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Motor V. Ütközés detektálás és válasz Szécsi László.

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1 Motor V. Ütközés detektálás és válasz Szécsi László

2 Letöltés diák: //l10-collision.ppt

3 Új osztály: FatCollider class FatCollider { friend class RigidBody; friend class RigidModel; protected: double thickness; double density; double restitution; double friction;

4 FatCollider folyt. FatCollider(double density, double thickness, double restitution, double friction); double getRestitution(); double getFriction(); virtual double getMass()=0; virtual void getAngularMass(D3DXMATRIX& massMatrix)=0;

5 FatCollider folyt. virtual void getNearestPointTo( const D3DXVECTOR3& b, D3DXVECTOR3& out)=0; virtual void getReferencePoint(D3DXVECTOR3& out)=0; virtual FatCollider* makeTransformedClone( const D3DXMATRIX& transformationMatrix)=0; virtual void translate(const D3DXVECTOR3& offset)=0; };

6 FatCollider.cpp FatCollider::FatCollider(double density, double thickness, double restitution, double friction) { this->density = density; this->thickness = thickness; this->restitution = restitution; this->friction = friction; } double FatCollider::getRestitution() { return restitution; } double FatCollider::getFriction() {return friction; }

7 Új class: FatCylinder class FatCylinder : public FatCollider { double radius; double height; D3DXVECTOR3 position; D3DXVECTOR3 discNormal;

8 FatCylinder folyt. public: FatCylinder(double density, double thickness, double restitution, double friction, double radius, double height, const D3DXVECTOR3& position, const D3DXVECTOR3& discNormal); double getMass(); void getAngularMass(D3DXMATRIX& massMatrix);

9 FatCylinder folyt. void getNearestPointTo(const D3DXVECTOR3& b, D3DXVECTOR3& out); void getReferencePoint(D3DXVECTOR3& out); FatCollider* makeTransformedClone(const D3DXMATRIX& transformationMatrix); void translate(const D3DXVECTOR3& offset); };

10 FatCylinder.cpp FatCylinder::FatCylinder(double density, double thickness, double restitution, double friction, double radius, double height, const D3DXVECTOR3& position, const D3DXVECTOR3& discNormal) :FatCollider(density, thickness, restitution, friction) { this->radius = radius; this->position = position; this->discNormal = discNormal; this->height = height; }

11 FatCylinder.cpp double FatCylinder::getMass() { return density * (radius + thickness) * (radius + thickness) * 3.14 * (height + thickness * 2.0); }

12 FatCylinder.cpp void FatCylinder::getAngularMass(D3DXMATRIX& massMatrix) { double mass = getMass(); double cylinderRadius = radius + thickness; double cylinderRadius2 = cylinderRadius * cylinderRadius; double cylinderHeight2 = (height + thickness * 2.0) * (height + thickness * 2.0); D3DXMatrixScaling(&massMatrix, mass * (3.0 * cylinderRadius2 + cylinderHeight2) / 12.0, mass * cylinderRadius2 * 0.5, mass * (3.0 * cylinderRadius2 + cylinderHeight2) / 12.0); D3DXVECTOR3 rotationAxis; D3DXVec3Cross(&rotationAxis, &discNormal, &D3DXVECTOR3(0.0f, 1.0f, 0.0f)); float rotationAngle = acos(discNormal.y); D3DXMATRIX transformMatrix, transposedTransformMatrix; D3DXMatrixRotationAxis(&transformMatrix, &rotationAxis, rotationAngle); D3DXMatrixTranspose(&transposedTransformMatrix, &transformMatrix); D3DXMATRIX translationMassMatrix; float mrr = mass * D3DXVec3LengthSq(&position); D3DXMatrixScaling(&translationMassMatrix, mrr, mrr, mrr); D3DXMATRIX posProducts( mass * position.x * position.x, mass * position.x * position.y, mass * position.x * position.z, 0.0f, mass * position.y * position.x, mass * position.y * position.y, mass * position.y * position.z, 0.0f, mass * position.z * position.x, mass * position.z * position.y, mass * position.z * position.z, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f ); translationMassMatrix -= posProducts; massMatrix = transposedTransformMatrix * massMatrix * transformMatrix + translationMassMatrix; }

13 FatCylinder.cpp void FatCylinder::getNearestPointTo(const D3DXVECTOR3& b, D3DXVECTOR3& out) { out = b; out -= position; D3DXVECTOR3 onNormal = discNormal * D3DXVec3Dot(&out, &discNormal); D3DXVECTOR3 onTangent = out - onNormal; float ln = D3DXVec3Length(&onNormal); if(ln > height * 0.5) onNormal *= height * 0.5 / ln; float ld = D3DXVec3Length(&onTangent); if(ld > radius) onTangent *= radius / ld; out = onNormal + onTangent + position; }

