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+/*************************************************************************
+ *                                                                       *
+ * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith.       *
+ * All rights reserved.  Email: russ@q12.org   Web: www.q12.org          *
+ *                                                                       *
+ * This library is free software; you can redistribute it and/or         *
+ * modify it under the terms of EITHER:                                  *
+ *   (1) The GNU Lesser General Public License as published by the Free  *
+ *       Software Foundation; either version 2.1 of the License, or (at  *
+ *       your option) any later version. The text of the GNU Lesser      *
+ *       General Public License is included with this library in the     *
+ *       file LICENSE.TXT.                                               *
+ *   (2) The BSD-style license that is included with this library in     *
+ *       the file LICENSE-BSD.TXT.                                       *
+ *                                                                       *
+ * This library is distributed in the hope that it will be useful,       *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of        *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files    *
+ * LICENSE.TXT and LICENSE-BSD.TXT for more details.                     *
+ *                                                                       *
+ *************************************************************************/
+
+#include "ode/ode.h"
+#include "objects.h"
+#include "joint.h"
+#include "util.h"
+
+#define ALLOCA dALLOCA16
+
+//****************************************************************************
+// Auto disabling
+
+void dInternalHandleAutoDisabling (dxWorld *world, dReal stepsize)
+{
+        dxBody *bb;
+        for ( bb=world->firstbody; bb; bb=(dxBody*)bb->next )
+        {
+                // don't freeze objects mid-air (patch 1586738)
+                if ( bb->firstjoint == NULL ) continue;
+
+                // nothing to do unless this body is currently enabled and has
+                // the auto-disable flag set
+                if ( (bb->flags & (dxBodyAutoDisable|dxBodyDisabled)) != dxBodyAutoDisable ) continue;
+
+                // if sampling / threshold testing is disabled, we can never sleep.
+                if ( bb->adis.average_samples == 0 ) continue;
+
+                //
+                // see if the body is idle
+                //
+                
+#ifndef dNODEBUG
+                // sanity check
+                if ( bb->average_counter >= bb->adis.average_samples )
+                {
+                        dUASSERT( bb->average_counter < bb->adis.average_samples, "buffer overflow" );
+
+                        // something is going wrong, reset the average-calculations
+                        bb->average_ready = 0; // not ready for average calculation
+                        bb->average_counter = 0; // reset the buffer index
+                }
+#endif // dNODEBUG
+
+                // sample the linear and angular velocity
+                bb->average_lvel_buffer[bb->average_counter][0] = bb->lvel[0];
+                bb->average_lvel_buffer[bb->average_counter][1] = bb->lvel[1];
+                bb->average_lvel_buffer[bb->average_counter][2] = bb->lvel[2];
+                bb->average_avel_buffer[bb->average_counter][0] = bb->avel[0];
+                bb->average_avel_buffer[bb->average_counter][1] = bb->avel[1];
+                bb->average_avel_buffer[bb->average_counter][2] = bb->avel[2];
+                bb->average_counter++;
+                
+                // buffer ready test
+                if ( bb->average_counter >= bb->adis.average_samples )
+                {
+                        bb->average_counter = 0; // fill the buffer from the beginning
+                        bb->average_ready = 1; // this body is ready now for average calculation
+                }
+
+                int idle = 0; // Assume it's in motion unless we have samples to disprove it.
+
+                // enough samples?
+                if ( bb->average_ready )
+                {
+                        idle = 1; // Initial assumption: IDLE
+
+                        // the sample buffers are filled and ready for calculation
+                        dVector3 average_lvel, average_avel;
+
+                        // Store first velocity samples
+                        average_lvel[0] = bb->average_lvel_buffer[0][0];
+                        average_avel[0] = bb->average_avel_buffer[0][0];
+                        average_lvel[1] = bb->average_lvel_buffer[0][1];
+                        average_avel[1] = bb->average_avel_buffer[0][1];
+                        average_lvel[2] = bb->average_lvel_buffer[0][2];
+                        average_avel[2] = bb->average_avel_buffer[0][2];
+                        
+                        // If we're not in "instantaneous mode"
+                        if ( bb->adis.average_samples > 1 )
+                        {
+                                // add remaining velocities together
+                                for ( unsigned int i = 1; i < bb->adis.average_samples; ++i )
+                                {
+                                        average_lvel[0] += bb->average_lvel_buffer[i][0];
+                                        average_avel[0] += bb->average_avel_buffer[i][0];
+                                        average_lvel[1] += bb->average_lvel_buffer[i][1];
+                                        average_avel[1] += bb->average_avel_buffer[i][1];
+                                        average_lvel[2] += bb->average_lvel_buffer[i][2];
+                                        average_avel[2] += bb->average_avel_buffer[i][2];
+                                }
+
+                                // make average
+                                dReal r1 = dReal( 1.0 ) / dReal( bb->adis.average_samples );
+
+                                average_lvel[0] *= r1;
+                                average_avel[0] *= r1;
+                                average_lvel[1] *= r1;
+                                average_avel[1] *= r1;
+                                average_lvel[2] *= r1;
+                                average_avel[2] *= r1;
+                        }
+
+                        // threshold test
+                        dReal av_lspeed, av_aspeed;
+                        av_lspeed = dDOT( average_lvel, average_lvel );
+                        if ( av_lspeed > bb->adis.linear_average_threshold )
+                        {
+                                idle = 0; // average linear velocity is too high for idle
+                        }
+                        else
+                        {
+                                av_aspeed = dDOT( average_avel, average_avel );
+                                if ( av_aspeed > bb->adis.angular_average_threshold )
+                                {
+                                        idle = 0; // average angular velocity is too high for idle
+                                }
+                        }
+                }
+
+                // if it's idle, accumulate steps and time.
