1/*
2* Copyright (c) 2006-2011 Erin Catto http://www.box2d.org
3*
4* This software is provided 'as-is', without any express or implied
5* warranty.  In no event will the authors be held liable for any damages
6* arising from the use of this software.
7* Permission is granted to anyone to use this software for any purpose,
8* including commercial applications, and to alter it and redistribute it
9* freely, subject to the following restrictions:
10* 1. The origin of this software must not be misrepresented; you must not
11* claim that you wrote the original software. If you use this software
12* in a product, an acknowledgment in the product documentation would be
13* appreciated but is not required.
14* 2. Altered source versions must be plainly marked as such, and must not be
15* misrepresented as being the original software.
16* 3. This notice may not be removed or altered from any source distribution.
17*/
18
19#include <Box2D/Dynamics/Joints/b2WeldJoint.h>
20#include <Box2D/Dynamics/b2Body.h>
21#include <Box2D/Dynamics/b2TimeStep.h>
22
23// Point-to-point constraint
24// C = p2 - p1
25// Cdot = v2 - v1
26//      = v2 + cross(w2, r2) - v1 - cross(w1, r1)
27// J = [-I -r1_skew I r2_skew ]
28// Identity used:
29// w k % (rx i + ry j) = w * (-ry i + rx j)
30
31// Angle constraint
32// C = angle2 - angle1 - referenceAngle
33// Cdot = w2 - w1
34// J = [0 0 -1 0 0 1]
35// K = invI1 + invI2
36
37void b2WeldJointDef::Initialize(b2Body* bA, b2Body* bB, const b2Vec2& anchor)
38{
39	bodyA = bA;
40	bodyB = bB;
41	localAnchorA = bodyA->GetLocalPoint(anchor);
42	localAnchorB = bodyB->GetLocalPoint(anchor);
43	referenceAngle = bodyB->GetAngle() - bodyA->GetAngle();
44}
45
46b2WeldJoint::b2WeldJoint(const b2WeldJointDef* def)
47: b2Joint(def)
48{
49	m_localAnchorA = def->localAnchorA;
50	m_localAnchorB = def->localAnchorB;
51	m_referenceAngle = def->referenceAngle;
52	m_frequencyHz = def->frequencyHz;
53	m_dampingRatio = def->dampingRatio;
54
55	m_impulse.SetZero();
56}
57
58void b2WeldJoint::InitVelocityConstraints(const b2SolverData& data)
59{
60	m_indexA = m_bodyA->m_islandIndex;
61	m_indexB = m_bodyB->m_islandIndex;
62	m_localCenterA = m_bodyA->m_sweep.localCenter;
63	m_localCenterB = m_bodyB->m_sweep.localCenter;
64	m_invMassA = m_bodyA->m_invMass;
65	m_invMassB = m_bodyB->m_invMass;
66	m_invIA = m_bodyA->m_invI;
67	m_invIB = m_bodyB->m_invI;
68
69	float32 aA = data.positions[m_indexA].a;
70	b2Vec2 vA = data.velocities[m_indexA].v;
71	float32 wA = data.velocities[m_indexA].w;
72
73	float32 aB = data.positions[m_indexB].a;
74	b2Vec2 vB = data.velocities[m_indexB].v;
75	float32 wB = data.velocities[m_indexB].w;
76
77	b2Rot qA(aA), qB(aB);
78
79	m_rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
80	m_rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
81
82	// J = [-I -r1_skew I r2_skew]
83	//     [ 0       -1 0       1]
84	// r_skew = [-ry; rx]
85
86	// Matlab
87	// K = [ mA+r1y^2*iA+mB+r2y^2*iB,  -r1y*iA*r1x-r2y*iB*r2x,          -r1y*iA-r2y*iB]
88	//     [  -r1y*iA*r1x-r2y*iB*r2x, mA+r1x^2*iA+mB+r2x^2*iB,           r1x*iA+r2x*iB]
89	//     [          -r1y*iA-r2y*iB,           r1x*iA+r2x*iB,                   iA+iB]
90
91	float32 mA = m_invMassA, mB = m_invMassB;
92	float32 iA = m_invIA, iB = m_invIB;
93
94	b2Mat33 K;