14 FatCylinder.cpp void FatCylinder::getReferencePoint( D3DXVECTOR3& out) { out = position; } void FatCylinder::translate(const D3DXVECTOR3& offset) { position += offset; }

15 FatCylinder.cpp FatCollider* FatCylinder::makeTransformedClone(const D3DXMATRIX& transformationMatrix) { D3DXVECTOR3transformedPosition, transformedNormal; D3DXVec3TransformCoord(&transformedPosition, &position, &transformationMatrix); D3DXVec3TransformNormal(&transformedNormal, &discNormal, &transformationMatrix); return new FatCylinder(density, thickness, restitution, friction, radius, height, transformedPosition, transformedNormal); }

16 RigidModel kieg. #include "FatCollider.h" class RigidModel{ D3DXVECTOR3 centreOfMass; std::vector colliders; void recomputeMass();

17 RigidModel public: void addFatCollider(FatCollider* collider); void translateToCentreOfMass(); const D3DXVECTOR3& getCentreOfMass();

18 RigidModel.cpp void RigidModel::addFatCollider(FatCollid er* collider) { colliders.push_back(collider); recomputeMass(); }

19 RigidModel.cpp void RigidModel::recomputeMass() { double mass = 0; D3DXMATRIX angularMass; D3DXMatrixScaling(&angularMass, 0.0f, 0.0f, 0.0f); std::vector ::iterator i = colliders.begin(); while(i != colliders.end()){ if( (*i)->density == 0.0){ invMass = 0.0;D3DXMatrixScaling(&invAngularMass, 0, 0, 0); return;} mass += (*i)->getMass(); D3DXMATRIX colliderAngularMass; (*i)->getAngularMass(colliderAngularMass); angularMass += colliderAngularMass; i++; } invMass = 1.0 / mass; angularMass._44 = 1.0f; D3DXMatrixInverse(&invAngularMass, NULL, &angularMass); }

20 RigidModel.cpp void RigidModel::translateToCentreOfMass() { centreOfMass = D3DXVECTOR3(0, 0, 0); std::vector ::iterator i = colliders.begin(); while(i != colliders.end()){ if( (*i)->density == 0.0) {centreOfMass == D3DXVECTOR3(0, 0, 0); return;} double m = (*i)->getMass(); D3DXVECTOR3 com; (*i)->getReferencePoint(com); centreOfMass += com * m; i++; } centreOfMass *= invMass; std::vector ::iterator ii = colliders.begin(); while(ii != colliders.end()){ (*ii)->translate(-centreOfMass);ii++;} recomputeMass(); }

21 RigidModel.cpp const D3DXVECTOR3& RigidModel::getCentreOfMass() { return centreOfMass; }

22 EngineCore::loadRigidModels loadFatCylinders(rigidModelNode, rigidModel); rigidModel->translateToCentreOfMass(); rigidModelDirectory[rigidModelName] = rigidModel;

23 EngineCore osztályba void loadFatCylinders( XMLNode& rigidModelNode, RigidModel* rigidModel);

24 EngineCore.cpp #include "FatCylinder.h" void EngineCore::loadFatCylinders(XMLNode& rigidModelNode, RigidModel* rigidModel) { int iFatCylinder = 0; XMLNode colliderNode; while( !(colliderNode = rigidModelNode.getChildNode(L"FatCylinder", iFatCylinder)).isEmpty() ) { double density = colliderNode.readDouble(L"density", 1.0); double restitution = colliderNode.readDouble(L"restitution", 0.7); double friction = colliderNode.readDouble(L"friction", 0.2); double thickness = colliderNode.readDouble(L"thickness", 1.0); double radius = colliderNode.readDouble(L"radius", 3.0); double height = colliderNode.readDouble(L"height", 3.0); D3DXVECTOR3 position = colliderNode.readVector(L"position"); D3DXVECTOR3 axis = colliderNode.readVector(L"axis"); rigidModel->addFatCollider(new FatCylinder(density, thickness, restitution, friction, radius, height, position, axis)); iFatCylinder++; }

25 XML

26 Próba Tömeg az ütköző geometria alapján számolva Kevés az erő és a forgatónyomaték ehhez Állítsuk nagyobbra a motorcontrolban |force| = 35 |torque| = 100