+                // these counters won't overflow because this code doesn't run for disabled bodies.
+                if (idle) {
+                        bb->adis_stepsleft--;
+                        bb->adis_timeleft -= stepsize;
+                }
+                else {
+                        // Reset countdowns
+                        bb->adis_stepsleft = bb->adis.idle_steps;
+                        bb->adis_timeleft = bb->adis.idle_time;
+                }
+
+                // disable the body if it's idle for a long enough time
+                if ( bb->adis_stepsleft <= 0 && bb->adis_timeleft <= 0 )
+                {
+                        bb->flags |= dxBodyDisabled; // set the disable flag
+
+                        // disabling bodies should also include resetting the velocity
+                        // should prevent jittering in big "islands"
+                        bb->lvel[0] = 0;
+                        bb->lvel[1] = 0;
+                        bb->lvel[2] = 0;
+                        bb->avel[0] = 0;
+                        bb->avel[1] = 0;
+                        bb->avel[2] = 0;
+                }
+        }
+}
+
+
+//****************************************************************************
+// body rotation
+
+// return sin(x)/x. this has a singularity at 0 so special handling is needed
+// for small arguments.
+
+static inline dReal sinc (dReal x)
+{
+  // if |x| < 1e-4 then use a taylor series expansion. this two term expansion
+  // is actually accurate to one LS bit within this range if double precision
+  // is being used - so don't worry!
+  if (dFabs(x) < 1.0e-4) return REAL(1.0) - x*x*REAL(0.166666666666666666667);
+  else return dSin(x)/x;
+}
+
+
+// given a body b, apply its linear and angular rotation over the time
+// interval h, thereby adjusting its position and orientation.
+
+void dxStepBody (dxBody *b, dReal h)
+{
+  int j;
+
+  // handle linear velocity
+  for (j=0; j<3; j++) b->posr.pos[j] += h * b->lvel[j];
+
+  if (b->flags & dxBodyFlagFiniteRotation) {
+    dVector3 irv;       // infitesimal rotation vector
+    dQuaternion q;      // quaternion for finite rotation
+
+    if (b->flags & dxBodyFlagFiniteRotationAxis) {
+      // split the angular velocity vector into a component along the finite
+      // rotation axis, and a component orthogonal to it.
+      dVector3 frv;             // finite rotation vector
+      dReal k = dDOT (b->finite_rot_axis,b->avel);
+      frv[0] = b->finite_rot_axis[0] * k;
+      frv[1] = b->finite_rot_axis[1] * k;
+      frv[2] = b->finite_rot_axis[2] * k;
+      irv[0] = b->avel[0] - frv[0];
+      irv[1] = b->avel[1] - frv[1];
+      irv[2] = b->avel[2] - frv[2];
+
+      // make a rotation quaternion q that corresponds to frv * h.
+      // compare this with the full-finite-rotation case below.
+      h *= REAL(0.5);
+      dReal theta = k * h;
+      q[0] = dCos(theta);
+      dReal s = sinc(theta) * h;
+      q[1] = frv[0] * s;
+      q[2] = frv[1] * s;
+      q[3] = frv[2] * s;
+    }
+    else {
+      // make a rotation quaternion q that corresponds to w * h
+      dReal wlen = dSqrt (b->avel[0]*b->avel[0] + b->avel[1]*b->avel[1] +
+                          b->avel[2]*b->avel[2]);
+      h *= REAL(0.5);
+      dReal theta = wlen * h;
+      q[0] = dCos(theta);
+      dReal s = sinc(theta) * h;
+      q[1] = b->avel[0] * s;
+      q[2] = b->avel[1] * s;
+      q[3] = b->avel[2] * s;
+    }
+
+    // do the finite rotation
+    dQuaternion q2;
+    dQMultiply0 (q2,q,b->q);
+    for (j=0; j<4; j++) b->q[j] = q2[j];
+
+    // do the infitesimal rotation if required
+    if (b->flags & dxBodyFlagFiniteRotationAxis) {
+      dReal dq[4];
+      dWtoDQ (irv,b->q,dq);
+      for (j=0; j<4; j++) b->q[j] += h * dq[j];
+    }
+  }
+  else {
+    // the normal way - do an infitesimal rotation
+    dReal dq[4];
+    dWtoDQ (b->avel,b->q,dq);
+    for (j=0; j<4; j++) b->q[j] += h * dq[j];
+  }
+
+  // normalize the quaternion and convert it to a rotation matrix
+  dNormalize4 (b->q);
+  dQtoR (b->q,b->posr.R);
+
+  // notify all attached geoms that this body has moved
+  for (dxGeom *geom = b->geom; geom; geom = dGeomGetBodyNext (geom))
+    dGeomMoved (geom);
+}
+
+//****************************************************************************
+// island processing
+
+// this groups all joints and bodies in a world into islands. all objects
+// in an island are reachable by going through connected bodies and joints.
