axiosengine/axios/Dynamics/Joints/WeldJoint.cs

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2012-03-19 23:57:59 +00:00
/*
* 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
{
// Point-to-point constraint
// C = p2 - p1
// Cdot = v2 - v1
// = v2 + cross(w2, r2) - v1 - cross(w1, r1)
// J = [-I -r1_skew I r2_skew ]
// Identity used:
// w k % (rx i + ry j) = w * (-ry i + rx j)
// Angle constraint
// C = angle2 - angle1 - referenceAngle
// Cdot = w2 - w1
// J = [0 0 -1 0 0 1]
// K = invI1 + invI2
/// <summary>
/// A weld joint essentially glues two bodies together. A weld joint may
/// distort somewhat because the island constraint solver is approximate.
/// </summary>
public class WeldJoint : Joint
{
public Vector2 LocalAnchorA;
public Vector2 LocalAnchorB;
private Vector3 _impulse;
private Mat33 _mass;
internal WeldJoint()
{
JointType = JointType.Weld;
}
/// <summary>
/// You need to specify a local anchor point
/// where they are attached and the relative body angle. The position
/// of the anchor point is important for computing the reaction torque.
/// You can change the anchor points relative to bodyA or bodyB by changing LocalAnchorA
/// and/or LocalAnchorB.
/// </summary>
/// <param name="bodyA">The first body</param>
/// <param name="bodyB">The second body</param>
/// <param name="localAnchorA">The first body anchor.</param>
/// <param name="localAnchorB">The second body anchor.</param>
public WeldJoint(Body bodyA, Body bodyB, Vector2 localAnchorA, Vector2 localAnchorB)
: base(bodyA, bodyB)
{
JointType = JointType.Weld;
LocalAnchorA = localAnchorA;
LocalAnchorB = localAnchorB;
ReferenceAngle = BodyB.Rotation - BodyA.Rotation;
}
public override Vector2 WorldAnchorA
{
get { return BodyA.GetWorldPoint(LocalAnchorA); }
}
public override Vector2 WorldAnchorB
{
get { return BodyB.GetWorldPoint(LocalAnchorB); }
set { Debug.Assert(false, "You can't set the world anchor on this joint type."); }
}
/// <summary>
/// The body2 angle minus body1 angle in the reference state (radians).
/// </summary>
public float ReferenceAngle { get; private set; }
public override Vector2 GetReactionForce(float inv_dt)
{
return inv_dt * new Vector2(_impulse.X, _impulse.Y);
}
public override float GetReactionTorque(float inv_dt)
{
return inv_dt * _impulse.Z;
}
internal override void InitVelocityConstraints(ref TimeStep step)
{
Body bA = BodyA;
Body bB = BodyB;
Transform xfA, xfB;
bA.GetTransform(out xfA);
bB.GetTransform(out xfB);
// Compute the effective mass matrix.
Vector2 rA = MathUtils.Multiply(ref xfA.R, LocalAnchorA - bA.LocalCenter);
Vector2 rB = MathUtils.Multiply(ref xfB.R, LocalAnchorB - bB.LocalCenter);
// J = [-I -r1_skew I r2_skew]
// [ 0 -1 0 1]
// r_skew = [-ry; rx]
// Matlab
// K = [ mA+r1y^2*iA+mB+r2y^2*iB, -r1y*iA*r1x-r2y*iB*r2x, -r1y*iA-r2y*iB]
// [ -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB, r1x*iA+r2x*iB]
// [ -r1y*iA-r2y*iB, r1x*iA+r2x*iB, iA+iB]
float mA = bA.InvMass, mB = bB.InvMass;
float iA = bA.InvI, iB = bB.InvI;
_mass.Col1.X = mA + mB + rA.Y * rA.Y * iA + rB.Y * rB.Y * iB;
_mass.Col2.X = -rA.Y * rA.X * iA - rB.Y * rB.X * iB;
_mass.Col3.X = -rA.Y * iA - rB.Y * iB;
_mass.Col1.Y = _mass.Col2.X;
_mass.Col2.Y = mA + mB + rA.X * rA.X * iA + rB.X * rB.X * iB;
_mass.Col3.Y = rA.X * iA + rB.X * iB;
_mass.Col1.Z = _mass.Col3.X;
_mass.Col2.Z = _mass.Col3.Y;
_mass.Col3.Z = iA + iB;
if (Settings.EnableWarmstarting)
{
// Scale impulses to support a variable time step.
