255 lines
8.5 KiB
C#
255 lines
8.5 KiB
C#
/*
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* Farseer Physics Engine based on Box2D.XNA port:
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* Copyright (c) 2010 Ian Qvist
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*
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* Box2D.XNA port of Box2D:
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* Copyright (c) 2009 Brandon Furtwangler, Nathan Furtwangler
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*
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* Original source Box2D:
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* Copyright (c) 2006-2009 Erin Catto http://www.gphysics.com
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*
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* This software is provided 'as-is', without any express or implied
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* warranty. In no event will the authors be held liable for any damages
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* arising from the use of this software.
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* Permission is granted to anyone to use this software for any purpose,
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* including commercial applications, and to alter it and redistribute it
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* freely, subject to the following restrictions:
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* 1. The origin of this software must not be misrepresented; you must not
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* claim that you wrote the original software. If you use this software
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* in a product, an acknowledgment in the product documentation would be
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* appreciated but is not required.
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* 2. Altered source versions must be plainly marked as such, and must not be
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* misrepresented as being the original software.
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* 3. This notice may not be removed or altered from any source distribution.
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*/
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using System;
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using System.Diagnostics;
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using FarseerPhysics.Common;
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using Microsoft.Xna.Framework;
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namespace FarseerPhysics.Dynamics.Joints
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{
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// 1-D rained system
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// m (v2 - v1) = lambda
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// v2 + (beta/h) * x1 + gamma * lambda = 0, gamma has units of inverse mass.
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// x2 = x1 + h * v2
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// 1-D mass-damper-spring system
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// m (v2 - v1) + h * d * v2 + h * k *
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// C = norm(p2 - p1) - L
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// u = (p2 - p1) / norm(p2 - p1)
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// Cdot = dot(u, v2 + cross(w2, r2) - v1 - cross(w1, r1))
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// J = [-u -cross(r1, u) u cross(r2, u)]
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// K = J * invM * JT
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// = invMass1 + invI1 * cross(r1, u)^2 + invMass2 + invI2 * cross(r2, u)^2
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/// <summary>
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/// A distance joint rains two points on two bodies
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/// to remain at a fixed distance from each other. You can view
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/// this as a massless, rigid rod.
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/// </summary>
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public class FixedDistanceJoint : Joint
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{
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/// <summary>
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/// The local anchor point relative to bodyA's origin.
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/// </summary>
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public Vector2 LocalAnchorA;
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private float _bias;
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private float _gamma;
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private float _impulse;
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private float _mass;
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private Vector2 _u;
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private Vector2 _worldAnchorB;
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/// <summary>
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/// This requires defining an
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/// anchor point on both bodies and the non-zero length of the
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/// distance joint. If you don't supply a length, the local anchor points
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/// is used so that the initial configuration can violate the constraint
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/// slightly. This helps when saving and loading a game.
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/// @warning Do not use a zero or short length.
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/// </summary>
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/// <param name="body">The body.</param>
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/// <param name="bodyAnchor">The body anchor.</param>
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/// <param name="worldAnchor">The world anchor.</param>
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public FixedDistanceJoint(Body body, Vector2 bodyAnchor, Vector2 worldAnchor)
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: base(body)
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{
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JointType = JointType.FixedDistance;
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LocalAnchorA = bodyAnchor;
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_worldAnchorB = worldAnchor;
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//Calculate the length
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Vector2 d = WorldAnchorB - WorldAnchorA;
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Length = d.Length();
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}
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/// <summary>
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/// The natural length between the anchor points.
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/// Manipulating the length can lead to non-physical behavior when the frequency is zero.
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/// </summary>
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public float Length { get; set; }
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/// <summary>
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/// The mass-spring-damper frequency in Hertz.
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/// </summary>
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public float Frequency { get; set; }
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/// <summary>
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/// The damping ratio. 0 = no damping, 1 = critical damping.
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/// </summary>
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public float DampingRatio { get; set; }
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public override sealed Vector2 WorldAnchorA
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{
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get { return BodyA.GetWorldPoint(LocalAnchorA); }
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}
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public override sealed Vector2 WorldAnchorB
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{
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get { return _worldAnchorB; }
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set { _worldAnchorB = value; }
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}
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public override Vector2 GetReactionForce(float invDt)
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{
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return (invDt * _impulse) * _u;
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}
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public override float GetReactionTorque(float invDt)
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{
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return 0.0f;
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}
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internal override void InitVelocityConstraints(ref TimeStep step)
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{
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Body b1 = BodyA;
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Transform xf1;
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b1.GetTransform(out xf1);
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// Compute the effective mass matrix.
