p2s
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A JavaScript 2D physics engine.
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JavaScript
var Constraint = require('./Constraint')
, ContactEquation = require('../equations/ContactEquation')
, Equation = require('../equations/Equation')
, vec2 = require('../math/vec2')
, RotationalLockEquation = require('../equations/RotationalLockEquation');
module.exports = PrismaticConstraint;
/**
* Constraint that only allows bodies to move along a line, relative to each other. See <a href="http://www.iforce2d.net/b2dtut/joints-prismatic">this tutorial</a>. Also called "slider constraint".
*
* @class PrismaticConstraint
* @constructor
* @extends Constraint
* @author schteppe
* @param {Body} bodyA
* @param {Body} bodyB
* @param {Object} [options]
* @param {Number} [options.maxForce] Max force to be applied by the constraint
* @param {Array} [options.localAnchorA] Body A's anchor point, defined in its own local frame.
* @param {Array} [options.localAnchorB] Body B's anchor point, defined in its own local frame.
* @param {Array} [options.localAxisA] An axis, defined in body A frame, that body B's anchor point may slide along.
* @param {Boolean} [options.disableRotationalLock] If set to true, bodyB will be free to rotate around its anchor point.
* @param {Number} [options.upperLimit]
* @param {Number} [options.lowerLimit]
* @todo Ability to create using only a point and a worldAxis
* @example
* var constraint = new PrismaticConstraint(bodyA, bodyB, {
* localAxisA: [0, 1]
* });
* world.addConstraint(constraint);
*/
function PrismaticConstraint(bodyA, bodyB, options){
options = options || {};
Constraint.call(this,bodyA,bodyB,Constraint.PRISMATIC,options);
// Get anchors
var localAnchorA = vec2.create(),
localAxisA = vec2.fromValues(1,0),
localAnchorB = vec2.create();
if(options.localAnchorA){ vec2.copy(localAnchorA, options.localAnchorA); }
if(options.localAxisA){ vec2.copy(localAxisA, options.localAxisA); }
if(options.localAnchorB){ vec2.copy(localAnchorB, options.localAnchorB); }
/**
* @property localAnchorA
* @type {Array}
*/
this.localAnchorA = localAnchorA;
/**
* @property localAnchorB
* @type {Array}
*/
this.localAnchorB = localAnchorB;
/**
* @property localAxisA
* @type {Array}
*/
this.localAxisA = localAxisA;
/*
The constraint violation for the common axis point is
g = ( xj + rj - xi - ri ) * t := gg*t
where r are body-local anchor points, and t is a tangent to the constraint axis defined in body i frame.
gdot = ( vj + wj x rj - vi - wi x ri ) * t + ( xj + rj - xi - ri ) * ( wi x t )
Note the use of the chain rule. Now we identify the jacobian
G*W = [ -t -ri x t + t x gg t rj x t ] * [vi wi vj wj]
The rotational part is just a rotation lock.
*/
var maxForce = this.maxForce = options.maxForce !== undefined ? options.maxForce : Number.MAX_VALUE;
// Translational part
var trans = new Equation(bodyA,bodyB,-maxForce,maxForce);
var ri = new vec2.create(),
rj = new vec2.create(),
gg = new vec2.create(),
t = new vec2.create();
trans.computeGq = function(){
// g = ( xj + rj - xi - ri ) * t
return vec2.dot(gg,t);
};
trans.updateJacobian = function(){
var G = this.G,
xi = bodyA.position,
xj = bodyB.position;
vec2.rotate(ri,localAnchorA,bodyA.angle);
vec2.rotate(rj,localAnchorB,bodyB.angle);
vec2.add(gg,xj,rj);
vec2.subtract(gg,gg,xi);
vec2.subtract(gg,gg,ri);
vec2.rotate(t,localAxisA,bodyA.angle+Math.PI/2);
G[0] = -t[0];
G[1] = -t[1];
G[2] = -vec2.crossLength(ri,t) + vec2.crossLength(t,gg);
G[3] = t[0];
G[4] = t[1];
G[5] = vec2.crossLength(rj,t);
};
this.equations.push(trans);
// Rotational part
if(!options.disableRotationalLock){
var rot = new RotationalLockEquation(bodyA,bodyB,-maxForce,maxForce);
this.equations.push(rot);
}
/**
* The position of anchor A relative to anchor B, along the constraint axis.