+// each island can be simulated separately.
+// note that joints that are not attached to anything will not be included
+// in any island, an so they do not affect the simulation.
+//
+// this function starts new island from unvisited bodies. however, it will
+// never start a new islands from a disabled body. thus islands of disabled
+// bodies will not be included in the simulation. disabled bodies are
+// re-enabled if they are found to be part of an active island.
+
+void dxProcessIslands (dxWorld *world, dReal stepsize, dstepper_fn_t stepper)
+{
+  dxBody *b,*bb,**body;
+  dxJoint *j,**joint;
+
+  // nothing to do if no bodies
+  if (world->nb <= 0) return;
+
+  // handle auto-disabling of bodies
+  dInternalHandleAutoDisabling (world,stepsize);
+
+  // make arrays for body and joint lists (for a single island) to go into
+  body = (dxBody**) ALLOCA (world->nb * sizeof(dxBody*));
+  joint = (dxJoint**) ALLOCA (world->nj * sizeof(dxJoint*));
+  int bcount = 0;       // number of bodies in `body'
+  int jcount = 0;       // number of joints in `joint'
+
+  // set all body/joint tags to 0
+  for (b=world->firstbody; b; b=(dxBody*)b->next) b->tag = 0;
+  for (j=world->firstjoint; j; j=(dxJoint*)j->next) j->tag = 0;
+
+  // allocate a stack of unvisited bodies in the island. the maximum size of
+  // the stack can be the lesser of the number of bodies or joints, because
+  // new bodies are only ever added to the stack by going through untagged
+  // joints. all the bodies in the stack must be tagged!
+  int stackalloc = (world->nj < world->nb) ? world->nj : world->nb;
+  dxBody **stack = (dxBody**) ALLOCA (stackalloc * sizeof(dxBody*));
+
+  for (bb=world->firstbody; bb; bb=(dxBody*)bb->next) {
+    // get bb = the next enabled, untagged body, and tag it
+    if (bb->tag || (bb->flags & dxBodyDisabled)) continue;
+    bb->tag = 1;
+
+    // tag all bodies and joints starting from bb.
+    int stacksize = 0;
+    b = bb;
+    body[0] = bb;
+    bcount = 1;
+    jcount = 0;
+    goto quickstart;
+    while (stacksize > 0) {
+      b = stack[--stacksize];   // pop body off stack
+      body[bcount++] = b;       // put body on body list
+      quickstart:
+
+      // traverse and tag all body's joints, add untagged connected bodies
+      // to stack
+      for (dxJointNode *n=b->firstjoint; n; n=n->next) {
+        if (!n->joint->tag) {
+          n->joint->tag = 1;
+          joint[jcount++] = n->joint;
+          if (n->body && !n->body->tag) {
+            n->body->tag = 1;
+            stack[stacksize++] = n->body;
+          }
+        }
+      }
+      dIASSERT(stacksize <= world->nb);
+      dIASSERT(stacksize <= world->nj);
+    }
+
+    // now do something with body and joint lists
+    stepper (world,body,bcount,joint,jcount,stepsize);
+
+    // what we've just done may have altered the body/joint tag values.
+    // we must make sure that these tags are nonzero.
+    // also make sure all bodies are in the enabled state.
+    int i;
+    for (i=0; i<bcount; i++) {
+      body[i]->tag = 1;
+      body[i]->flags &= ~dxBodyDisabled;
+    }
+    for (i=0; i<jcount; i++) joint[i]->tag = 1;
+  }
+
+  // if debugging, check that all objects (except for disabled bodies,
+  // unconnected joints, and joints that are connected to disabled bodies)
+  // were tagged.
+# ifndef dNODEBUG
+  for (b=world->firstbody; b; b=(dxBody*)b->next) {
+    if (b->flags & dxBodyDisabled) {
+      if (b->tag) dDebug (0,"disabled body tagged");
+    }
+    else {
+      if (!b->tag) dDebug (0,"enabled body not tagged");
+    }
+  }
+  for (j=world->firstjoint; j; j=(dxJoint*)j->next) {
+    if ((j->node[0].body && (j->node[0].body->flags & dxBodyDisabled)==0) ||
+        (j->node[1].body && (j->node[1].body->flags & dxBodyDisabled)==0)) {
+      if (!j->tag) dDebug (0,"attached enabled joint not tagged");
+    }
+    else {
+      if (j->tag) dDebug (0,"unattached or disabled joint tagged");
+    }
+  }
+# endif
+}