_impulse *= step.dtRatio;
Vector2 P = new Vector2(_impulse.X, _impulse.Y);
bA.LinearVelocityInternal -= mA * P;
bA.AngularVelocityInternal -= iA * (MathUtils.Cross(rA, P) + _impulse.Z);
bB.LinearVelocityInternal += mB * P;
bB.AngularVelocityInternal += iB * (MathUtils.Cross(rB, P) + _impulse.Z);
}
else
{
_impulse = Vector3.Zero;
}
}
internal override void SolveVelocityConstraints(ref TimeStep step)
{
Body bA = BodyA;
Body bB = BodyB;
Vector2 vA = bA.LinearVelocityInternal;
float wA = bA.AngularVelocityInternal;
Vector2 vB = bB.LinearVelocityInternal;
float wB = bB.AngularVelocityInternal;
float mA = bA.InvMass, mB = bB.InvMass;
float iA = bA.InvI, iB = bB.InvI;
Transform xfA, xfB;
bA.GetTransform(out xfA);
bB.GetTransform(out xfB);
Vector2 rA = MathUtils.Multiply(ref xfA.R, LocalAnchorA - bA.LocalCenter);
Vector2 rB = MathUtils.Multiply(ref xfB.R, LocalAnchorB - bB.LocalCenter);
// Solve point-to-point constraint
Vector2 Cdot1 = vB + MathUtils.Cross(wB, rB) - vA - MathUtils.Cross(wA, rA);
float Cdot2 = wB - wA;
Vector3 Cdot = new Vector3(Cdot1.X, Cdot1.Y, Cdot2);
Vector3 impulse = _mass.Solve33(-Cdot);
_impulse += impulse;
Vector2 P = new Vector2(impulse.X, impulse.Y);
vA -= mA * P;
wA -= iA * (MathUtils.Cross(rA, P) + impulse.Z);
vB += mB * P;
wB += iB * (MathUtils.Cross(rB, P) + impulse.Z);
bA.LinearVelocityInternal = vA;
bA.AngularVelocityInternal = wA;
bB.LinearVelocityInternal = vB;
bB.AngularVelocityInternal = wB;
}
internal override bool SolvePositionConstraints()
{
Body bA = BodyA;
Body bB = BodyB;
float mA = bA.InvMass, mB = bB.InvMass;
float iA = bA.InvI, iB = bB.InvI;
Transform xfA;
Transform xfB;
bA.GetTransform(out xfA);
bB.GetTransform(out xfB);
Vector2 rA = MathUtils.Multiply(ref xfA.R, LocalAnchorA - bA.LocalCenter);
Vector2 rB = MathUtils.Multiply(ref xfB.R, LocalAnchorB - bB.LocalCenter);
Vector2 C1 = bB.Sweep.C + rB - bA.Sweep.C - rA;
float C2 = bB.Sweep.A - bA.Sweep.A - ReferenceAngle;
// Handle large detachment.
const float k_allowedStretch = 10.0f * Settings.LinearSlop;
float positionError = C1.Length();
float angularError = Math.Abs(C2);
if (positionError > k_allowedStretch)
{
iA *= 1.0f;
iB *= 1.0f;
}
_mass.Col1.X = mA + mB + rA.Y * rA.Y * iA + rB.Y * rB.Y * iB;
_mass.Col2.X = -rA.Y * rA.X * iA - rB.Y * rB.X * iB;
_mass.Col3.X = -rA.Y * iA - rB.Y * iB;
_mass.Col1.Y = _mass.Col2.X;
_mass.Col2.Y = mA + mB + rA.X * rA.X * iA + rB.X * rB.X * iB;
_mass.Col3.Y = rA.X * iA + rB.X * iB;
_mass.Col1.Z = _mass.Col3.X;
_mass.Col2.Z = _mass.Col3.Y;
_mass.Col3.Z = iA + iB;
Vector3 C = new Vector3(C1.X, C1.Y, C2);
Vector3 impulse = _mass.Solve33(-C);
Vector2 P = new Vector2(impulse.X, impulse.Y);
bA.Sweep.C -= mA * P;
bA.Sweep.A -= iA * (MathUtils.Cross(rA, P) + impulse.Z);
bB.Sweep.C += mB * P;
bB.Sweep.A += iB * (MathUtils.Cross(rB, P) + impulse.Z);
bA.SynchronizeTransform();
bB.SynchronizeTransform();
return positionError <= Settings.LinearSlop && angularError <= Settings.AngularSlop;
}
}
}