27 Entity kieg. virtual RigidBody* asRigidBody(); //cpp RigidBody* Entity::asRigidBody() { return NULL; }

28 RigidBody RigidBody* asRigidBody(); //cpp RigidBody* RigidBody::asRigidBody() { return this; }

29 RigidBody class RigidBody { D3DXVECTOR3 positionCorrection; D3DXVECTOR3 impulse; D3DXVECTOR3 angularImpulse; public: virtual void interact(Entity* target); virtual void affect(Entity* affector); D3DXVECTOR3 getPointVelocity(const D3DXVECTOR3& point);

30 RigidBody::animate momentum += force * dt + impulse; D3DXVECTOR3 velocity = momentum * rigidModel->invMass; position += velocity * dt + positionCorrection; angularMomentum += torque * dt + angularImpulse;

31 RigidBody::control force = D3DXVECTOR3(0.0, 0.0, 0.0); torque = D3DXVECTOR3(0.0, 0.0, 0.0); impulse = D3DXVECTOR3(0.0, 0.0, 0.0); angularImpulse = D3DXVECTOR3(0.0, 0.0, 0.0); positionCorrection = D3DXVECTOR3(0.0, 0.0, 0.0);

32 RigidBody::control if(controller) controller->apply(this, context); context.interactors->interact(this); }

33 void RigidBody::interact(Entity* target) { if(target == this) return; target->affect(this); }

34 RigidBody::getPointVelocity D3DXVECTOR3 RigidBody::getPointVelocity( const D3DXVECTOR3& point) { D3DXVECTOR3 rp = point - position; D3DXMATRIX worldSpaceInvMassMatrix; getWorldInvMassMatrix(worldSpaceInvMassMatrix); // compute angular velocity vector D3DXVECTOR3 angularVelocity; D3DXVec3TransformCoord(&angularVelocity, &angularMomentum, &worldSpaceInvMassMatrix); // compute tangential velocity from angular velocity D3DXVECTOR3 velo; D3DXVec3Cross(&velo, &angularVelocity, &rp); // add object velocity velo += momentum * rigidModel->invMass; return velo; }

35 RigidBody::affect Másik entitás RigidBody-e? A másik fatCollidereit áttranszformáljuk a mi modellezési koordináta rendszerünkbe –model 2 ->world->model 1 Minden collider párra –Iteratívan megkeressük a legközelebbi pontokat –Ha közelebb vannak, mint amilyen vastagok, akkor ütközés-válasz Impulzus: képlet szerint