* @property position
* @type {Number}
*/
this.position = 0;
// Is this one used at all?
this.velocity = 0;
/**
* Set to true to enable lower limit.
* @property lowerLimitEnabled
* @type {Boolean}
*/
this.lowerLimitEnabled = options.lowerLimit !== undefined ? true : false;
/**
* Set to true to enable upper limit.
* @property upperLimitEnabled
* @type {Boolean}
*/
this.upperLimitEnabled = options.upperLimit !== undefined ? true : false;
/**
* Lower constraint limit. The constraint position is forced to be larger than this value.
* @property lowerLimit
* @type {Number}
*/
this.lowerLimit = options.lowerLimit !== undefined ? options.lowerLimit : 0;
/**
* Upper constraint limit. The constraint position is forced to be smaller than this value.
* @property upperLimit
* @type {Number}
*/
this.upperLimit = options.upperLimit !== undefined ? options.upperLimit : 1;
// Equations used for limits
this.upperLimitEquation = new ContactEquation(bodyA,bodyB);
this.lowerLimitEquation = new ContactEquation(bodyA,bodyB);
// Set max/min forces
this.upperLimitEquation.minForce = this.lowerLimitEquation.minForce = 0;
this.upperLimitEquation.maxForce = this.lowerLimitEquation.maxForce = maxForce;
/**
* Equation used for the motor.
* @property motorEquation
* @type {Equation}
*/
this.motorEquation = new Equation(bodyA,bodyB);
/**
* The current motor state. Enable or disable the motor using .enableMotor
* @property motorEnabled
* @type {Boolean}
*/
this.motorEnabled = false;
/**
* Set the target speed for the motor.
* @property motorSpeed
* @type {Number}
*/
this.motorSpeed = 0;
var that = this;
var motorEquation = this.motorEquation;
motorEquation.computeGq = function(){ return 0; };
motorEquation.computeGW = function(){
var G = this.G,
bi = this.bodyA,
bj = this.bodyB,
vi = bi.velocity,
vj = bj.velocity,
wi = bi.angularVelocity,
wj = bj.angularVelocity;
return this.gmult(G,vi,wi,vj,wj) + that.motorSpeed;
};
}
PrismaticConstraint.prototype = new Constraint();
PrismaticConstraint.prototype.constructor = PrismaticConstraint;
var worldAxisA = vec2.create(),
worldAnchorA = vec2.create(),
worldAnchorB = vec2.create(),
orientedAnchorA = vec2.create(),
orientedAnchorB = vec2.create(),
tmp = vec2.create();
/**
* Update the constraint equations. Should be done if any of the bodies changed position, before solving.
