/*
* Farseer Physics Engine based on Box2D.XNA port:
* Copyright (c) 2010 Ian Qvist
*
* Box2D.XNA port of Box2D:
* Copyright (c) 2009 Brandon Furtwangler, Nathan Furtwangler
*
* Original source Box2D:
* Copyright (c) 2006-2009 Erin Catto http://www.gphysics.com
*
* This software is provided 'as-is', without any express or implied
* warranty. In no event will the authors be held liable for any damages
* arising from the use of this software.
* Permission is granted to anyone to use this software for any purpose,
* including commercial applications, and to alter it and redistribute it
* freely, subject to the following restrictions:
* 1. The origin of this software must not be misrepresented; you must not
* claim that you wrote the original software. If you use this software
* in a product, an acknowledgment in the product documentation would be
* appreciated but is not required.
* 2. Altered source versions must be plainly marked as such, and must not be
* misrepresented as being the original software.
* 3. This notice may not be removed or altered from any source distribution.
*/
using System;
using System.Diagnostics;
using FarseerPhysics.Common;
using Microsoft.Xna.Framework;
namespace FarseerPhysics.Dynamics.Joints
{
// Linear constraint (point-to-line)
// d = p2 - p1 = x2 + r2 - x1 - r1
// C = dot(perp, d)
// Cdot = dot(d, cross(w1, perp)) + dot(perp, v2 + cross(w2, r2) - v1 - cross(w1, r1))
// = -dot(perp, v1) - dot(cross(d + r1, perp), w1) + dot(perp, v2) + dot(cross(r2, perp), v2)
// J = [-perp, -cross(d + r1, perp), perp, cross(r2,perp)]
//
// Angular constraint
// C = a2 - a1 + a_initial
// Cdot = w2 - w1
// J = [0 0 -1 0 0 1]
//
// K = J * invM * JT
//
// J = [-a -s1 a s2]
// [0 -1 0 1]
// a = perp
// s1 = cross(d + r1, a) = cross(p2 - x1, a)
// s2 = cross(r2, a) = cross(p2 - x2, a)
// Motor/Limit linear constraint
// C = dot(ax1, d)
// Cdot = = -dot(ax1, v1) - dot(cross(d + r1, ax1), w1) + dot(ax1, v2) + dot(cross(r2, ax1), v2)
// J = [-ax1 -cross(d+r1,ax1) ax1 cross(r2,ax1)]
// Block Solver
// We develop a block solver that includes the joint limit. This makes the limit stiff (inelastic) even
// when the mass has poor distribution (leading to large torques about the joint anchor points).
//
// The Jacobian has 3 rows:
// J = [-uT -s1 uT s2] // linear
// [0 -1 0 1] // angular
// [-vT -a1 vT a2] // limit
//
// u = perp
// v = axis
// s1 = cross(d + r1, u), s2 = cross(r2, u)
// a1 = cross(d + r1, v), a2 = cross(r2, v)
// M * (v2 - v1) = JT * df
// J * v2 = bias
//
// v2 = v1 + invM * JT * df
// J * (v1 + invM * JT * df) = bias
// K * df = bias - J * v1 = -Cdot
// K = J * invM * JT
// Cdot = J * v1 - bias
//
// Now solve for f2.
// df = f2 - f1
// K * (f2 - f1) = -Cdot
// f2 = invK * (-Cdot) + f1
//
// Clamp accumulated limit impulse.
// lower: f2(3) = max(f2(3), 0)
// upper: f2(3) = min(f2(3), 0)
//
// Solve for correct f2(1:2)
// K(1:2, 1:2) * f2(1:2) = -Cdot(1:2) - K(1:2,3) * f2(3) + K(1:2,1:3) * f1
// = -Cdot(1:2) - K(1:2,3) * f2(3) + K(1:2,1:2) * f1(1:2) + K(1:2,3) * f1(3)
// K(1:2, 1:2) * f2(1:2) = -Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3)) + K(1:2,1:2) * f1(1:2)
// f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
//
// Now compute impulse to be applied:
// df = f2 - f1
///
/// A prismatic joint. This joint provides one degree of freedom: translation
/// along an axis fixed in body1. Relative rotation is prevented. You can
/// use a joint limit to restrict the range of motion and a joint motor to
/// drive the motion or to model joint friction.
