p2 distance constraint

var Constraint = require('./Constraint')
,   Equation = require('../equations/Equation')
,   vec2 = require('../math/vec2');

module.exports = DistanceConstraint;

/**
 * Constraint that tries to keep the distance between two bodies constant.
 *
 * @class DistanceConstraint
 * @constructor
 * @author schteppe
 * @param {Body} bodyA
 * @param {Body} bodyB
 * @param {object} [options]
 * @param {number} [options.distance] The distance to keep between the anchor points. Defaults to the current distance between the bodies.
 * @param {Array} [options.localAnchorA] The anchor point for bodyA, defined locally in bodyA frame. Defaults to [0,0].
 * @param {Array} [options.localAnchorB] The anchor point for bodyB, defined locally in bodyB frame. Defaults to [0,0].
 * @param {object} [options.maxForce=Number.MAX_VALUE] Maximum force to apply.
 * @extends Constraint
 *
 * @example
 *     // If distance is not given as an option, then the current distance between the bodies is used.
 *     // In this example, the bodies will be constrained to have a distance of 2 between their centers.
 *     var bodyA = new Body({ mass: 1, position: [-1, 0] });
 *     var bodyB = new Body({ mass: 1, position: [1, 0] });
 *     var constraint = new DistanceConstraint(bodyA, bodyB);
 *     world.addConstraint(constraint);
 *
 * @example
 *     // Manually set the distance and anchors
 *     var constraint = new DistanceConstraint(bodyA, bodyB, {
 *         distance: 1,          // Distance to keep between the points
 *         localAnchorA: [1, 0], // Point on bodyA
 *         localAnchorB: [-1, 0] // Point on bodyB
 *     });
 *     world.addConstraint(constraint);
 */
function DistanceConstraint(bodyA,bodyB,options){
    options = options || {};

    Constraint.call(this,bodyA,bodyB,Constraint.DISTANCE,options);

    /**
     * Local anchor in body A.
     * @property localAnchorA
     * @type {Array}
     */
    this.localAnchorA = options.localAnchorA ? vec2.clone(options.localAnchorA) : vec2.create();

    /**
     * Local anchor in body B.
     * @property localAnchorB
     * @type {Array}
     */
    this.localAnchorB = options.localAnchorB ? vec2.clone(options.localAnchorB) : vec2.create();

    var localAnchorA = this.localAnchorA;
    var localAnchorB = this.localAnchorB;

    /**
     * The distance to keep.
     * @property distance
     * @type {Number}
     */
    this.distance = 0;

    if(typeof(options.distance) === 'number'){
        this.distance = options.distance;
    } else {
        // Use the current world distance between the world anchor points.
        var worldAnchorA = vec2.create(),
            worldAnchorB = vec2.create(),
            r = vec2.create();

        // Transform local anchors to world
        vec2.rotate(worldAnchorA, localAnchorA, bodyA.angle);
        vec2.rotate(worldAnchorB, localAnchorB, bodyB.angle);

        vec2.add(r, bodyB.position, worldAnchorB);
        vec2.subtract(r, r, worldAnchorA);
        vec2.subtract(r, r, bodyA.position);

        this.distance = vec2.length(r);
    }

    var maxForce;
    if(typeof(options.maxForce)==="undefined" ){
        maxForce = Number.MAX_VALUE;
    } else {
        maxForce = options.maxForce;
    }

    var normal = new Equation(bodyA,bodyB,-maxForce,maxForce); // Just in the normal direction
    this.equations = [ normal ];

    /**
     * Max force to apply.
     * @property {number} maxForce
     */
    this.maxForce = maxForce;

    // g = (xi - xj).dot(n)
    // dg/dt = (vi - vj).dot(n) = G*W = [n 0 -n 0] * [vi wi vj wj]'

