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grid.cpp
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grid.cpp
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#include "grid.h"
/**
* @brief Constructs a new Cuboid instance.
*
* This constructor initializes a new Cuboid instance with the specified position, dimensions,
* and other parameters. Note that the position and dimensions are given in terms of
* world-spatial coordinates.
*
* @param parent Pointer to the FluidGrid that this cuboid is a part of.
* @param centrex X-coordinate of the cuboid's center.
* @param centrey Y-coordinate of the cuboid's center.
* @param centrez Z-coordinate of the cuboid's center.
* @param width Width of the cuboid.
* @param height Height of the cuboid.
* @param depth Depth of the cuboid.
* @param alph Initial rotation of cuboid in radians.
* @param omg Angular velocity of cuboid in radians/s.
*/
Cuboid::Cuboid(FluidGrid* parent, double centrex, double centrey, double centrez, double width, double height, double depth, double alph, double omg) {
parentgrid = parent;
auto bbox = parent->getBBox();
openvdb::Vec3d size = bbox.max() - bbox.min();
centrepos(0) = centrex * size[0];
centrepos(1) = centrey * size[1];
centrepos(2) = centrez * size[2];
w = width * size[0];
h = height * size[1];
d = depth * size[2];
alpha = alph;
omega = omg;
}
/**
* Determines whether a given point is located within the cuboid.
*
* This method takes the coordinates of a point (x, y, z) and checks if it lies
* within the spatial domain of the cuboid. The cuboid's rotation is taken into
* account based on the current time of the parent fluid grid. A rotation matrix
* is formed from `alpha` and `omega` parameters, which represent
* a rotation angle and an angular velocity, respectively. The rotation of the
* cuboid oscillates over time with the frequency of `omega` and the phase of
* `alpha`, both in radians.
*
* @param x The x-coordinate of the point.
* @param y The y-coordinate of the point.
* @param z The z-coordinate of the point.
* @return True if the point is inside the cuboid, false otherwise.
*/
bool Cuboid::PointIsInside(double x, double y, double z){
openvdb::Vec3d cellpos(x,y,z);
double t = parentgrid->getCurrtime();
bool temp;
openvdb::Mat3d invtransform;
//rotation of -theta about z-axis
invtransform(2,0) = 0;
invtransform(0,2) = 0;
invtransform(2,1) = 0;
invtransform(1,2) = 0;
invtransform(0,0) = cos(alpha + omega*t);
invtransform(1,0) = -sin(alpha + omega*t);
invtransform(0,1) = sin(alpha + omega*t);
invtransform(1,1) = cos(alpha + omega*t);
invtransform(2,2) = 1.0;
cellpos = invtransform*(cellpos - centrepos);
temp = (cellpos(0) >= - w/2) && (cellpos(0) <= + w/2) &&
(cellpos(1) >= - h/2) && (cellpos(1) <= + h/2) &&
(cellpos(2) >= - d/2) && (cellpos(2) <= + d/2);
return temp;
}
/**
* Computes the velocity at a given point in the cuboid.
*
* This function calculates the velocity vector for a point located at coordinates
* (x, y, z) within the cuboid. The cuboid is assumed to be rotating about the z-axis
* with angular velocity `omega`. The velocity of a point in a rotating body is
* proportional to its radial distance from the axis of rotation and the direction
* of velocity is perpendicular to the radial vector (following the right-hand rule).
* The magnitude of the velocity is then scaled by the width of the cells in the
* parent grid.
*
* @param x The x-coordinate of the point.
* @param y The y-coordinate of the point.
* @param z The z-coordinate of the point.
* @return The velocity vector at the given point (x, y, z).
*/
openvdb::Vec3d Cuboid::getVelocity(openvdb::Vec3d xyz){
//vector from axis of rotation (z-axis) to x,y,z
double rx = xyz[0] - centrepos(0);
double ry = xyz[1] - centrepos(1);
double distance = sqrt(rx*rx + ry*ry);
//get the unit normal to vector (rx,ry)
double normx = -ry / distance;
double normy = rx / distance;
//get magnitude of velocity at x,y, scale the norm vector by this
normx *= distance*omega;
normy *= distance*omega;
openvdb::Vec3d temp(normx, normy, 0);
return temp;
}
/**
* Computes the normal vector at a given point in the cuboid.
*
* This function calculates the normal vector for a point located at coordinates
* (x, y, z) within the cuboid. The cuboid is assumed to be rotating about the z-axis
* with angular velocity `omega`. The rotation is characterized by an angle `alpha`
* which varies with time (t = `omega` * current_time).
*
* The function first transforms the point coordinates into the rotating frame of
* the cuboid and determines which face of the cuboid the point is closest to.
* It assigns a unit normal vector corresponding to that face. The normal vector
* is then transformed back to the original frame by inverse rotation.
*
* @param x The x-coordinate of the point.
* @param y The y-coordinate of the point.
* @param z The z-coordinate of the point.
