How to set initial position of draggable points in JSXGraph in an equation graph?

Question

I'm developing a web software that plots an interactive polynomial equation with 2 variables on JSXGraph, I need that every point where the derivative of the equation is 0 to have a draggable point, and that when I drag one point, only the interval between 1 point after and 1 before the dragged point of the curve goes together does anyone knows how I could do that?

Answer 1

Sorry for the delay. I guess, what you need is Hermite interpolation. I gave an example recently in Google groups (https://groups.google.com/forum/#!topic/jsxgraph/OHls2NTOmUA). Hermite interpolation is not yet integrated in JSXGraph, but there seem to be a demand for it, so we may think about it.

Here is the code:

JXG.Math.Numerics.hermitePolynomial = function (p, derivatives) {
        var w = [],
            Lii = [],

            /** @ignore */
            fct = function (x, suspendedUpdate) {
                var i, k, xi, s,
                    L, Hi, Hi_hat,
                    len = p.length,
                    num = 0,
                    denom = 0;

                if (!suspendedUpdate) {
                    // Compute denominator
                    for (i = 0; i < len; i++) {
                        w[i] = 1.0;
                        Lii[i] = 0.0;
                        xi = p[i].X();

                        for (k = 0; k < len; k++) {
                            if (k !== i) {
                                w[i] *= (xi - p[k].X());
                                Lii[i] += 1 / (xi - p[k].X());
                            }
                        }

                        w[i] = 1 / w[i];
                    }
                }

                s = 0.0;
                for (i = 0; i < len; i++) {
                    xi = p[i].X();
                    L = w[i];
                    for (k = 0; k < len; k++) {
                        if (k !== i) {
                            L *= (x - p[k].X());
                        }
                    }

                    Hi = (1.0 - 2 * (x - xi) * Lii[i]) * L * L;
                    Hi_hat = (x -xi) * L * L;
                    s += p[i].Y() * Hi + derivatives[i] * Hi_hat;
                }
                return s;
            };

        return fct;
    };

var board = JXG.JSXGraph.initBoard("jxgbox", {
            boundingbox: [-5, 6, 6, -5],
            axis: true
});

var p = [];
// Define the points
p[0] = board.create('point', [-1,2], {size:4});
p[1] = board.create('point', [1,-2], {size:4});
p[2] = board.create('point', [3,-1], {size:4});

// The derivates at this points are all zero.
var derivatives = [0, 0, 0];

var f = JXG.Math.Numerics.hermitePolynomial(p, derivatives);
var graph = board.create('functiongraph', [f, -10, 10], {strokeWidth:2});

A live demo is at https://jsfiddle.net/vcL7aepo/278/

Best wishes, Alfred