text: /*
   Written by Xuchen Han <xuchenhan2015@u.northwestern.edu>
   
   Bullet Continuous Collision Detection and Physics Library
   Copyright (c) 2019 Google Inc. http://bulletphysics.org
   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.
   */
  
  #ifndef BT_DEFORMABLE_LAGRANGIAN_FORCE_H
  #define BT_DEFORMABLE_LAGRANGIAN_FORCE_H
  
  #include "btSoftBody.h"
  #include <LinearMath/btHashMap.h>
  #include <iostream>
  
  enum btDeformableLagrangianForceType
  {
      BT_GRAVITY_FORCE = 1,
      BT_MASSSPRING_FORCE = 2,
      BT_COROTATED_FORCE = 3,
      BT_NEOHOOKEAN_FORCE = 4,
      BT_LINEAR_ELASTICITY_FORCE = 5,
      BT_MOUSE_PICKING_FORCE = 6
  };
  
  static inline double randomDouble(double low, double high)
  {
      return low + static_cast<double>(rand()) / RAND_MAX * (high - low);
  }
  
  class btDeformableLagrangianForce
  {
  public:
      typedef btAlignedObjectArray<btVector3> TVStack;
      btAlignedObjectArray<btSoftBody *> m_softBodies;
      const btAlignedObjectArray<btSoftBody::Node*>* m_nodes;
      
      btDeformableLagrangianForce()
      {
      }
      
      virtual ~btDeformableLagrangianForce(){}
      
      // add all forces
      virtual void addScaledForces(btScalar scale, TVStack& force) = 0;
      
      // add damping df
      virtual void addScaledDampingForceDifferential(btScalar scale, const TVStack& dv, TVStack& df) = 0;
      
      // add elastic df
      virtual void addScaledElasticForceDifferential(btScalar scale, const TVStack& dx, TVStack& df) = 0;
      
      // add all forces that are explicit in explicit solve
      virtual void addScaledExplicitForce(btScalar scale, TVStack& force) = 0;
      
      // add all damping forces 
      virtual void addScaledDampingForce(btScalar scale, TVStack& force) = 0;
      
      virtual btDeformableLagrangianForceType getForceType() = 0;
      
      virtual void reinitialize(bool nodeUpdated)
      {
      }
      
      // get number of nodes that have the force
      virtual int getNumNodes()
      {
          int numNodes = 0;
          for (int i = 0; i < m_softBodies.size(); ++i)
          {
              numNodes += m_softBodies[i]->m_nodes.size();
          }
          return numNodes;
      }
      
      // add a soft body to be affected by the particular lagrangian force
      virtual void addSoftBody(btSoftBody* psb)
      {
          m_softBodies.push_back(psb);
      }
      
      virtual void removeSoftBody(btSoftBody* psb)
      {
          m_softBodies.remove(psb);
      }
      
      virtual void setIndices(const btAlignedObjectArray<btSoftBody::Node*>* nodes)
      {
          m_nodes = nodes;
      }
      
       // Calculate the incremental deformable generated from the input dx
      virtual btMatrix3x3 Ds(int id0, int id1, int id2, int id3, const TVStack& dx)
      {
          btVector3 c1 = dx[id1] - dx[id0];
          btVector3 c2 = dx[id2] - dx[id0];
          btVector3 c3 = dx[id3] - dx[id0];
          return btMatrix3x3(c1,c2,c3).transpose();
      }
      
      // Calculate the incremental deformable generated from the current velocity
      virtual btMatrix3x3 DsFromVelocity(const btSoftBody::Node* n0, const btSoftBody::Node* n1, const btSoftBody::Node* n2, const btSoftBody::Node* n3)
      {
          btVector3 c1 = n1->m_v - n0->m_v;
          btVector3 c2 = n2->m_v - n0->m_v;
          btVector3 c3 = n3->m_v - n0->m_v;
          return btMatrix3x3(c1,c2,c3).transpose();
      }
      
      // test for addScaledElasticForce function
      virtual void testDerivative()
      {
          for (int i = 0; i<m_softBodies.size();++i)
          {
              btSoftBody* psb = m_softBodies[i];
              for (int j = 0; j < psb->m_nodes.size(); ++j)
              {
                  psb->m_nodes[j].m_q += btVector3(randomDouble(-.1, .1), randomDouble(-.1, .1), randomDouble(-.1, .1));
              }
              psb->updateDeformation();
          }
          
          TVStack dx;
          dx.resize(getNumNodes());
          TVStack dphi_dx;
          dphi_dx.resize(dx.size());
          for (int i =0; i < dphi_dx.size();++i)
          {
              dphi_dx[i].setZero();
          }
          addScaledForces(-1, dphi_dx);
          
          // write down the current position
          TVStack x;
          x.resize(dx.size());
          int counter = 0;
          for (int i = 0; i<m_softBodies.size();++i)
          {
              btSoftBody* psb = m_softBodies[i];
              for (int j = 0; j < psb->m_nodes.size(); ++j)
              {
                  x[counter] = psb->m_nodes[j].m_q;
                  counter++;
              }
          }
          counter = 0;
          
          // populate dx with random vectors
          for (int i = 0; i < dx.size(); ++i)
          {
              dx[i].setX(randomDouble(-1, 1));
              dx[i].setY(randomDouble(-1, 1));
              dx[i].setZ(randomDouble(-1, 1));
          }
          
          btAlignedObjectArray<double> errors;
          for (int it = 0; it < 10; ++it)
          {
              for (int i = 0; i < dx.size(); ++i)
              {
                  dx[i] *= 0.5;
              }
              