* @return The normal vector at the given point (x, y, z).
*/
openvdb::Vec3d Cuboid::getNormal(openvdb::Vec3d xyz){
openvdb::Vec3d temp;
openvdb::Mat3d transform;
double t = parentgrid->getCurrtime();
//rotation of -theta about z-axis
transform(2,0) = 0;
transform(0,2) = 0;
transform(2,1) = 0;
transform(1,2) = 0;
transform(0,0) = cos(alpha + omega*t);
transform(1,0) = -sin(alpha + omega*t);
transform(0,1) = sin(alpha + omega*t);
transform(1,1) = cos(alpha + omega*t);
transform(2,2) = 1.0;
xyz = transform*(xyz - centrepos);
double x = xyz[0];
double y = xyz[1];
double z = xyz[2];
if ((y >= fabs(z)*h/d) && (y >= fabs(x)*h/w)){
temp(0) = 0;
temp(1) = 1;
temp(2) = 0;
}
else if ((y <= fabs(z)*h/d) && (y <= fabs(x)*h/w)){
temp(0) = 0;
temp(1) = -1;
temp(2) = 0;
}
else if ((x >= fabs(z)*w/d) && (x >= fabs(y)*w/h)){
temp(0) = 1;
temp(1) = 0;
temp(2) = 0;
}
else if ((x <= fabs(z)*w/d) && (x <= fabs(y)*w/h)){
temp(0) = -1;
temp(1) = 0;
temp(2) = 0;
}
else if ((z >= fabs(x)*d/w) && (z >= fabs(y)*d/h)){
temp(0) = 0;
temp(1) = 0;
temp(2) = 1;
}
else if ((z <= fabs(x)*d/w) && (z <= fabs(y)*d/h)){
temp(0) = 0;
temp(1) = 0;
temp(2) = -1;
}
//rotation of +theta about z-axis
transform(2,0) = 0;
transform(0,2) = 0;
transform(2,1) = 0;
transform(1,2) = 0;
transform(0,0) = cos(alpha + omega*t);
transform(1,0) = sin(alpha + omega*t);
transform(0,1) = -sin(alpha + omega*t);
transform(1,1) = cos(alpha + omega*t);
transform(2,2) = 1.0;
temp = transform * temp;
return temp;
}
/**
* Modifies the input coordinates (x, y, z) to represent the closest surface point
* on the cuboid if the original point is inside the cuboid.
*
* This function checks if a given point (x, y, z) is located inside a rotating cuboid.
* If so, it transforms the point into the rotating frame of the cuboid, calculates
* the distances to the cuboid's surfaces in each direction, and adjusts the point
* coordinates to match the closest surface point.
*
* The function then transforms the updated point back into the original frame.
* The cuboid's rotation is characterized by an angle `alpha` which varies with time
* (t = `omega` * current_time).
*
* The original point coordinates are modified in-place.
*
* @param x Reference to the x-coordinate of the point.
* Modified to match the x-coordinate of the closest surface point if the
* original point is inside the cuboid.
* @param y Reference to the y-coordinate of the point.
* Modified to match the y-coordinate of the closest surface point if the
* original point is inside the cuboid.
* @param z Reference to the z-coordinate of the point.
* Modified to match the z-coordinate of the closest surface point if the
* original point is inside the cuboid.
*/
void Cuboid::ClosestSurface(double &x, double &y, double &z) {
openvdb::Mat3d transform;
openvdb::Vec3d r(x,y,z);
double t = parentgrid->getCurrtime();
//rotation of -theta about z-axis
transform(2,0) = 0;
transform(0,2) = 0;
transform(2,1) = 0;
transform(1,2) = 0;
transform(0,0) = cos(alpha + omega*t);
transform(1,0) = -sin(alpha + omega*t);
transform(0,1) = sin(alpha + omega*t);
transform(1,1) = cos(alpha + omega*t);
transform(2,2) = 1.0;
r = transform*(r - centrepos);
double dx = w - 2*fabs(x);
double dy = h - 2*fabs(y);
double dz = d - 2*fabs(z);
if ((dx <= dy) && (dx <= dz))
x = (fabs(x)/x)*w/2;
else if ((dy <= dx) && (dy <= dz))
y = (fabs(y)/y)*h/2;
else
z = (fabs(z)/z)*d/2;
//rotation of +theta about z-axis
transform(2,0) = 0;
transform(0,2) = 0;
transform(2,1) = 0;
transform(1,2) = 0;
transform(0,0) = cos(alpha + omega*t);
transform(1,0) = sin(alpha + omega*t);
transform(0,1) = -sin(alpha + omega*t);
transform(1,1) = cos(alpha + omega*t);
transform(2,2) = 1.0;
r = centrepos + transform*r;
x = r(0);
y = r(1);
z = r(2);
}
/**
* Constructor for the `Sphere` class.
*
* This constructor initializes a `Sphere` object, which represents a sphere within a fluid grid.
