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