              // get dphi/dx * dx
              double dphi = 0;
              for (int i = 0; i < dx.size(); ++i)
              {
                  dphi += dphi_dx[i].dot(dx[i]);
              }
              
  
              for (int i = 0; i<m_softBodies.size();++i)
              {
                  btSoftBody* psb = m_softBodies[i];
                  for (int j = 0; j < psb->m_nodes.size(); ++j)
                  {
                      psb->m_nodes[j].m_q = x[counter] + dx[counter];
                      counter++;
                  }
                  psb->updateDeformation();
              }
              counter = 0;
              double f1 = totalElasticEnergy(0);
              
              for (int i = 0; i<m_softBodies.size();++i)
              {
                  btSoftBody* psb = m_softBodies[i];
                  for (int j = 0; j < psb->m_nodes.size(); ++j)
                  {
                      psb->m_nodes[j].m_q = x[counter] - dx[counter];
                      counter++;
                  }
                  psb->updateDeformation();
              }
              counter = 0;
              
              double f2 = totalElasticEnergy(0);
              
              //restore m_q
              for (int i = 0; i<m_softBodies.size();++i)
              {
                  btSoftBody* psb = m_softBodies[i];
                  for (int j = 0; j < psb->m_nodes.size(); ++j)
                  {
                      psb->m_nodes[j].m_q = x[counter];
                      counter++;
                  }
                  psb->updateDeformation();
              }
              counter = 0;
              double error = f1-f2-2*dphi;
              errors.push_back(error);
              std::cout << "Iteration = " << it <<", f1 = " << f1 << ", f2 = " << f2 << ", error = " << error << std::endl;
          }
          for (int i = 1; i < errors.size(); ++i)
          {
              std::cout << "Iteration = " << i << ", ratio = " << errors[i-1]/errors[i] << std::endl;
          }
      }
      
      // test for addScaledElasticForce function
      virtual void testHessian()
      {
          for (int i = 0; i<m_softBodies.size();++i)
          {
              btSoftBody* psb = m_softBodies[i];
              for (int j = 0; j < psb->m_nodes.size(); ++j)
              {
                  psb->m_nodes[j].m_q += btVector3(randomDouble(-.1, .1), randomDouble(-.1, .1), randomDouble(-.1, .1));
              }
              psb->updateDeformation();
          }
          
          
          TVStack dx;
          dx.resize(getNumNodes());
          TVStack df;
          df.resize(dx.size());
          TVStack f1;
          f1.resize(dx.size());
          TVStack f2;
          f2.resize(dx.size());
          
          
          // write down the current position
          TVStack x;
          x.resize(dx.size());
          int counter = 0;
          for (int i = 0; i<m_softBodies.size();++i)
          {
              btSoftBody* psb = m_softBodies[i];
              for (int j = 0; j < psb->m_nodes.size(); ++j)
              {
                  x[counter] = psb->m_nodes[j].m_q;
                  counter++;
              }
          }
          counter = 0;
          
          // populate dx with random vectors
          for (int i = 0; i < dx.size(); ++i)
          {
              dx[i].setX(randomDouble(-1, 1));
              dx[i].setY(randomDouble(-1, 1));
              dx[i].setZ(randomDouble(-1, 1));
          }
          
          btAlignedObjectArray<double> errors;
          for (int it = 0; it < 10; ++it)
          {
              for (int i = 0; i < dx.size(); ++i)
              {
                  dx[i] *= 0.5;
              }
              
              // get df
              for (int i =0; i < df.size();++i)
              {
                  df[i].setZero();
                  f1[i].setZero();
                  f2[i].setZero();
              }
  
              //set df
              addScaledElasticForceDifferential(-1, dx, df);
              
              for (int i = 0; i<m_softBodies.size();++i)
              {
                  btSoftBody* psb = m_softBodies[i];
                  for (int j = 0; j < psb->m_nodes.size(); ++j)
                  {
                      psb->m_nodes[j].m_q = x[counter] + dx[counter];
                      counter++;
                  }
                  psb->updateDeformation();
              }
              counter = 0;
              
              //set f1
              addScaledForces(-1, f1);
              
              for (int i = 0; i<m_softBodies.size();++i)
              {
                  btSoftBody* psb = m_softBodies[i];
                  for (int j = 0; j < psb->m_nodes.size(); ++j)
                  {
                      psb->m_nodes[j].m_q = x[counter] - dx[counter];
                      counter++;
                  }
                  psb->updateDeformation();
              }
              counter = 0;
              
              //set f2
              addScaledForces(-1, f2);
              
              //restore m_q
              for (int i = 0; i<m_softBodies.size();++i)
              {
                  btSoftBody* psb = m_softBodies[i];
                  for (int j = 0; j < psb->m_nodes.size(); ++j)
                  {
                      psb->m_nodes[j].m_q = x[counter];
                      counter++;
                  }
                  psb->updateDeformation();
              }
              counter = 0;
              double error = 0;
              for (int i = 0; i < df.size();++i)
              {
                  btVector3 error_vector = f1[i]-f2[i]-2*df[i];
                  error += error_vector.length2();
              }
              error = btSqrt(error);
              errors.push_back(error);
              std::cout << "Iteration = " << it << ", error = " << error << std::endl;
          }
          for (int i = 1; i < errors.size(); ++i)
          {
              std::cout << "Iteration = " << i << ", ratio = " << errors[i-1]/errors[i] << std::endl;
          }
      }
      
      //
      virtual double totalElasticEnergy(btScalar dt)
      {
          return 0;
      }
      
      //
      virtual double totalDampingEnergy(btScalar dt)
      {
          return 0;
      }
      
      // total Energy takes dt as input because certain energies depend on dt
      virtual double totalEnergy(btScalar dt)
      {
          return totalElasticEnergy(dt) + totalDampingEnergy(dt);
      }
  };
  #endif /* BT_DEFORMABLE_LAGRANGIAN_FORCE */
  