///
public class FixedPrismaticJoint : Joint
{
private Mat33 _K;
private float _a1, _a2;
private Vector2 _axis;
private bool _enableLimit;
private bool _enableMotor;
private Vector3 _impulse;
private LimitState _limitState;
private Vector2 _localXAxis1;
private Vector2 _localYAxis1;
private float _lowerTranslation;
private float _maxMotorForce;
private float _motorMass; // effective mass for motor/limit translational constraint.
private float _motorSpeed;
private Vector2 _perp;
private float _refAngle;
private float _s1, _s2;
private float _upperTranslation;
///
/// This requires defining a line of
/// motion using an axis and an anchor point. The definition uses local
/// anchor points and a local axis so that the initial configuration
/// can violate the constraint slightly. The joint translation is zero
/// when the local anchor points coincide in world space. Using local
/// anchors and a local axis helps when saving and loading a game.
///
/// The body.
/// The anchor.
/// The axis.
public FixedPrismaticJoint(Body body, Vector2 worldAnchor, Vector2 axis)
: base(body)
{
JointType = JointType.FixedPrismatic;
BodyB = BodyA;
LocalAnchorA = worldAnchor;
LocalAnchorB = BodyB.GetLocalPoint(worldAnchor);
_localXAxis1 = axis;
_localYAxis1 = MathUtils.Cross(1.0f, _localXAxis1);
_refAngle = BodyB.Rotation;
_limitState = LimitState.Inactive;
}
public Vector2 LocalAnchorA { get; set; }
public Vector2 LocalAnchorB { get; set; }
public override Vector2 WorldAnchorA
{
get { return LocalAnchorA; }
}
public override Vector2 WorldAnchorB
{
get { return BodyA.GetWorldPoint(LocalAnchorB); }
set { Debug.Assert(false, "You can't set the world anchor on this joint type."); }
}
///
/// Get the current joint translation, usually in meters.
///
///
public float JointTranslation
{
get
{
Vector2 d = BodyB.GetWorldPoint(LocalAnchorB) - LocalAnchorA;
Vector2 axis = _localXAxis1;
return Vector2.Dot(d, axis);
}
}
///
/// Get the current joint translation speed, usually in meters per second.
///
///
public float JointSpeed
{
get
{
Transform xf2;
BodyB.GetTransform(out xf2);
Vector2 r1 = LocalAnchorA;
Vector2 r2 = MathUtils.Multiply(ref xf2.R, LocalAnchorB - BodyB.LocalCenter);
Vector2 p1 = r1;
Vector2 p2 = BodyB.Sweep.C + r2;
Vector2 d = p2 - p1;
Vector2 axis = _localXAxis1;
Vector2 v1 = Vector2.Zero;
Vector2 v2 = BodyB.LinearVelocityInternal;
const float w1 = 0.0f;
float w2 = BodyB.AngularVelocityInternal;
float speed = Vector2.Dot(d, MathUtils.Cross(w1, axis)) +
Vector2.Dot(axis, v2 + MathUtils.Cross(w2, r2) - v1 - MathUtils.Cross(w1, r1));
return speed;
}
}
///
/// Is the joint limit enabled?
///
/// true if [limit enabled]; otherwise, false.
public bool LimitEnabled
{
get { return _enableLimit; }
set
{
Debug.Assert(BodyA.FixedRotation == false, "Warning: limits does currently not work with fixed rotation");
WakeBodies();
_enableLimit = value;
}
}
///
/// Get the lower joint limit, usually in meters.
///
///
public float LowerLimit
{
get { return _lowerTranslation; }
set
{
WakeBodies();
_lowerTranslation = value;
}
}
///
/// Get the upper joint limit, usually in meters.
///
///
public float UpperLimit
{
get { return _upperTranslation; }
set
{
WakeBodies();
_upperTranslation = value;
}
}
///
/// Is the joint motor enabled?
