph.prototype.setCodomain = function(y1, y2) {
this.codomain.lo = y1;
this.codomain.hi = y2;
this.codomain.range = y2 - y1;
}
/**
* Adds a function definition to the graph, which can either be a
* literal function or an object with `function` defined, and
* optionally `color`, `thickness` and `step` defined too.
*
* @param f literal function or function definition object with
* optional parameters
* @return added function definition
*/
Graph.prototype.addFunction = function(f, color) {
if (typeof f === 'function') {
f = {
function: f,
color: color
};
}
f.color = f.color || '#000';
f.thickness = f.thickness || 1;
f.step = f.step > 0 ? f.step : this.domain.range / this.canvas.width;
this.functions.push(f);
return f;
};
Graph.prototype.removeFunction = function(f) {
var i = this.functions.indexOf(f);
if (i !== -1)
this.functions.splice(i, 1);
};
Graph.prototype.draw = function() {
var canvas = this.canvas,
context = this.context;
// clear canvas
context.clearRect(0, 0, canvas.width, canvas.height);
// draw axes
var zero = this.pointToCanvas({x: 0, y: 0});
context.beginPath();
context.moveTo(0, zero.y);
context.lineTo(canvas.width, zero.y);
context.moveTo(zero.x, 0);
context.lineTo(zero.x, canvas.height);
context.lineWidth = 1;
context.strokeStyle = '#000';
context.stroke();
// draw functions
for (var i = 0; i < this.functions.length; i++) {
var functionDefinition = this.functions[i];
f = functionDefinition.function,
x = this.domain.lo,
y = f(x),
pt = this.pointToCanvas({x: x, y: y});
context.beginPath();
context.moveTo(pt.x, pt.y);
do {
x = x + functionDefinition.step;
y = f(x);
pt = this.pointToCanvas({x: x, y: y});
context.lineTo(pt.x, pt.y);
} while (x < this.domain.hi);
context.lineWidth = functionDefinition.thickness;
context.strokeStyle = functionDefinition.color;
context.stroke();
}
};
Graph.prototype.pointToCanvas = function(pt) {
return {
x: (pt.x - this.domain.lo) * this.canvas.width / this.domain.range,
y: (this.codomain.hi - pt.y) * this.canvas.height / this.codomain.range
};
};
return Graph;
})(document);
// assumptions
// screen has 10k pixels
// for ratio = 1, font-size: 10vw fills the screen
// graphs
function ideal(ratio) {
// this would be perfect but you can't use
// multiplication in calc with 2 units
// calc(10 * 1vw * 1vh)
var vw = Math.sqrt(ratio),
vh = Math.sqrt(1/ratio);
return Math.pow(10 * vw * vh, 2);
}
function onlyVmin(ratio) {
var vw = Math.sqrt(ratio),
vh = Math.sqrt(1/ratio),
vmin = Math.min(vw, vh);
return Math.pow(10 * vmin, 2);
}
function vwAndVh(ratio) {
var vw = Math.sqrt(ratio),
vh = Math.sqrt(1/ratio);
return Math.pow(5 * vw + 5 * vh, 2);
}
function all(ratio) {
var vw = Math.sqrt(ratio),
vh = Math.sqrt(1/ratio),
vmin = Math.min(vw, vh);
return Math.pow(4 * vw + 4 * vh + 2 * vmin, 2);
}
// draw them to a canvas graph!
var graph = new Graph(640, 640);
graph.setDomain(0, 4);
graph.setCodomain(0, 120);
graph.addFunction(ideal, '#2ecc71');
graph.addFunction(onlyVmin, '#3498db');
graph.addFunction(vwAndVh, '#3498db');
graph.addFunction({
function: all,
thickness: 2,
color: '#c0392b'
});
graph.draw();
document.body.appendChild(graph.canvas);
```

999px

Also see: Tab Triggers