* The position of the sphere and its radius are given in terms of cell counts, not physical space.
*
* @param parent Pointer to the parent `FluidGrid` object in which this sphere exists.
* The `Sphere` object uses this reference to access properties of the fluid grid.
* @param centrex The x-coordinate of the sphere's center, in cell units.
* @param centrey The y-coordinate of the sphere's center, in cell units.
* @param centrez The z-coordinate of the sphere's center, in cell units.
* @param rd The radius of the sphere, in cell units.
*/
Sphere::Sphere(FluidGrid* parent, double centrex, double centrey, double centrez, double rd) {
parentgrid = parent;
centrepos(0) = centrex;
centrepos(1) = centrey;
centrepos(2) = centrez;
radius = rd;
}
/**
* @brief Determines if a point is inside the sphere.
*
* This function checks if the given point (x, y, z) is inside the sphere. It does this by
* calculating the squared distance from the center of the sphere to the point. If this
* distance is less than or equal to the square of the radius of the sphere, the point is
* inside the sphere.
*
* @param x The x-coordinate of the point.
* @param y The y-coordinate of the point.
* @param z The z-coordinate of the point.
* @return true if the point is inside the sphere, false otherwise.
*/
bool Sphere::PointIsInside(double x, double y, double z){
openvdb::Vec3d cellpos(x,y,z);
double sqrdistance = (centrepos - cellpos).dot(centrepos - cellpos);
return (sqrdistance <= radius*radius);
}
/**
* @brief Retrieves the velocity of the sphere at the specified point.
*
* As the sphere has no velocity component normal to its surface, this function always returns zero
* regardless of the input position (x, y, z). This is represented by an openvdb::Vec3d containing three zeroes.
*
* @param x The x-coordinate of the point.
* @param y The y-coordinate of the point.
* @param z The z-coordinate of the point.
* @return An openvdb::Vec3d representing the velocity of the sphere at the point, which is always (0,0,0).
*/
openvdb::Vec3d Sphere::getVelocity(openvdb::Vec3d xyz){
openvdb::Vec3d temp(0,0,0);
return temp;
}
/**
* @brief Retrieves the velocity of the sphere at the specified point.
*
* As the sphere has no velocity component normal to its surface, this function always returns zero
* regardless of the input position (x, y, z). This is represented by an openvdb::Vec3d containing three zeroes.
*
* @param x The x-coordinate of the point.
* @param y The y-coordinate of the point.
* @param z The z-coordinate of the point.
* @return An openvdb::Vec3d representing the velocity of the sphere at the point, which is always (0,0,0).
*/
openvdb::Vec3d Sphere::getNormal(openvdb::Vec3d xyz){
xyz = (xyz - centrepos);
double mod = sqrt(xyz.dot(xyz));
if (mod == 0)
return xyz;
xyz = (1/mod)*xyz;
return xyz;
}
/**
* @brief Backprojects a point from the sphere's interior to its surface.
*
* If the provided point (x, y, z) is inside the sphere, this function adjusts its coordinates
* to correspond to the nearest point on the sphere's surface. It uses the surface normal for the
* backprojection.
*
* Note that the arguments are passed by reference and will be modified by this function.
*
* @param x The x-coordinate of the point, replaced by the x-coordinate of the nearest surface point if inside the sphere.
* @param y The y-coordinate of the point, replaced by the y-coordinate of the nearest surface point if inside the sphere.
* @param z The z-coordinate of the point, replaced by the z-coordinate of the nearest surface point if inside the sphere.
*/
void Sphere::ClosestSurface(double &x, double &y, double &z) {
openvdb::Vec3d r;
openvdb::Vec3d norm = getNormal(openvdb::Vec3d(x,y,z));
r = centrepos + radius*norm;
x = r(0);
y = r(1);
z = r(2);
}
/**
* @brief Constructor for FluidGrid class.
*
* Creates a FluidGrid object with specified dimensions, timestep, density, and file path for output.
* Grid dimensions are in number of cells, and the shortest dimension is normalized to 1 unit of spatial measure.
* Each quantity of interest (velocity in three directions, smoke, and temperature) is represented by a FluidQuantity object.
* OpenVDB library is initialized to create an empty floating-point grid.
*
* @param wh Width of the grid in cells.
* @param ht Height of the grid in cells.
* @param dh Depth of the grid in cells.
* @param tstep Time interval between frames.
* @param rh Density of the fluid.
* @param filepath Path to the output file for storing simulation results.