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Vector2 r1 = MathUtils.Multiply(ref xf1.R, LocalAnchorA - b1.LocalCenter);
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Vector2 r2 = _worldAnchorB;
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_u = r2 - b1.Sweep.C - r1;
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// Handle singularity.
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float length = _u.Length();
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if (length > Settings.LinearSlop)
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{
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_u *= 1.0f / length;
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}
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else
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{
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_u = Vector2.Zero;
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}
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float cr1u = MathUtils.Cross(r1, _u);
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float cr2u = MathUtils.Cross(r2, _u);
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float invMass = b1.InvMass + b1.InvI * cr1u * cr1u + 0 * cr2u * cr2u;
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Debug.Assert(invMass > Settings.Epsilon);
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_mass = invMass != 0.0f ? 1.0f / invMass : 0.0f;
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if (Frequency > 0.0f)
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{
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float C = length - Length;
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// Frequency
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float omega = 2.0f * Settings.Pi * Frequency;
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// Damping coefficient
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float d = 2.0f * _mass * DampingRatio * omega;
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// Spring stiffness
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float k = _mass * omega * omega;
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// magic formulas
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_gamma = step.dt * (d + step.dt * k);
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_gamma = _gamma != 0.0f ? 1.0f / _gamma : 0.0f;
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_bias = C * step.dt * k * _gamma;
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_mass = invMass + _gamma;
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_mass = _mass != 0.0f ? 1.0f / _mass : 0.0f;
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}
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if (Settings.EnableWarmstarting)
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{
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// Scale the impulse to support a variable time step.
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_impulse *= step.dtRatio;
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Vector2 P = _impulse * _u;
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b1.LinearVelocityInternal -= b1.InvMass * P;
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b1.AngularVelocityInternal -= b1.InvI * MathUtils.Cross(r1, P);
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}
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else
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{
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_impulse = 0.0f;
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}
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}
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internal override void SolveVelocityConstraints(ref TimeStep step)
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{
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Body b1 = BodyA;
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Transform xf1;
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b1.GetTransform(out xf1);
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Vector2 r1 = MathUtils.Multiply(ref xf1.R, LocalAnchorA - b1.LocalCenter);
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// Cdot = dot(u, v + cross(w, r))
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Vector2 v1 = b1.LinearVelocityInternal + MathUtils.Cross(b1.AngularVelocityInternal, r1);
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Vector2 v2 = Vector2.Zero;
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float Cdot = Vector2.Dot(_u, v2 - v1);
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float impulse = -_mass * (Cdot + _bias + _gamma * _impulse);
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_impulse += impulse;
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Vector2 P = impulse * _u;
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b1.LinearVelocityInternal -= b1.InvMass * P;
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b1.AngularVelocityInternal -= b1.InvI * MathUtils.Cross(r1, P);
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}
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internal override bool SolvePositionConstraints()
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{
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if (Frequency > 0.0f)
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{
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// There is no position correction for soft distance constraints.
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return true;
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}
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Body b1 = BodyA;
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Transform xf1;
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b1.GetTransform(out xf1);
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Vector2 r1 = MathUtils.Multiply(ref xf1.R, LocalAnchorA - b1.LocalCenter);
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Vector2 r2 = _worldAnchorB;
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Vector2 d = r2 - b1.Sweep.C - r1;
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float length = d.Length();
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if (length == 0.0f)
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return true;
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d /= length;
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float C = length - Length;
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C = MathUtils.Clamp(C, -Settings.MaxLinearCorrection, Settings.MaxLinearCorrection);
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float impulse = -_mass * C;
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_u = d;
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Vector2 P = impulse * _u;
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b1.Sweep.C -= b1.InvMass * P;
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b1.Sweep.A -= b1.InvI * MathUtils.Cross(r1, P);
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b1.SynchronizeTransform();
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return Math.Abs(C) < Settings.LinearSlop;
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}
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}
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} |