///
/// true if [motor enabled]; otherwise, false.
public bool MotorEnabled
{
get { return _enableMotor; }
set
{
WakeBodies();
_enableMotor = value;
}
}
///
/// Set the motor speed, usually in meters per second.
///
/// The speed.
public float MotorSpeed
{
set
{
WakeBodies();
_motorSpeed = value;
}
get { return _motorSpeed; }
}
///
/// Set the maximum motor force, usually in N.
///
/// The force.
public float MaxMotorForce
{
set
{
WakeBodies();
_maxMotorForce = value;
}
}
///
/// Get the current motor force, usually in N.
///
///
public float MotorForce { get; set; }
public Vector2 LocalXAxis1
{
get { return _localXAxis1; }
set
{
_localXAxis1 = value;
_localYAxis1 = MathUtils.Cross(1.0f, _localXAxis1);
}
}
public override Vector2 GetReactionForce(float inv_dt)
{
return inv_dt * (_impulse.X * _perp + (MotorForce + _impulse.Z) * _axis);
}
public override float GetReactionTorque(float inv_dt)
{
return inv_dt * _impulse.Y;
}
internal override void InitVelocityConstraints(ref TimeStep step)
{
Body bB = BodyB;
LocalCenterA = Vector2.Zero;
LocalCenterB = bB.LocalCenter;
Transform xf2;
bB.GetTransform(out xf2);
// Compute the effective masses.
Vector2 r1 = LocalAnchorA;
Vector2 r2 = MathUtils.Multiply(ref xf2.R, LocalAnchorB - LocalCenterB);
Vector2 d = bB.Sweep.C + r2 - /* b1._sweep.Center - */ r1;
InvMassA = 0.0f;
InvIA = 0.0f;
InvMassB = bB.InvMass;
InvIB = bB.InvI;
// Compute motor Jacobian and effective mass.
{
_axis = _localXAxis1;
_a1 = MathUtils.Cross(d + r1, _axis);
_a2 = MathUtils.Cross(r2, _axis);
_motorMass = InvMassA + InvMassB + InvIA * _a1 * _a1 + InvIB * _a2 * _a2;
if (_motorMass > Settings.Epsilon)
{
_motorMass = 1.0f / _motorMass;
}
}
// Prismatic constraint.
{
_perp = _localYAxis1;
_s1 = MathUtils.Cross(d + r1, _perp);
_s2 = MathUtils.Cross(r2, _perp);
float m1 = InvMassA, m2 = InvMassB;
float i1 = InvIA, i2 = InvIB;
float k11 = m1 + m2 + i1 * _s1 * _s1 + i2 * _s2 * _s2;
float k12 = i1 * _s1 + i2 * _s2;
float k13 = i1 * _s1 * _a1 + i2 * _s2 * _a2;
float k22 = i1 + i2;
float k23 = i1 * _a1 + i2 * _a2;
float k33 = m1 + m2 + i1 * _a1 * _a1 + i2 * _a2 * _a2;
_K.Col1 = new Vector3(k11, k12, k13);
_K.Col2 = new Vector3(k12, k22, k23);
_K.Col3 = new Vector3(k13, k23, k33);
}
// Compute motor and limit terms.
if (_enableLimit)
{
float jointTranslation = Vector2.Dot(_axis, d);
if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * Settings.LinearSlop)
{
_limitState = LimitState.Equal;
}
else if (jointTranslation <= _lowerTranslation)
{
if (_limitState != LimitState.AtLower)
{
_limitState = LimitState.AtLower;
_impulse.Z = 0.0f;
}
}
else if (jointTranslation >= _upperTranslation)
{
if (_limitState != LimitState.AtUpper)
{
_limitState = LimitState.AtUpper;
_impulse.Z = 0.0f;
}
}
else
{
_limitState = LimitState.Inactive;
_impulse.Z = 0.0f;
}
}
else
{
_limitState = LimitState.Inactive;
}
if (_enableMotor == false)
{
MotorForce = 0.0f;
}
if (Settings.EnableWarmstarting)
{
// Account for variable time step.
