Cloth Simulation By Chris Szendrovits o based on Jim Adams “Soft Body Mesh” demo

Cloth Points & Springs Mesh vertices need the ability to deform and then recover This is done by adding cloth points and cloth springs Cloth Points have a position and a mass, and begin with the same position as the mesh vertices Cloth Springs contain two points, a resting length, a damping value, and a stiffness value Cloth Point (mesh vertex) Cloth Spring (polygon edge)

Cloth Point Example struct sClothPoint { D3DXVECTOR3 m_vecPos;// Current point coords D3DXVECTOR3 m_vecForce;// Force applied to point D3DXVECTOR3 m_vecVelocity;// Velocity of point float m_Mass;// Mass of object };

Cloth Spring Example class cClothSpring { public: int m_Point1; // First point in spring intm_Point2; // Second point in spring floatm_RestingLength; // Resting length of spring floatm_Stiffness; // Spring stiffness constant value floatm_Damping; // Spring damping value cClothSpring *m_Next; // Next in linked list public: cClothSpring() { m_Next = NULL; } ~cClothSpring() { delete m_Next; m_Next = NULL; } };

Applying Forces to Cloth A number of different forces may affect a cloth’s points: wind, gravity, friction, and collision The springs themselves also apply forces to eachother A Spring will expand and contract according to their damping and stiffness values Stiffness defines how much force a spring exerts in an attempt to return to its natural length Damping smooths out the motion of the points by reducing the amount of force a spring exerts

Wind Forces Applying wind forces isn’t as simple as adding a directional vector to the cloth points (eg. Gravity) The applied force is proportional to the surface area of the triangle Luckily, using the cross product to calculate the triangle normal gives you a length vector that is proportional to the area of the triangle D3DXVec3Cross(&vecNormal, &vecEdge1, &vecEdge2); D3DXVec3Normalize(&vecNormal, &vecNormal);

Wind Forces continued.. The wind force will always be in the direction of the triangle normal First we need to find, using a dot product calculation, the angle between the wind and the normal. float angle = D3DXVec3Dot(&vecNormal, vecWind); By using the angle to scale the normal we can calculate the amount of force to apply to each cloth point D3DXVECTOR3 vecWindForce = vecNormal * angle; ClothPoint[i].m_vecForce += vecWindForce; Normal Wind Force

Spring Forces Each spring begins with an initial resting length This is the distance between the two points that the spring connects D3DXVECTOR3 vecSpring = ClothPoint[a].m_vecPos – ClothPoint[b].m_vecPos; float SpringLength = D3DXVec3Length(&vecSpring);

Spring Forces continued.. When the cloth points begin to move, we need to calculate its current length in comparison with its resting length With this value we either pull or push the cloth points back to their natural resting length float SpringForce = m_Stiffness * (SpringLength – m_RestingLength); vecSpring /= SpringLength; // Normal the spring to get the direction vecSpring *= SpringForce; // Calculate a force vector // Add forces to cloth points ClothPoint[a].m_vecForce += vecSpring; ClothPoint[b].m_vecForce -= vecSpring;

Damping Forces As the cloth moves through air, friction forces, or linear damping, will slow it down Damping is a force that is proportional to the velocity (F=kV) D3DXVECTOR3 vecRelVelocity = ClothPoint[a].m_vecVelocity – ClothPoint[b].m_vecVelocity; float Velocity = D3DXVec3Dot(&vecRelVelocity, &vecSpring) / SpringLength; float DampingForce = m_Damping * Velocity; vecSpring *= (SpringForce + DampingForce);

Summary First create the cloth points and cloth springs Next update the cloth points based on all the forces being exerted on them  Damping, Spring, Wind, Gravity, Collision Finally, rebuild the mesh based on the new position of the cloth points