Opposite of ease cubic-bezier function

Question

I have the ease cubic-bezier function: cubic-bezier(.25,.1,.25,1) (http://cubic-bezier.com/#.25,.1,.25,1)

I want the opposite of this. Here is graphic representation of what I'm trying to accomplish:

The graph on left is what I have, and the function for the graph on the right is what I'm trying to achieve.

Answer 1

If you want to do a rotation as in your updated answer, all we have to do is... well, that. Rotate around (0.5,0.5) by a 180 degree, or π radians, angle. Let's assume we have a curve encoded as an array c with four point objects { x:..., y... }, then we can effect this rotation as:

c = [ {x:...,y:...}, ..., ..., ...];

function halfUnitTurn(v) {
  // Note: it's actually 0.5 + ((v.x-0.5)*cos(pi) - (v.x-0.5)*sin(pi)),
  // (and x*sin + y*cos for the y:... part) but: cos(pi) is just -1, and
  // sin(pi) is 0, so things REALLY simplify!
  return {
    x: 0.5 - (v.x-0.5),
    y: 0.5 - (v.y-0.5)
  };
}

var rotated = c.map(function(p) { return halfUnitTurn(p); });

And as demonstrator code: http://jsfiddle.net/mokg77fq/

Answer 2

Here is Mike's awesome code put into a reusable function:

function reverseCssCubicBezier(cubicBezier) {
    var maxX = Math.max(cubicBezier[0].x, cubicBezier[1].x, cubicBezier[2].x, cubicBezier[3].x);
    var maxY = Math.max(cubicBezier[0].y, cubicBezier[1].y, cubicBezier[2].y, cubicBezier[3].y);
    var halfUnitTurn = function(v) {
        var tx = maxX/2, ty = maxY/2;
        return { x: tx - (v.x-tx), y: ty - (v.y-ty) };
    };
    var revd = cubicBezier.map(halfUnitTurn);
    return revd.reverse();
}

And this is how to use it:

var ease = [{x:0,y:0}, {x:.25,y:.1}, {x:.25,y:1}, {x:1,y:1}]; //cubic-bezier(.25, .1, .25, 1)
var ease_reversed = reverseCssCubicBezier(ease);
var ease_css_string = 'cubic_bezier(' + [ease[1].x, ease[1].y, ease[2].x, ease[2].y].join(', ') + ')';
var ease_reversed_css_string = 'cubic_bezier(' + [ease_reversed[1].x, ease_reversed[1].y, ease_reversed[2].x, ease_reversed[2].y].join(', ') + ')';

This returns:

ease: [{x:0, y:0}, {x:0.25, y:0.1}, {x:0.25, y:1}, {x:1, y:1}]
ease-reversed: [{x:0, y:0}, {x:0.75, y:0}, {x:0.75, y:0.9}, {x:1, y:1}]

ease: cubic_bezier(0.25, 0.1, 0.25, 1)
ease-reversed: cubic_bezier(0.75, 0, 0.75, 0.9)

Graphically we see its perfect overlap, i shifted the green one to left a little bit to show its perfectly overlapping.

Thanks Mike!