_impulse *= step.dtRatio;
MotorForce *= step.dtRatio;
Vector2 P = _impulse.X * _perp + (MotorForce + _impulse.Z) * _axis;
float L2 = _impulse.X * _s2 + _impulse.Y + (MotorForce + _impulse.Z) * _a2;
bB.LinearVelocityInternal += InvMassB * P;
bB.AngularVelocityInternal += InvIB * L2;
}
else
{
_impulse = Vector3.Zero;
MotorForce = 0.0f;
}
}
internal override void SolveVelocityConstraints(ref TimeStep step)
{
Body bB = BodyB;
Vector2 v1 = Vector2.Zero;
float w1 = 0.0f;
Vector2 v2 = bB.LinearVelocityInternal;
float w2 = bB.AngularVelocityInternal;
// Solve linear motor constraint.
if (_enableMotor && _limitState != LimitState.Equal)
{
float Cdot = Vector2.Dot(_axis, v2 - v1) + _a2 * w2 - _a1 * w1;
float impulse = _motorMass * (_motorSpeed - Cdot);
float oldImpulse = MotorForce;
float maxImpulse = step.dt * _maxMotorForce;
MotorForce = MathUtils.Clamp(MotorForce + impulse, -maxImpulse, maxImpulse);
impulse = MotorForce - oldImpulse;
Vector2 P = impulse * _axis;
float L1 = impulse * _a1;
float L2 = impulse * _a2;
v1 -= InvMassA * P;
w1 -= InvIA * L1;
v2 += InvMassB * P;
w2 += InvIB * L2;
}
Vector2 Cdot1 = new Vector2(Vector2.Dot(_perp, v2 - v1) + _s2 * w2 - _s1 * w1, w2 - w1);
if (_enableLimit && _limitState != LimitState.Inactive)
{
// Solve prismatic and limit constraint in block form.
float Cdot2 = Vector2.Dot(_axis, v2 - v1) + _a2 * w2 - _a1 * w1;
Vector3 Cdot = new Vector3(Cdot1.X, Cdot1.Y, Cdot2);
Vector3 f1 = _impulse;
Vector3 df = _K.Solve33(-Cdot);
_impulse += df;
if (_limitState == LimitState.AtLower)
{
_impulse.Z = Math.Max(_impulse.Z, 0.0f);
}
else if (_limitState == LimitState.AtUpper)
{
_impulse.Z = Math.Min(_impulse.Z, 0.0f);
}
// f2(1:2) = invK(1:2,1:2) * (-Cdot(1:2) - K(1:2,3) * (f2(3) - f1(3))) + f1(1:2)
Vector2 b = -Cdot1 - (_impulse.Z - f1.Z) * new Vector2(_K.Col3.X, _K.Col3.Y);
Vector2 f2r = _K.Solve22(b) + new Vector2(f1.X, f1.Y);
_impulse.X = f2r.X;
_impulse.Y = f2r.Y;
df = _impulse - f1;
Vector2 P = df.X * _perp + df.Z * _axis;
float L2 = df.X * _s2 + df.Y + df.Z * _a2;
v2 += InvMassB * P;
w2 += InvIB * L2;
}
else
{
// Limit is inactive, just solve the prismatic constraint in block form.
Vector2 df = _K.Solve22(-Cdot1);
_impulse.X += df.X;
_impulse.Y += df.Y;
Vector2 P = df.X * _perp;
float L2 = df.X * _s2 + df.Y;
v2 += InvMassB * P;
w2 += InvIB * L2;
}
bB.LinearVelocityInternal = v2;
bB.AngularVelocityInternal = w2;
}
internal override bool SolvePositionConstraints()
{
//Body b1 = BodyA;
Body b2 = BodyB;
Vector2 c1 = Vector2.Zero; // b1._sweep.Center;
float a1 = 0.0f; // b1._sweep.Angle;
Vector2 c2 = b2.Sweep.C;
float a2 = b2.Sweep.A;
// Solve linear limit constraint.