*/
FluidGrid::FluidGrid(int wh, int ht, int dh, double tstep, double rh, std::string filepath){
// make cellwidth be 1 / no. of cells in shortest dimension
// this results in a volume of unit length when measured along its shortest side
cellwidth = 1.0/std::min(std::min(wh, ht),dh);
nwidth = wh;
nheight = ht;
ndepth = dh;
ncells = wh*ht*dh;
openvdb::Vec3d min(0, 0, 0);
openvdb::Vec3d max(nwidth * cellwidth, nheight * cellwidth, ndepth * cellwidth);
bbox = openvdb::BBoxd(min, max);
density = rh;
CFLnumber = 5;
framenumber = 0;
currtime = 0;
framedeltaT = tstep;
nextframetime = tstep;
bool writetocache = false;
outputpath = filepath;
r = new SymmBandMatrix::VectorType(wh*ht*dh);
pressure = new SymmBandMatrix::VectorType(wh*ht*dh);
A = new SymmBandMatrix(wh*ht*dh);
u = new FluidQuantity(this, 0,0.5,0.5);
v = new FluidQuantity(this, 0.5,0,0.5);
w = new FluidQuantity(this, 0.5,0.5,0);
smoke = new FluidQuantity(this, 0.5,0.5,0.5);
temperature = new FluidQuantity(this, 0.5,0.5,0.5,AMBIENT_TEMPERATURE);
}
//destructor
FluidGrid::~FluidGrid(){
delete u;
delete v;
delete w;
delete smoke;
delete temperature;
delete pressure;
delete r;
delete A;
}
/**
* Add a value to the specified offsets in the sparse matrix A.
*
* This function adds the specified value to the elements of the matrix A based on the given offset and index.
* The offset determines the position of the elements to modify relative to the current index.
*
* @param i The index of the row/column to modify.
* @param offset The offset indicating the position of the elements to modify relative to the current index.
* @param value The value to add to the specified elements.
*/
void FluidGrid::addToA(int i, int offset, double value){
switch (offset){
case 0:
A->setValue(i, i, A->getValue(i, i) + value);
break;
case 1:
if (i + 1 < ncells){
A->setValue(i, i+1, A->getValue(i, i+1) + value);
A->setValue(i+1, i, A->getValue(i+1, i) + value);
}
break;
case 2:
if (i + nwidth < ncells){
A->setValue(i, i + nwidth, A->getValue(i, i + nwidth) + value);
A->setValue(i + nwidth, i, A->getValue(i + nwidth, i) + value);
}
break;
case 3:
if (i + nwidth*nheight < ncells){
A->setValue(i, i + nwidth*nheight, A->getValue(i, i + nwidth*nheight) + value);
A->setValue(i + nwidth*nheight, i, A->getValue(i + nwidth*nheight, i) + value);
}
break;
}
}
// MODIFY THIS ONE.................................JK
/**
* @brief Constructs the system of linear equations, Ap = b, to solve for pressure.
*
* This function builds the matrix A of pressure coefficients and the vector b of
* additional terms that account for external influences such as the divergence of
* the velocity field and solid boundaries. The pressure is calculated based on the
* volumes weighted by the fluid quantities within each grid cell. The function
* constructs these matrices by iterating through the 3D fluid grid.
*/
void FluidGrid::BuildLinearSystem(){
double Ascale = deltaT/(density*cellwidth*cellwidth);
double rscale = 1.0/cellwidth;
int row, column;
r->fill(0);
A->scale(0);
//Setup up the matrix of pressure coefficients, weighted by volumes
for(int k=0; k<ndepth; k++)
for(int j=0; j<nheight; j++)
for(int i=0; i<nwidth; i++){
row = i+j*nwidth+k*nwidth*nheight;
column = row;
addToA(row, 0, Ascale*u->getVolume(i,j,k));
addToA(row, 0, Ascale*v->getVolume(i,j,k));
addToA(row, 0, Ascale*w->getVolume(i,j,k));
addToA(row, 0, Ascale*u->getVolume(i+1,j,k));
addToA(row, 1, -Ascale*u->getVolume(i+1,j,k));
addToA(row, 0, Ascale*v->getVolume(i,j+1,k));
addToA(row, 2, -Ascale*v->getVolume(i,j+1,k));
addToA(row, 0, Ascale*w->getVolume(i,j,k+1));
addToA(row, 3, -Ascale*w->getVolume(i,j,k+1));
// HACK! Set zero diagonal elements to be very small instead
// this is an attempt to pass a validation test in openvdb's PCG solver
if (!A->getValue(row, row))
A->setValue(row, row, 1e-5);
(*r)[row] = -rscale*(u->getVolume(i+1,j,k)*u->getQuantity(i+1,j,k) - u->getVolume(i,j,k)*u->getQuantity(i,j,k) +
v->getVolume(i,j+1,k)*v->getQuantity(i,j+1,k) - v->getVolume(i,j,k)*v->getQuantity(i,j,k) +
w->getVolume(i,j,k+1)*w->getQuantity(i,j,k+1) - w->getVolume(i,j,k)*w->getQuantity(i,j,k));
if (solid != nullptr){
// This is derived from figure 4.3 on page 49 of Bridson's book
(*r)[row] += rscale*((u->getVolume(i+1,j,k) - smoke->getVolume(i,j,k))*
solid->getVelocity(u->indexToWorld(i+1,j,k))(0) -
(u->getVolume(i,j,k) - smoke->getVolume(i,j,k))*
solid->getVelocity(u->indexToWorld(i,j,k))(0) +
(v->getVolume(i,j+1,k) - smoke->getVolume(i,j,k))*
solid->getVelocity(v->indexToWorld(i,j+1,k))(1) -
(v->getVolume(i,j,k) - smoke->getVolume(i,j,k))*
solid->getVelocity(v->indexToWorld(i,j,k))(1) +
(w->getVolume(i,j,k+1) - smoke->getVolume(i,j,k))*
solid->getVelocity(w->indexToWorld(i,j,k+1))(2) -
(w->getVolume(i,j,k) - smoke->getVolume(i,j,k))*
solid->getVelocity(w->indexToWorld(i,j,k))(2));
}
};
// DEBUG!!!!!!!
