Vega FEM Library (v1.1) User's Manual - University of Southern ...

Constructs a mass-spring system of numParticles particles and numEdges springs. masses specifies
the mass of each particle, and restPositions contains three subsequent entries for the three-dimensional
coordinates of each particle. edges contains 2 · numParticles particle indices, with each pair defining the
endpoints of a spring. edgeGroups specifies for each spring the index of which of the numMaterialGroups
material property groups it belongs to, while groupStiffness and groupDamping specify the stiffness and
damping parameters for each of these groups.
MassSpringSystem(int numParticles, double * restPositions,
int numQuads, int * quads, double surfaceDensity,
double tensileStiffness, double shearStiffness,
double bendStiffness, double damping, int addGravity=0)
Constructs a mass-spring system based upon an organization of the numParticles particles into numQuads
quads in a quad mesh. The 4 · numQuads-entry array quads specifies each quad with four subsequent particle
indices. Particle rest positions are defined as above, and particle masses are defined based upon
surfaceDensity and the quad surface areas. The stiffness and damping settings determine the spring
properties.
MassSpringSystem(int numParticles, double * restPositions,
MassSpringSystemElementType elementType, int numElements,
int * elements, double density, double tensileStiffness,
double damping, int addGravity=0)
Constructs a mass-spring system based upon a tetrahedral mesh or cubic mesh, depending on whether
elementType is set to TET or CUBE. The numParticles particles are organized into numElements tetrahedra
or cubes, which are specified in the array elements (of size 4 times or 8 times numElements) by four or
eight subsequent particle indices per element. Particle masses are set according to density and the element
volumes, while spring properties are set according to the stiffness and damping variables.
void SetGravity(bool addGravity, double g=9.81)
Sets whether gravity is enabled, and optionally sets the gravitational constant.
void ComputeForce(double * u, double * f, bool addForce=false)
Computes the forces acting on the mass-spring particles given their displacements u and writes the result
to the pre-allocated array f. If addForce is true, the forces are added to any existing force values in f.
Important: the force f has the same sign as with the other deformable models in Vega, i.e., it appears on
the left side in equation Mü + D ˙u + f = fext. If you want f to be interpreted as an external mass-spring
force acting on the particles, you must flip the sign of f. The same applies to the damping forces, stiffness
matrices and their Hessian corrections.
void ComputeDampingForce(double * uvel, double * f, bool addForce=false)
Computes the damping forces acting on the mass-spring particles given their current velocities uvel, and
writes the result to the pre-allocated array f. If addForce is true, the forces are added to any existing forces
in f.
void GetStiffnessMatrixTopology(SparseMatrix ** stiffnessMatrixTopology)
Writes to *stiffnessMatrixTopology a newly allocated (using new) zero matrix containing the pattern
of non-zero entries of the stiffness matrix.
void ComputeStiffnessMatrix(double * u, SparseMatrix * K, bool addMatrix=false)
Computes the stiffness matrix of the mass-spring system given the vertex displacements u and writes
the result to the SparseMatrix pointed to by K. If addMatrix is true, the stiffness matrix is added to the
existing entries of *K.
class MassSpringSystemFromTetMesh
static int GenerateMassSpringSystem(TetMesh * tetMesh,
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