95	K.ex.x = mA + mB + m_rA.y * m_rA.y * iA + m_rB.y * m_rB.y * iB;
96	K.ey.x = -m_rA.y * m_rA.x * iA - m_rB.y * m_rB.x * iB;
97	K.ez.x = -m_rA.y * iA - m_rB.y * iB;
98	K.ex.y = K.ey.x;
99	K.ey.y = mA + mB + m_rA.x * m_rA.x * iA + m_rB.x * m_rB.x * iB;
100	K.ez.y = m_rA.x * iA + m_rB.x * iB;
101	K.ex.z = K.ez.x;
102	K.ey.z = K.ez.y;
103	K.ez.z = iA + iB;
104
105	if (m_frequencyHz > 0.0f)
106	{
107		K.GetInverse22(&m_mass);
108
109		float32 invM = iA + iB;
110		float32 m = invM > 0.0f ? 1.0f / invM : 0.0f;
111
112		float32 C = aB - aA - m_referenceAngle;
113
114		// Frequency
115		float32 omega = 2.0f * b2_pi * m_frequencyHz;
116
117		// Damping coefficient
118		float32 d = 2.0f * m * m_dampingRatio * omega;
119
120		// Spring stiffness
121		float32 k = m * omega * omega;
122
123		// magic formulas
124		float32 h = data.step.dt;
125		m_gamma = h * (d + h * k);
126		m_gamma = m_gamma != 0.0f ? 1.0f / m_gamma : 0.0f;
127		m_bias = C * h * k * m_gamma;
128
129		invM += m_gamma;
130		m_mass.ez.z = invM != 0.0f ? 1.0f / invM : 0.0f;
131	}
132	else if (K.ez.z == 0.0f)
133	{
134		K.GetInverse22(&m_mass);
135		m_gamma = 0.0f;
136		m_bias = 0.0f;
137	}
138	else
139	{
140		K.GetSymInverse33(&m_mass);
141		m_gamma = 0.0f;
142		m_bias = 0.0f;
143	}
144
145	if (data.step.warmStarting)
146	{
147		// Scale impulses to support a variable time step.
148		m_impulse *= data.step.dtRatio;
149
150		b2Vec2 P(m_impulse.x, m_impulse.y);
151
152		vA -= mA * P;
153		wA -= iA * (b2Cross(m_rA, P) + m_impulse.z);
154
155		vB += mB * P;
156		wB += iB * (b2Cross(m_rB, P) + m_impulse.z);
157	}
158	else
159	{
160		m_impulse.SetZero();
161	}
162
163	data.velocities[m_indexA].v = vA;
164	data.velocities[m_indexA].w = wA;
165	data.velocities[m_indexB].v = vB;
166	data.velocities[m_indexB].w = wB;
167}
168
169void b2WeldJoint::SolveVelocityConstraints(const b2SolverData& data)
170{
171	b2Vec2 vA = data.velocities[m_indexA].v;
172	float32 wA = data.velocities[m_indexA].w;
173	b2Vec2 vB = data.velocities[m_indexB].v;
174	float32 wB = data.velocities[m_indexB].w;
175
176	float32 mA = m_invMassA, mB = m_invMassB;
177	float32 iA = m_invIA, iB = m_invIB;
178
179	if (m_frequencyHz > 0.0f)
180	{
181		float32 Cdot2 = wB - wA;
182
183		float32 impulse2 = -m_mass.ez.z * (Cdot2 + m_bias + m_gamma * m_impulse.z);
184		m_impulse.z += impulse2;
185
186		wA -= iA * impulse2;
187		wB += iB * impulse2;
188
189		b2Vec2 Cdot1 = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
190
191		b2Vec2 impulse1 = -b2Mul22(m_mass, Cdot1);
192		m_impulse.x += impulse1.x;
193		m_impulse.y += impulse1.y;
194
195		b2Vec2 P = impulse1;
196
197		vA -= mA * P;
198		wA -= iA * b2Cross(m_rA, P);
199
200		vB += mB * P;
201		wB += iB * b2Cross(m_rB, P);
202	}
203	else
204	{
205		b2Vec2 Cdot1 = vB + b2Cross(wB, m_rB) - vA - b2Cross(wA, m_rA);
206		float32 Cdot2 = wB - wA;
207		b2Vec3 Cdot(Cdot1.x, Cdot1.y, Cdot2);
208
209		b2Vec3 impulse = -b2Mul(m_mass, Cdot);
210		m_impulse += impulse;
211
212		b2Vec2 P(impulse.x, impulse.y);
213
214		vA -= mA * P;
215		wA -= iA * (b2Cross(m_rA, P) + impulse.z);
216
217		vB += mB * P;
218		wB += iB * (b2Cross(m_rB, P) + impulse.z);
219	}
220
221	data.velocities[m_indexA].v = vA;
222	data.velocities[m_indexA].w = wA;
223	data.velocities[m_indexB].v = vB;
224	data.velocities[m_indexB].w = wB;