36 RigidBody::affect void RigidBody::affect(Entity* affector) { RigidBody* antiBody = affector->asRigidBody(); // rigid body collision detection if(antiBody) { std::vector & antiColliders = antiBody->rigidModel->colliders; // for each collider i in antiColliders std::vector ::iterator i = antiColliders.begin(); while(i != antiColliders.end()) { // transform i to my model space // other * o.rotationMatrix * o.translation / t.translationMatrix / t.rotationMatrix D3DXMATRIX otherPosMinusMyPosMatrix; D3DXMatrixTranslation(&otherPosMinusMyPosMatrix, antiBody->position.x - position.x, antiBody->position.y - position.y, antiBody->position.z - position.z); D3DXMATRIX rotateBackMatrix; D3DXMatrixTranspose(&rotateBackMatrix, &rotationMatrix); FatCollider* otherColliderInMyModelSpace = (*i)->makeTransformedClone(antiBody->rotationMatrix * otherPosMinusMyPosMatrix * rotateBackMatrix); // for each collider j in colliders std::vector & myColliders = rigidModel->colliders; std::vector ::iterator j = myColliders.begin(); while(j != myColliders.end()) { D3DXVECTOR3 a, b; (*j)->getReferencePoint(a); for(int c=0; c<10; c++) { otherColliderInMyModelSpace->getNearestPointTo(a, b); (*j)->getNearestPointTo(b, a); } D3DXVECTOR3 collisionNormal = a - b; float abDistance = D3DXVec3Length(&collisionNormal); if(abDistance < 0.1) { D3DXVECTOR3 aCenter, bCenter; (*j)->getReferencePoint(aCenter); aCenter -= a; D3DXVec3Normalize(&aCenter, &aCenter); aCenter *= (*j)->thickness * 0.5; a += aCenter; (*i)->getReferencePoint(bCenter); bCenter -= b; D3DXVec3Normalize(&bCenter, &bCenter); bCenter *= (*i)->thickness * 0.5; b += bCenter; } float objectDistance = abDistance - (*i)->thickness - (*j)->thickness; if(objectDistance < 0) { // to world collision point and normal D3DXVec3Normalize(&collisionNormal, &collisionNormal); D3DXVECTOR3 collisionPoint = (a - collisionNormal * (*j)->thickness + b + collisionNormal * (*i)->thickness) * 0.5; D3DXVec3TransformNormal(&collisionNormal, &collisionNormal, &rotationMatrix); D3DXVec3TransformNormal(&collisionPoint, &collisionPoint, &rotationMatrix); collisionPoint += position; // compute relative velocity of colliding points D3DXVECTOR3 relativeVelocity = antiBody- >getPointVelocity(collisionPoint) - getPointVelocity(collisionPoint); float normalVelocityLength = D3DXVec3Dot( &relativeVelocity, &collisionNormal); D3DXVECTOR3 normalVelocity = collisionNormal * normalVelocityLength; D3DXVECTOR3 frictionVelocity = relativeVelocity - normalVelocity; if( D3DXVec3Length(&frictionVelocity) > 1.0) D3DXVec3Normalize(&frictionVelocity, &frictionVelocity); // compute impulse float invMassDiv = 0.0; invMassDiv += rigidModel->invMass; invMassDiv += antiBody->rigidModel->invMass; D3DXVECTOR3 arma = collisionPoint - position; D3DXVECTOR3 armb = collisionPoint - antiBody->position; D3DXVECTOR3 kan, kbn, ikan, ikbn, ikank, ikbnk; // compute inverse mass matrix D3DXMATRIX myWorldInvMassMatrix, antiWorldInvMassMatrix; this->getWorldInvMassMatrix(myWorldInvMassMatrix); antiBody->getWorldInvMassMatrix(antiWorldInvMassMatrix); D3DXVec3Cross(&kan, &arma, &collisionNormal); D3DXVec3Cross(&kbn, &armb, &collisionNormal); D3DXVec3TransformNormal(&ikan, &kan, &myWorldInvMassMatrix); D3DXVec3TransformNormal(&ikbn, &kbn, &antiWorldInvMassMatrix); D3DXVec3Cross(&ikank, &ikan, &arma); D3DXVec3Cross(&ikbnk, &ikbn, &armb); invMassDiv += D3DXVec3Dot(&collisionNormal, &ikank); invMassDiv += D3DXVec3Dot(&collisionNormal, &ikbnk); D3DXVECTOR3 impulse = (1 + (*i)->getRestitution() * (*j)->getRestitution()) * (normalVelocity + frictionVelocity * (*i)->getFriction() * (*j)->getFriction()) / invMassDiv; // add collision response this->impulse += impulse; D3DXVECTOR3 angularImpulse; D3DXVec3Cross(&angularImpulse, &arma, &impulse); this->angularImpulse += angularImpulse; this->positionCorrection -= collisionNormal * (objectDistance * 0.55f) * rigidModel->invMass / (rigidModel->invMass + antiBody->rigidModel->invMass); } j++; } delete otherColliderInMyModelSpace; i++; }

37 XML – másik RigidBody

38 Próba nekitolatunk: elpördülnek.fx-ben a lámpákat kivehetjük, hogy lássuk is mi történik. Pl. float4 psBasic(TrafoOutput input) : COLOR0 { float3 lighting = abs(input.normal.y) * 2; /*for(int il=0; il

39 Pozíció nem stimmel Ütközőket elmozgattuk, hogy az origóban legyen a tömegközéppont A rajzolt modellt is mozgassuk el

40 RigidBody::render D3DXMATRIX positionMatrix; D3DXMatrixTranslation(&positionMatrix, position.x, position.y, position.z); D3DXMATRIX massOffsetMatrix; D3DXMatrixTranslation( &massOffsetMatrix, -rigidModel->centreOfMass.x, -rigidModel->centreOfMass.y, -rigidModel->centreOfMass.z); D3DXMATRIX bodyModelMatrix = massOffsetMatrix * rotationMatrix * positionMatrix;

41 Próba Ütközés működik Mozogjon ez is: Vezérlés célokkal Target ~ Motor TargetControl ~ MotorControl

42 XML

43 Új class: Target class Entity; class Target { friend class TargetControl; D3DXVECTOR3 position; double radius; Entity* mark; public: Target(const D3DXVECTOR3& position, double radius); void setMark(Entity* mark); };

44 Target.cpp Target::Target(const D3DXVECTOR3& position, double radius) { mark = NULL; this->radius = radius; this->position = position; } void Target::setMark(Entity* mark) { this->mark = mark; }