* @method update
*/
PrismaticConstraint.prototype.update = function(){
var eqs = this.equations,
trans = eqs[0],
upperLimit = this.upperLimit,
lowerLimit = this.lowerLimit,
upperLimitEquation = this.upperLimitEquation,
lowerLimitEquation = this.lowerLimitEquation,
bodyA = this.bodyA,
bodyB = this.bodyB,
localAxisA = this.localAxisA,
localAnchorA = this.localAnchorA,
localAnchorB = this.localAnchorB;
trans.updateJacobian();
// Transform local things to world
vec2.rotate(worldAxisA, localAxisA, bodyA.angle);
vec2.rotate(orientedAnchorA, localAnchorA, bodyA.angle);
vec2.add(worldAnchorA, orientedAnchorA, bodyA.position);
vec2.rotate(orientedAnchorB, localAnchorB, bodyB.angle);
vec2.add(worldAnchorB, orientedAnchorB, bodyB.position);
var relPosition = this.position = vec2.dot(worldAnchorB,worldAxisA) - vec2.dot(worldAnchorA,worldAxisA);
// Motor
if(this.motorEnabled){
// G = [ a a x ri -a -a x rj ]
var G = this.motorEquation.G;
G[0] = worldAxisA[0];
G[1] = worldAxisA[1];
G[2] = vec2.crossLength(worldAxisA,orientedAnchorB);
G[3] = -worldAxisA[0];
G[4] = -worldAxisA[1];
G[5] = -vec2.crossLength(worldAxisA,orientedAnchorA);
}
/*
Limits strategy:
Add contact equation, with normal along the constraint axis.
min/maxForce is set so the constraint is repulsive in the correct direction.
Some offset is added to either equation.contactPointA or .contactPointB to get the correct upper/lower limit.
^
|
upperLimit x
| ------
anchorB x<---| B |
| | |
------ | ------
| | |
| A |-->x anchorA
------ |
x lowerLimit
|
axis
*/
if(this.upperLimitEnabled && relPosition > upperLimit){
// Update contact constraint normal, etc
vec2.scale(upperLimitEquation.normalA, worldAxisA, -1);
vec2.subtract(upperLimitEquation.contactPointA, worldAnchorA, bodyA.position);
vec2.subtract(upperLimitEquation.contactPointB, worldAnchorB, bodyB.position);
vec2.scale(tmp,worldAxisA,upperLimit);
vec2.add(upperLimitEquation.contactPointA,upperLimitEquation.contactPointA,tmp);
if(eqs.indexOf(upperLimitEquation) === -1){
eqs.push(upperLimitEquation);
}
} else {
var idx = eqs.indexOf(upperLimitEquation);
if(idx !== -1){
eqs.splice(idx,1);
}
}
if(this.lowerLimitEnabled && relPosition < lowerLimit){
// Update contact constraint normal, etc
vec2.scale(lowerLimitEquation.normalA, worldAxisA, 1);
vec2.subtract(lowerLimitEquation.contactPointA, worldAnchorA, bodyA.position);
vec2.subtract(lowerLimitEquation.contactPointB, worldAnchorB, bodyB.position);
vec2.scale(tmp,worldAxisA,lowerLimit);
vec2.subtract(lowerLimitEquation.contactPointB,lowerLimitEquation.contactPointB,tmp);
if(eqs.indexOf(lowerLimitEquation) === -1){
eqs.push(lowerLimitEquation);
}
} else {
var idx = eqs.indexOf(lowerLimitEquation);
if(idx !== -1){
eqs.splice(idx,1);
}
}
};
/**
* Enable the motor
* @method enableMotor
*/
PrismaticConstraint.prototype.enableMotor = function(){
if(this.motorEnabled){
return;
}
this.equations.push(this.motorEquation);
this.motorEnabled = true;
};
/**
* Disable the rotational motor
* @method disableMotor
*/
PrismaticConstraint.prototype.disableMotor = function(){
if(!this.motorEnabled){
return;
}
var i = this.equations.indexOf(this.motorEquation);
this.equations.splice(i,1);
this.motorEnabled = false;
};
/**
* Set the constraint limits.
* @method setLimits
* @param {number} lower Lower limit.
* @param {number} upper Upper limit.
*/
PrismaticConstraint.prototype.setLimits = function (lower, upper) {
if(typeof(lower) === 'number'){
this.lowerLimit = lower;
this.lowerLimitEnabled = true;
} else {
this.lowerLimit = lower;
this.lowerLimitEnabled = false;
}
if(typeof(upper) === 'number'){
this.upperLimit = upper;
this.upperLimitEnabled = true;
} else {
this.upperLimit = upper;
this.upperLimitEnabled = false;
}
};