// Test if A is valid (the 'apply' method raises if a failure bool
// which was set in CholeskyPrecondMatrix is false)
// CholeskyPrecondMatrix precond(*A);
// precond.apply(*r, *r);
}
/**
* @brief Calculates the volume fractions of fluid quantity in each cell of its parent grid.
*
* This function iterates over the samples of the fluid quantity, calculates their positions in 'cell space',
* and uses these positions to access corresponding supervoxel fractions from the input `supervol` array. These fractions
* are subtracted from the initial volume (set as 8.0) to yield a volume fraction that represents the proportion of the cell
* not occupied by solid matter. This calculated volume fraction is stored back into the fluid quantity's volume field.
* A calculated volume of 1.0 indicates that the cell is not occupied by any solid.
*
* This function assumes that the `supervol` array is filled with supervoxel fractions that represent whether each supervoxel
* in the grid is inside a solid or not. This array is typically provided by `FluidGrid::CalculateVolumes()`.
*
* Note: The function skips the samples at the boundaries of the grid (i.e., u volume samples at (0,j,k) and (nwidth,j,k)).
*
* @param supervol Pointer to an array of supervoxel fractions, typically obtained from `FluidGrid::CalculateVolumes()`.
* This array should have dimensions twice as large as the parent grid in each dimension (hence, 2x2x2 supersampling).
*/
void FluidQuantity::CalculateVolumes(double* supervol){
int nwidth = parentgrid->getWidth();
int nheight = parentgrid->getHeight();
//Note that u volume samples at (0,j,k) and (nwidth,j,k) are unchanged as zero
//so we don't need to set them. To achieve this, we iterate from int(1-offset) to samples - int(1-offset)
//because if offset == 0, int(1-offset) will be 1, otherwise it will be zero, so this ensures we skip over
//volume samples for grid-aligned, offset == 0 samples
for (int k=int(1-offsetz); k<getzSamples()-int(1-offsetz); k++)
for (int j=int(1-offsety); j<getySamples()-int(1-offsety); j++)
for (int i=int(1-offsetx); i<getxSamples()-int(1-offsetx); i++){
//get position of sample in 'cell space'
double posx = i+getOffsetx();
double posy = j+getOffsety();
double posz = k+getOffsetz();
int ix0 = floor((posx-0.25)*2);
int ix1 = ix0 + 1;
int iy0 = floor((posy-0.25)*2);
int iy1 = iy0 + 1;
int iz0 = floor((posz-0.25)*2);
int iz1 = iz0 + 1;
setVolume(i,j,k, 8.0);
setVolume(i,j,k, getVolume(i,j,k) - supervol[ix0+iy0*2*nwidth+iz0*4*nwidth*nheight]);
setVolume(i,j,k, getVolume(i,j,k) - supervol[ix0+iy1*2*nwidth+iz0*4*nwidth*nheight]);
setVolume(i,j,k, getVolume(i,j,k) - supervol[ix0+iy0*2*nwidth+iz1*4*nwidth*nheight]);
setVolume(i,j,k, getVolume(i,j,k) - supervol[ix0+iy1*2*nwidth+iz1*4*nwidth*nheight]);
setVolume(i,j,k, getVolume(i,j,k) - supervol[ix1+iy0*2*nwidth+iz0*4*nwidth*nheight]);
setVolume(i,j,k, getVolume(i,j,k) - supervol[ix1+iy1*2*nwidth+iz0*4*nwidth*nheight]);
setVolume(i,j,k, getVolume(i,j,k) - supervol[ix1+iy0*2*nwidth+iz1*4*nwidth*nheight]);
setVolume(i,j,k, getVolume(i,j,k) - supervol[ix1+iy1*2*nwidth+iz1*4*nwidth*nheight]);
setVolume(i,j,k, getVolume(i,j,k)/8.0);
}
}
/**
* @brief This function calculates the volume fractions of the fluid grid cells by 2x2x2 supersampling.
