Transcript Chris Szendrovits on Cloth Simulation

Cloth Simulation
By Chris Szendrovits
o
based on Jim Adams “Soft Body Mesh” demo
Cloth Points & Springs
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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;
D3DXVECTOR3 m_vecVelocity;
// Force applied to point
// Velocity of point
float
// Mass of object
m_Mass;
Cloth Spring Example
class cClothSpring
{
public:
int
m_Point1; // First point in spring
int
m_Point2; // Second point in spring
float m_RestingLength; // Resting length of spring
float m_Stiffness; // Spring stiffness constant value
float m_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
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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
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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..
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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.
Normal
Force
float angle = D3DXVec3Dot(&vecNormal, vecWind);
Wind
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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;
Spring Forces
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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..
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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
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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
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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
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Finally, rebuild the mesh based on the
new position of the cloth points