float linearError = 0.0f;
bool active = false;
float C2 = 0.0f;
Mat22 R1 = new Mat22(a1);
Mat22 R2 = new Mat22(a2);
Vector2 r1 = MathUtils.Multiply(ref R1, LocalAnchorA - LocalCenterA);
Vector2 r2 = MathUtils.Multiply(ref R2, LocalAnchorB - LocalCenterB);
Vector2 d = c2 + r2 - c1 - r1;
if (_enableLimit)
{
_axis = MathUtils.Multiply(ref R1, _localXAxis1);
_a1 = MathUtils.Cross(d + r1, _axis);
_a2 = MathUtils.Cross(r2, _axis);
float translation = Vector2.Dot(_axis, d);
if (Math.Abs(_upperTranslation - _lowerTranslation) < 2.0f * Settings.LinearSlop)
{
// Prevent large angular corrections
C2 = MathUtils.Clamp(translation, -Settings.MaxLinearCorrection, Settings.MaxLinearCorrection);
linearError = Math.Abs(translation);
active = true;
}
else if (translation <= _lowerTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.Clamp(translation - _lowerTranslation + Settings.LinearSlop,
-Settings.MaxLinearCorrection, 0.0f);
linearError = _lowerTranslation - translation;
active = true;
}
else if (translation >= _upperTranslation)
{
// Prevent large linear corrections and allow some slop.
C2 = MathUtils.Clamp(translation - _upperTranslation - Settings.LinearSlop, 0.0f,
Settings.MaxLinearCorrection);
linearError = translation - _upperTranslation;
active = true;
}
}
_perp = MathUtils.Multiply(ref R1, _localYAxis1);
_s1 = MathUtils.Cross(d + r1, _perp);
_s2 = MathUtils.Cross(r2, _perp);
Vector3 impulse;
Vector2 C1 = new Vector2(Vector2.Dot(_perp, d), a2 - a1 - _refAngle);
linearError = Math.Max(linearError, Math.Abs(C1.X));
float angularError = Math.Abs(C1.Y);
if (active)
{
float m1 = InvMassA, m2 = InvMassB;
float i1 = InvIA, i2 = InvIB;
float k11 = m1 + m2 + i1 * _s1 * _s1 + i2 * _s2 * _s2;
float k12 = i1 * _s1 + i2 * _s2;
float k13 = i1 * _s1 * _a1 + i2 * _s2 * _a2;
float k22 = i1 + i2;
float k23 = i1 * _a1 + i2 * _a2;
float k33 = m1 + m2 + i1 * _a1 * _a1 + i2 * _a2 * _a2;
_K.Col1 = new Vector3(k11, k12, k13);
_K.Col2 = new Vector3(k12, k22, k23);
_K.Col3 = new Vector3(k13, k23, k33);
Vector3 C = new Vector3(-C1.X, -C1.Y, -C2);
impulse = _K.Solve33(C); // negated above
}
else
{
float m1 = InvMassA, m2 = InvMassB;
float i1 = InvIA, i2 = InvIB;
float k11 = m1 + m2 + i1 * _s1 * _s1 + i2 * _s2 * _s2;
float k12 = i1 * _s1 + i2 * _s2;
float k22 = i1 + i2;
_K.Col1 = new Vector3(k11, k12, 0.0f);
_K.Col2 = new Vector3(k12, k22, 0.0f);
Vector2 impulse1 = _K.Solve22(-C1);
impulse.X = impulse1.X;
impulse.Y = impulse1.Y;
impulse.Z = 0.0f;
}
Vector2 P = impulse.X * _perp + impulse.Z * _axis;
float L2 = impulse.X * _s2 + impulse.Y + impulse.Z * _a2;
c2 += InvMassB * P;
a2 += InvIB * L2;
// TODO_ERIN remove need for this.
b2.Sweep.C = c2;
b2.Sweep.A = a2;
b2.SynchronizeTransform();
return linearError <= Settings.LinearSlop && angularError <= Settings.AngularSlop;
}
}
}