*
* First, it creates an array of supervoxel volume fractions by checking whether each supervoxel (a
* sub-division of a cell in the fluid grid) is inside a solid. This is done by iterating over a grid
* twice as dense as the fluid grid in all dimensions (hence, 2x2x2 supersampling). It then passes this
* array to the `CalculateVolumes()` function of each of the u, v, w, and smoke fluid quantities.
*
* @param none.
* @return void.
*/
void FluidGrid::CalculateVolumes(){
double* supervol = new double[ncells*8];
double pointisinside;
//Perform 2x2x2 supersampling over entire grid, so each ijk cell will be sampled 8 times
for (int k=0; k<2*ndepth; k++)
for (int j=0; j<2*nheight; j++)
for (int i=0; i<2*nwidth; i++){
pointisinside = 0;
if (solid != nullptr)
if (solid->PointIsInside((0.25+i*0.5)*cellwidth, (0.25+j*0.5)*cellwidth, (0.25+k*0.5)*cellwidth))
pointisinside = 1;
supervol[i+j*2*nwidth+k*4*nwidth*nheight] = pointisinside;
}
u->CalculateVolumes(supervol);
v->CalculateVolumes(supervol);
w->CalculateVolumes(supervol);
smoke->CalculateVolumes(supervol);
delete[] supervol;
}
/**
* @brief Updates the velocity fields of the fluid grid based on the current pressure field.
*
* This function iterates over all the velocity components (u, v, w) stored in the grid. For each component,
* the function calculates the velocity update based on the pressure gradient between neighboring cells.
* This calculation is done according to the fluid dynamics equation:
* Δv = - (Δt / ρΔx) * ΔP, where Δt is the time step, ρ is the fluid density, Δx is the cell width, and ΔP is the pressure difference.
* If the volume of the cell is non-zero, the function updates the velocity component by subtracting the calculated update.
* If the volume of the cell is zero, the function sets the velocity component to zero.
* After the velocity components have been updated, the function extrapolates the velocity fields
* of temperature, smoke, u, v, and w and then enforces the boundary conditions.
*/
void FluidGrid::updateVelocities() {
double scale = deltaT/(density*cellwidth);
//We don't touch the samples that are aligned with the edges of the grid here
for (int k = 0; k < u->getzSamples(); k++)
for (int j = 0; j < u->getySamples(); j++)
for (int i = 1; i < u->getxSamples()-1; i++) {
if (u->getVolume(i,j,k) > 0)
u->setQuantity(i,j,k, u->getQuantity(i,j,k) - scale*(getPressure(i,j,k) - getPressure(i-1,j,k)));
else
u->setQuantity(i,j,k, 0);
}
for (int k = 0; k < v->getzSamples(); k++)
for (int j = 1; j < v->getySamples()-1; j++)
for (int i = 0; i < v->getxSamples(); i++) {
if (v->getVolume(i,j,k) > 0)
v->setQuantity(i,j,k, v->getQuantity(i,j,k) - scale*(getPressure(i,j,k) - getPressure(i,j-1,k)));
else
v->setQuantity(i,j,k, 0);
}
for (int k = 1; k < w->getzSamples()-1; k++)
for (int j = 0; j < w->getySamples(); j++)
for (int i = 0; i < w->getxSamples(); i++) {
if (w->getVolume(i,j,k) > 0)
w->setQuantity(i,j,k, w->getQuantity(i,j,k) - scale*(getPressure(i,j,k) - getPressure(i,j,k-1)));
else
w->setQuantity(i,j,k, 0);
}
// temperature->ExtrapolateVelocity();
// smoke->ExtrapolateVelocity();
u->ExtrapolateVelocity();
v->ExtrapolateVelocity();
w->ExtrapolateVelocity();
if (solid != nullptr)
SetSolidBoundaries();
SetWallBoundaries();
}
void FluidGrid::SetWallBoundaries(){
//Boundary conditions for the walls of the box
//Set the normal component to the wall to zero
for (int k = 0; k < ndepth; k++)
for (int j = 0; j < nheight; j++){
u->setQuantity(0,j,k, 0.0);
u->setQuantity(nwidth,j,k, 0.0);
}
for (int k = 0; k < ndepth; k++)
for (int i = 0; i < nwidth; i++){
v->setQuantity(i,0,k, 0.0);
v->setQuantity(i,nheight,k, 0.0);
}
for (int j = 0; j < nheight; j++)
for (int i = 0; i < nwidth; i++){
w->setQuantity(i,j,0, 0.0);
w->setQuantity(i,j,ndepth, 0.0);
}
}
/**
* @brief Retrieves the fluid velocity at a specific point in the grid.
*
* This function interpolates the fluid velocity from the surrounding grid points
* at the given position (x, y, z) using a linear method. The three components
* of the velocity vector (u, v, w) are each interpolated separately and then
* combined into the final velocity vector.
*
* @param x The x-coordinate of the point in the grid.
* @param y The y-coordinate of the point in the grid.
* @param z The z-coordinate of the point in the grid.
* @return The interpolated fluid velocity vector at the point (x, y, z).