    // ...and if we were to include offset points:
    // g =
    //      (xj + rj - xi - ri).dot(n) - distance
    //
    // dg/dt =
    //      (vj + wj x rj - vi - wi x ri).dot(n) =
    //      { term 2 is near zero } =
    //      [-n   -ri x n   n   rj x n] * [vi wi vj wj]' =
    //      G * W
    //
    // => G = [-n -rixn n rjxn]

    var r = vec2.create();
    var ri = vec2.create(); // worldAnchorA
    var rj = vec2.create(); // worldAnchorB
    var that = this;
    normal.computeGq = function(){
        var bodyA = this.bodyA,
            bodyB = this.bodyB,
            xi = bodyA.position,
            xj = bodyB.position;

        // Transform local anchors to world
        vec2.rotate(ri, localAnchorA, bodyA.angle);
        vec2.rotate(rj, localAnchorB, bodyB.angle);

        vec2.add(r, xj, rj);
        vec2.subtract(r, r, ri);
        vec2.subtract(r, r, xi);

        //vec2.subtract(r, bodyB.position, bodyA.position);
        return vec2.length(r) - that.distance;
    };

    // Make the contact constraint bilateral
    this.setMaxForce(maxForce);

    /**
     * If the upper limit is enabled or not.
     * @property {Boolean} upperLimitEnabled
     */
    this.upperLimitEnabled = false;

    /**
     * The upper constraint limit.
     * @property {number} upperLimit
     */
    this.upperLimit = 1;

    /**
     * If the lower limit is enabled or not.
     * @property {Boolean} lowerLimitEnabled
     */
    this.lowerLimitEnabled = false;

    /**
     * The lower constraint limit.
     * @property {number} lowerLimit
     */
    this.lowerLimit = 0;

    /**
     * Current constraint position. This is equal to the current distance between the world anchor points.
     * @property {number} position
     */
    this.position = 0;
}
DistanceConstraint.prototype = new Constraint();
DistanceConstraint.prototype.constructor = DistanceConstraint;

/**
 * Update the constraint equations. Should be done if any of the bodies changed position, before solving.
 * @method update
 */
var n = vec2.create();
var ri = vec2.create(); // worldAnchorA
var rj = vec2.create(); // worldAnchorB
DistanceConstraint.prototype.update = function(){
    var normal = this.equations[0],
        bodyA = this.bodyA,
        bodyB = this.bodyB,
        xi = bodyA.position,
        xj = bodyB.position,
        normalEquation = this.equations[0],
        G = normal.G;

    // Transform local anchors to world
    vec2.rotate(ri, this.localAnchorA, bodyA.angle);
    vec2.rotate(rj, this.localAnchorB, bodyB.angle);

    // Get world anchor points and normal
    vec2.add(n, xj, rj);
    vec2.subtract(n, n, ri);
    vec2.subtract(n, n, xi);
    this.position = vec2.length(n);

    var violating = false;
    if(this.upperLimitEnabled){
        if(this.position > this.upperLimit){
            normalEquation.maxForce = 0;
            normalEquation.minForce = -this.maxForce;
            this.distance = this.upperLimit;
            violating = true;
        }
    }

    if(this.lowerLimitEnabled){
        if(this.position < this.lowerLimit){
            normalEquation.maxForce = this.maxForce;
            normalEquation.minForce = 0;
            this.distance = this.lowerLimit;
            violating = true;
        }
    }

    if((this.lowerLimitEnabled || this.upperLimitEnabled) && !violating){
        // No constraint needed.
        normalEquation.enabled = false;
        return;
    }

    normalEquation.enabled = true;

    vec2.normalize(n,n);

    // Caluclate cross products
    var rixn = vec2.crossLength(ri, n),
        rjxn = vec2.crossLength(rj, n);

    // G = [-n -rixn n rjxn]
    G[0] = -n[0];
    G[1] = -n[1];
    G[2] = -rixn;
    G[3] = n[0];
    G[4] = n[1];
    G[5] = rjxn;
};

/**
 * Set the max force to be used
 * @method setMaxForce
 * @param {Number} maxForce
 */
DistanceConstraint.prototype.setMaxForce = function(maxForce){
    var normal = this.equations[0];
    normal.minForce = -maxForce;
    normal.maxForce =  maxForce;
};

/**
 * Get the max force
 * @method getMaxForce
 * @return {Number}
 */
DistanceConstraint.prototype.getMaxForce = function(){
    var normal = this.equations[0];
    return normal.maxForce;
};