45 Új class: TargetControl #include class Target; class TargetControl : public RigidBodyControl { std::vector targets; std::vector ::iterator currentTarget; double maxForce; double maxTorque; public: TargetControl(double maxForce, double maxTorque); ~TargetControl(void); void addTarget(Target* target); void apply(RigidBody* controlledBody, const ControlContext& context); };

46 TargetControl.cpp TargetControl::TargetControl(double maxForce, double maxTorque) { currentTarget = targets.end(); this->maxForce = maxForce; this->maxTorque = maxTorque; }

47 TargetControl.cpp void TargetControl::addTarget(Target* target) { targets.push_back(target); currentTarget = targets.begin(); } TargetControl::~TargetControl(void) { std::vector ::iterator i = targets.begin(); while(i != targets.end()) { delete *i; i++; }

48 TargetControl::apply void TargetControl::apply(RigidBody* controlledBody, const ControlContext& context) { if(!targets.empty()) { Target* target = *currentTarget; D3DXVECTOR3 markDifference = target->position - controlledBody->position; if(target->mark) markDifference += target->mark->getPosition(); if(D3DXVec3Length(&markDifference) radius) { currentTarget++; if(currentTarget == targets.end()) currentTarget = targets.begin(); }

49 TargetControl::apply D3DXVECTOR3 markDirection; D3DXVec3Normalize(&markDirection, &markDifference); D3DXMATRIX modelMatrix; controlledBody->getModelMatrix(modelMatrix); D3DXVECTOR3 ahead; D3DXVec3TransformNormal(&ahead, &D3DXVECTOR3(1, 0, 0), &modelMatrix); D3DXVECTOR3 turnAxis; D3DXVec3Cross(&turnAxis, &ahead, &markDirection); controlledBody->torque += turnAxis * maxTorque; controlledBody->force += ahead * D3DXVec3Dot(&ahead, &markDirection) * maxForce; }

50 RigidBody-hoz hozzáférés class RigidBody : public Entity { friend class TargetControl;

51 EngineCore // vezérlők legyártása entitások betöltése előtt void loadTargetControls(XMLNode& xMainNode); // célpontok bekötése entitások betöltése után void finishTargetControls(XMLNode& xMainNode); void loadTargets(XMLNode& targetControlNode, TargetControl* targetControl);

52 EngineCore::loadTargetControls void EngineCore::loadTargetControls(XMLNode& xMainNode) { int iTargetControl = 0; XMLNode targetControlNode; while( !(targetControlNode = xMainNode.getChildNode(L"TargetControl", iTargetControl)).isEmpty() ) { const wchar_t* targetControlName = targetControlNode|L"name"; TargetControl* targetControl = new TargetControl( targetControlNode.readDouble(L"maxForce"), targetControlNode.readDouble(L"maxTorque")); rigidBodyControlDirectory[targetControlName] = targetControl; iTargetControl++; }

53 EngineCore::finishTargetControls void EngineCore::finishTargetControls(XMLNode& xMainNode) { int iTargetControl = 0; XMLNode targetControlNode; while( !(targetControlNode = xMainNode.getChildNode(L"targetControl", iTargetControl)).isEmpty() ) { const wchar_t* targetControlName = targetControlNode|L"name"; TargetControl* targetControl = (TargetControl*)rigidBodyControlDirectory [targetControlName]; loadTargets(targetControlNode, targetControl); iTargetControl++; }

54 EngineCore::loadTargets void EngineCore::loadTargets(XMLNode& targetControlNode, TargetControl* targetControl) { int iTarget = 0; XMLNode targetNode; while( !(targetNode = targetControlNode.getChildNode(L"Target", iTarget)).isEmpty() ) { D3DXVECTOR3 pos = targetNode.readVector(L"position"); double radius = targetNode.readDouble(L"radius", 10); Target* target = new Target(pos, radius); const wchar_t* markEntityName = targetNode|L"mark"; if(markEntityName != NULL) { EntityDirectory::iterator iEntity = entityDirectory.find(markEntityName); if(iEntity != entityDirectory.end()) target->setMark(iEntity->second); } targetControl->addTarget(target); iTarget++; }

55 EngineCore::loadLevel loadTargetControls(xMainNode); XMLNode groupNode = xMainNode.getChildNode(L"Group"); sceneRoot = NULL; loadGroup(groupNode, sceneRoot); finishTargetControls(xMainNode);

56 XML

57 RigidBody::getPosition D3DXVECTOR3 RigidBody::getPosition() { return position; } // kell, mert az Entity::getPosition nem jó pozíciót ad vissza

58 Próba Legyen a control cruiser helyett interceptor Üldözi a játékos hajóját és nekimegy


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