*/
openvdb::Vec3d FluidGrid::getVelocity(openvdb::Vec3d xyz){
double x = xyz[0];
double y = xyz[1];
double z = xyz[2];
openvdb::Vec3d temp;
temp(0) = u->InterpolateLinear(x,y,z);
temp(1) = v->InterpolateLinear(x,y,z);
temp(2) = w->InterpolateLinear(x,y,z);
return temp;
}
/**
* @brief Sets the solid boundaries within the fluid grid.
*
* This function is responsible for properly setting the solid boundaries within the
* fluid grid. The boundary conditions are set in such a way that the velocity
* of the fluid is zero relative to the solid boundary. The function iterates over
* all cells in the grid, and for cells with zero volume (assumed to be solid cells),
* it sets the velocities of the fluid in the bordering cells so that there is no
* relative velocity in the direction of the solid boundary. This is achieved by
* subtracting from the fluid velocity the component of the fluid velocity that
* is along the normal to the solid boundary.
*
* The function also sets the boundary conditions for the walls of the box, where the
* fluid velocity is set to zero.
*
* This method uses a buffer to store intermediate velocity values, and at the end,
* the buffer values are swapped with the actual fluid velocities.
*
* This method does not return any value.
*/
void FluidGrid::SetSolidBoundaries(){
u->CopyQuantitytoBuffer();
v->CopyQuantitytoBuffer();
w->CopyQuantitytoBuffer();
openvdb::Vec3d vfluid;
openvdb::Vec3d vsolid;
openvdb::Vec3d normal;
//For cells which have zero volume, set the velocity samples bordering to have zero relative velocity in the
//direction of the normal to the solid boundary
for (int k = 0; k < ndepth; k++)
for (int j = 0; j < nheight; j++)
for (int i = 0; i < nwidth; i++) {
if (smoke->getVolume(i,j,k) == 0)
{
vsolid = solid->getVelocity(u->indexToWorld(i,j,k));
vfluid = getVelocity(u->indexToWorld(i,j,k));
normal = solid->getNormal(u->indexToWorld(i,j,k));
u->setBuffer(i,j,k, (vfluid - (vfluid - vsolid).dot(normal)*normal)(0));
vsolid = solid->getVelocity(u->indexToWorld(i+1,j,k));
vfluid = getVelocity(u->indexToWorld(i+1,j,k));
normal = solid->getNormal(u->indexToWorld(i+1,j,k));
u->setBuffer(i+1,j,k, (vfluid - (vfluid - vsolid).dot(normal)*normal)(0));
vsolid = solid->getVelocity(v->indexToWorld(i,j,k));
vfluid = getVelocity(v->indexToWorld(i,j,k));
normal = solid->getNormal(v->indexToWorld(i,j,k));
v->setBuffer(i,j,k, (vfluid - (vfluid - vsolid).dot(normal)*normal)(1));
vsolid = solid->getVelocity(v->indexToWorld(i,j+1,k));
vfluid = getVelocity(v->indexToWorld(i,j+1,k));
normal = solid->getNormal(v->indexToWorld(i,j+1,k));
v->setBuffer(i,j+1,k, (vfluid - (vfluid - vsolid).dot(normal)*normal)(1));
vsolid = solid->getVelocity(w->indexToWorld(i,j,k));
vfluid = getVelocity(w->indexToWorld(i,j,k));
normal = solid->getNormal(w->indexToWorld(i,j,k));
w->setBuffer(i,j,k, (vfluid - (vfluid - vsolid).dot(normal)*normal)(2));
vsolid = solid->getVelocity(w->indexToWorld(i,j,k+1));
vfluid = getVelocity(w->indexToWorld(i,j,k+1));
normal = solid->getNormal(w->indexToWorld(i,j,k+1));
w->setBuffer(i,j,k+1, (vfluid - (vfluid - vsolid).dot(normal)*normal)(2));
}
}
u->swap();
v->swap();
w->swap();
}
/**
* @brief Calculates and returns the maximum divergence in the fluid grid.
*
* This function computes the divergence at each point in the grid, which is
* a measure of the rate at which fluid is exiting or entering a small volume
* around the point. The divergence is calculated based on the fluid velocities
* in the x, y, and z directions (`u`, `v`, and `w` respectively).
* The maximum absolute divergence value across all points in the grid is then
* returned. This function is useful for checking the accuracy of the simulation,
* as the divergence should be zero in incompressible flows.
*
* @return double The maximum absolute divergence value in the grid.
*/
double FluidGrid::maxDivergence() const{
double maxdiv = 0;
double div;
for (int k=0; k<ndepth; k++)
for (int j=0; j<nheight; j++)
for (int i=0; i<nwidth; i++){
div = fabs( u->getQuantity(i+1,j,k) - u->getQuantity(i,j,k)
+ v->getQuantity(i,j+1,k) - v->getQuantity(i,j,k)
+ w->getQuantity(i,j,k+1) - w->getQuantity(i,j,k))/cellwidth;
maxdiv = fmax(div,maxdiv);
}
return maxdiv;
}
/**
* @brief Adds smoke and temperature within a specified cuboid region of the fluid grid.