225}
226
227bool b2WeldJoint::SolvePositionConstraints(const b2SolverData& data)
228{
229	b2Vec2 cA = data.positions[m_indexA].c;
230	float32 aA = data.positions[m_indexA].a;
231	b2Vec2 cB = data.positions[m_indexB].c;
232	float32 aB = data.positions[m_indexB].a;
233
234	b2Rot qA(aA), qB(aB);
235
236	float32 mA = m_invMassA, mB = m_invMassB;
237	float32 iA = m_invIA, iB = m_invIB;
238
239	b2Vec2 rA = b2Mul(qA, m_localAnchorA - m_localCenterA);
240	b2Vec2 rB = b2Mul(qB, m_localAnchorB - m_localCenterB);
241
242	float32 positionError, angularError;
243
244	b2Mat33 K;
245	K.ex.x = mA + mB + rA.y * rA.y * iA + rB.y * rB.y * iB;
246	K.ey.x = -rA.y * rA.x * iA - rB.y * rB.x * iB;
247	K.ez.x = -rA.y * iA - rB.y * iB;
248	K.ex.y = K.ey.x;
249	K.ey.y = mA + mB + rA.x * rA.x * iA + rB.x * rB.x * iB;
250	K.ez.y = rA.x * iA + rB.x * iB;
251	K.ex.z = K.ez.x;
252	K.ey.z = K.ez.y;
253	K.ez.z = iA + iB;
254
255	if (m_frequencyHz > 0.0f)
256	{
257		b2Vec2 C1 =  cB + rB - cA - rA;
258
259		positionError = C1.Length();
260		angularError = 0.0f;
261
262		b2Vec2 P = -K.Solve22(C1);
263
264		cA -= mA * P;
265		aA -= iA * b2Cross(rA, P);
266
267		cB += mB * P;
268		aB += iB * b2Cross(rB, P);
269	}
270	else
271	{
272		b2Vec2 C1 =  cB + rB - cA - rA;
273		float32 C2 = aB - aA - m_referenceAngle;
274
275		positionError = C1.Length();
276		angularError = b2Abs(C2);
277
278		b2Vec3 C(C1.x, C1.y, C2);
279
280		b2Vec3 impulse;
281		if (K.ez.z > 0.0f)
282		{
283			impulse = -K.Solve33(C);
284		}
285		else
286		{
287			b2Vec2 impulse2 = -K.Solve22(C1);
288			impulse.Set(impulse2.x, impulse2.y, 0.0f);
289		}
290
291		b2Vec2 P(impulse.x, impulse.y);
292
293		cA -= mA * P;
294		aA -= iA * (b2Cross(rA, P) + impulse.z);
295
296		cB += mB * P;
297		aB += iB * (b2Cross(rB, P) + impulse.z);
298	}
299
300	data.positions[m_indexA].c = cA;
301	data.positions[m_indexA].a = aA;
302	data.positions[m_indexB].c = cB;
303	data.positions[m_indexB].a = aB;
304
305	return positionError <= b2_linearSlop && angularError <= b2_angularSlop;
306}
307
308b2Vec2 b2WeldJoint::GetAnchorA() const
309{
310	return m_bodyA->GetWorldPoint(m_localAnchorA);
311}
312
313b2Vec2 b2WeldJoint::GetAnchorB() const
314{
315	return m_bodyB->GetWorldPoint(m_localAnchorB);
316}
317
318b2Vec2 b2WeldJoint::GetReactionForce(float32 inv_dt) const
319{
320	b2Vec2 P(m_impulse.x, m_impulse.y);
321	return inv_dt * P;
322}
323
324float32 b2WeldJoint::GetReactionTorque(float32 inv_dt) const
325{
326	return inv_dt * m_impulse.z;
327}
328
329void b2WeldJoint::Dump()
330{
331	int32 indexA = m_bodyA->m_islandIndex;
332	int32 indexB = m_bodyB->m_islandIndex;
333
334	b2Log("  b2WeldJointDef jd;\n");
335	b2Log("  jd.bodyA = bodies[%d];\n", indexA);
336	b2Log("  jd.bodyB = bodies[%d];\n", indexB);
337	b2Log("  jd.collideConnected = bool(%d);\n", m_collideConnected);
338	b2Log("  jd.localAnchorA.Set(%.15lef, %.15lef);\n", m_localAnchorA.x, m_localAnchorA.y);
339	b2Log("  jd.localAnchorB.Set(%.15lef, %.15lef);\n", m_localAnchorB.x, m_localAnchorB.y);
340	b2Log("  jd.referenceAngle = %.15lef;\n", m_referenceAngle);
341	b2Log("  jd.frequencyHz = %.15lef;\n", m_frequencyHz);
342	b2Log("  jd.dampingRatio = %.15lef;\n", m_dampingRatio);
343	b2Log("  joints[%d] = m_world->CreateJoint(&jd);\n", m_index);
344}
345