*
* This function is designed to add smoke and temperature inside a cuboid region within the fluid grid.
* The size and position of the cuboid are specified by the user in the form of the input parameters.
* The added temperature and smoke are modelled as emitters in the specified region. The temperature
* and smoke density values for these emitters are also user-defined.
*
* @param x X-coordinate of the cuboid's starting point.
* @param y Y-coordinate of the cuboid's starting point.
* @param z Z-coordinate of the cuboid's starting point.
* @param wh Width of the cuboid along the X-axis.
* @param h Height of the cuboid along the Y-axis.
* @param l Length of the cuboid along the Z-axis.
* @param density_value Smoke density value for the emitter.
* @param temperature_value Temperature value for the emitter.
*/
void FluidGrid::addSmoke(double x, double y, double z, double wh, double h, double l, double density_value, double temperature_value) {
double x0 = int(x*nwidth);
double x1 = int((x+wh)*nwidth);
double y0 = int(y*nheight);
double y1 = int((y+h)*nheight);
double z0 = int(z*ndepth);
double z1 = int((z+l)*ndepth);
temperature->addEmitter(x0, y0, z0, x1, y1, z1, temperature_value);;
smoke->addEmitter(x0, y0, z0, x1, y1, z1, density_value);
}
/**
* Sets the FluidQuantity value within a specified rectangular volume in the grid.
*
* This function assigns a new value to each point inside a given volume specified by
* the rectangular region from (x0, y0, z0) to (x1, y1, z1). The value is only assigned
* if the absolute value of the current fluid quantity at the grid point is less than the
* absolute value of 'v'. The function also ensures that the rectangular region lies within
* the valid boundaries of the fluid grid.
*
* @param x0 The starting x-coordinate of the rectangular volume.
* @param y0 The starting y-coordinate of the rectangular volume.
* @param z0 The starting z-coordinate of the rectangular volume.
* @param x1 The ending x-coordinate of the rectangular volume.
* @param y1 The ending y-coordinate of the rectangular volume.
* @param z1 The ending z-coordinate of the rectangular volume.
* @param value The fluid quantity value to assign within the given volume.
*/
void FluidQuantity::addEmitter(int x0, int y0, int z0, int x1, int y1, int z1, double value) {
for (int z = std::max(z0, 0); z < std::min(z1, zsamples); z++)
for (int y = std::max(y0, 0); y < std::min(y1, ysamples); y++)
for (int x = std::max(x0, 0); x < std::min(x1, xsamples); x++)
if (fabs(getQuantity(x,y,z)) < fabs(value))
setQuantity(x,y,z, value);
}
/**
* @brief Updates the time step (`deltaT`) for the simulation based on the fluid's maximum velocity and
* the Courant-Friedrichs-Lewy (CFL) condition.
*
* This method adjusts the simulation's time step based on the current maximum velocity in the fluid grid to
* ensure numerical stability according to the CFL condition.
* If the maximum velocity is zero, the time step is set equal to the frame time step. Otherwise, it is set as
* the CFL number multiplied by the cell width, divided by the maximum velocity.
* Additionally, if the next simulation time (current time + 1.01 * `deltaT`) is greater or equal to the next
* frame time, the time step is adjusted to match the remaining time to the next frame, and a flag to write
* the current simulation state to the cache is activated.
*
* @note This method will output diagnostic information to the console, including the maximum velocity before projection.
*/
void FluidGrid::setDeltaT(){
double maxvel = std::max(w->max(),std::max(u->max(),v->max()));
printf("max velocity before project = %f\n",maxvel);
if (maxvel==0)
deltaT = framedeltaT;
else
deltaT = CFLnumber*cellwidth / maxvel;
if (currtime + 1.01*deltaT >= nextframetime){
deltaT = nextframetime - currtime;
writetocache = true;
nextframetime += framedeltaT;
}
printf("deltaT=%f, currtime=%f, writetocache=%d, framenumber= %d\n" ,deltaT,currtime,writetocache,framenumber);
}
/**
* @brief Performs advection of the fluid quantity in the grid.
*
* This method advects a fluid quantity across the fluid grid based on
* the grid's current velocity field. The advection is computed using a
* second-order Runge-Kutta method.
*
* The method works by updating the fluid quantity at each point in the
* grid based on the local velocity and the time step. The method also
* checks whether the advection has moved the fluid quantity inside a
* solid object in the grid, and if so, it moves the fluid quantity to
* the closest point on the surface of the solid object.
*
* The new fluid quantity values are stored in a buffer to ensure that
* the advection of all points is based on the same initial state, and
* are later swapped with the current fluid quantities.
*
* @note The function uses Catmull-Rom interpolation for the final
* advection step.
*/
void FluidQuantity::Advect(){