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The Gas Wavelets DOP is a microsolver used in building larger fluid
simulations. The 
Fluid Solver and 
Smoke Solver DOPs that allow
microsolvers to be added before or after the main solver step to extend
or tweak the simulation. Alternatively, enterprising people may attempt
to build an entire new solver out of microsolvers.
The Gas Wavelets DOP performs a wavelet transform on a field.
One pass of a 1D wavelet transform takes a waveform of N samples and turns it into two waveforms of N/2 samples. The first waveform represents a coarser view of the original waveform. The second waveform stores the detail lost in the coarse representation. This process can then be repeated on the coarse samples to construct a pyramid of detail waveforms.
One pass of a 3d wavelet transform is very similar. A volume with NxNxN voxels is turned into an average volume of N/2xN/2xN/2 samples and seven detail volumes of N/2xN/2xN/2 samples.
Rather than output the resulting pyramid of volumes as separate fields, they are all packed into the original field.
The Gas Wavelets DOP can take a packed field and perform the inverse transform to turn it back into the original field.
Parameters
Dest Field
The field to store the result into. Must be the same type (scalar, vector, matrix) as the source field.
Source Field
The field to apply the wavelet operation to. Can be any of scalar, vector, or matrix fields.
Mode
The type of wavelet transform to perform.
Wavelet
The type of wavelet transform to perform. This controls how the waveform is split into average and detail components.
Limit Passes
Normally the entire wavelet pyramid is built by repeatedly applying the transform until reduced to a 1×1×1 volume. For a minor efficiency improvement you can limit the transform to those levels you are interestd in. More importantly, the average detail vector of a given level is replaced by the next level’s decomposition, so if one wants to extract this component one must limit the pyramid accordingly.
Max Passes
How many wavelet passes to perform. Only used in Transform and Invert modes. To perform a proper inversion of a wavelet pyramid, the number of passes must match that which it was constructed with.
Level
When Computing the Power or Extracting a Component, the level controls which level of the pyramid will be computed or extracted. 0 refers to the first level which has the resultof the first pass of the wavelet transform.
Component
Which of the eight wavelet coefficients to extract in Extract Components mode. 0 corresponds to the average vectors which only will be valid of the transform was limited to the given level. One through Seven correspond to the tensor products of the X, Y, and Z wavelet functions with the bit field of one to seven used to determine which products are used. X is bit 0, Y bit 1, and Z bit 2.
Parameter Operations
Each data option parameter has an associated menu which specifies how that parameter operates.
Use Default
Use the value from the Default Operation menu.
Set Initial
Set the value of this parameter only when this data is created. On all subsequent timesteps, the value of this parameter is not altered. This is useful for setting up initial conditions like position and velocity.
Set Always
Always set the value of this parameter. This is useful when specific keyframed values are required over time. This could be used to keyframe the position of an object over time, or to cause the geometry from a SOP to be refetched at each timestep if the geometry is deforming.
You can also use this setting in
conjunction with the local variables for a parameter value to
modify a value over time. For example, in the X Position, an
expression like $tx + 0.1 would cause the object to
move 0.1 units to the right on each timestep.
Set Never
Do not ever set the value of this parameter. This option is most useful when using this node to modify an existing piece of data connected through the first input.
For example, an 
RBD State
DOP may want to animate just the mass of an
object, and nothing else. The Set Never option could be used
on all parameters except for Mass, which would use Set
Always.
Default Operation
For any parameters with their Operation menu set to Use Default, this parameter controls what operation is used.
This parameter has the same menu options and meanings as the Parameter Operations menus, but without the Use Default choice.
Make Objects Mutual Affectors
All objects connected to the first input of this node become mutual affectors.
This is equivalent to using an 
Affector
DOP to create an affector relationship between
* and * before connecting it to this node. This option makes it
convenient to have all objects feeding into a solver node affect
each other.
Group
When an object connector is attached to the first input of this node, this parameter can be used to choose a subset of those objects to be affected by this node.
Data Name
Indicates the name that should be used to attach the data to an object or other piece of data. If the Data Name contains a "/" (or several), that indicates traversing inside subdata.
For example, if the 
Fan Force DOP has the default Data Name
"Forces/Fan". This attaches the data with the name "Fan" to an
existing piece of data named "Forces". If no data named "Forces"
exists, a simple piece of container data is created to hold the
"Fan" subdata.
Different pieces of data have different requirements on what names should be used for them. Except in very rare situations, the default value should be used. Some exceptions are described with particular pieces of data or with solvers that make use of some particular type of data.
Unique Data Name
Turning on this parameter modifies the Data Name parameter value to ensure that the data created by this node is attached with a unique name so it will not overwrite any existing data.
With this parameter turned off, attaching two pieces of data with the same name will cause the second one to replace the first. There are situations where each type of behavior is desirable.
If an object
needs to have several Fan Forces blowing on it, it is
much easier to use the Unique Data Name feature to ensure that
each fan does not overwrite a previous fan rather than trying to
change the Data Name of each fan individually to avoid
conflicts.
On the other hand, if an object is known to have RBD
State data already attached to it, leaving this
option turned off will allow some new RBD State
data to overwrite the existing data.
Solver Per Object
The default behavior for solvers is to attach the exact same solver to all
of the objects specified in the group. This allows the objects to be
processed in a single pass by the solver, since the parameters are identical
for each object. However, some objects operate more logically on a single
object at a time. In these cases, one may want to use $OBJID expressions
to vary the solver parameters across the objects. Setting this toggle will
create a separate solver per object, allowing $OBJID to vary as expected.
Inputs
First Input
This optional input can be used to control which simulation objects are modified by this node. Any objects connected through this input and which match the Group parameter field will be modified.
If this input is not connected, this node can be used in conjunction with an Apply Data node, or can be used as an input to another data node.
All Other Inputs
If this node has more input connectors, other data nodes can be attached to act as modifiers for the data created by this node.
The specific types of subdata that are meaningful vary from node to
node. Click 
an input connector to see a list of available
data nodes that can be meaningfully attached.
Outputs
First Output
The operation of this output depends on what inputs are connected to this node. If an object stream is input to this node, the output is also an object stream containing the same objects as the input (but with the data from this node attached).
If no object stream is
connected to this node, the output is a data output. This data
output can be connected to an 
Apply Data DOP,
or connected directly to a data input of another data node, to
attach the data from this node to an object or another piece of
data.
Locals
channelname
This DOP node defines a local variable for each channel and parameter on the Data Options page, with the same name as the channel. So for example, the node may have channels for Position (positionx, positiony, positionz) and a parameter for an object name (objectname).
Then there will also be local variables with the names positionx, positiony, positionz, and objectname. These variables will evaluate to the previous value for that parameter.
This previous value is always stored as part of the data attached to the object being processed. This is essentially a shortcut for a dopfield expression like:
dopfield($DOPNET, $OBJID, dataName, "Options", 0, channelname)
If the data does not already exist, then a value of zero or an empty string will be returned.
DATACT
This value is the simulation time (see variable ST) at which the current data was created. This value may not be the same as the current simulation time if this node is modifying existing data, rather than creating new data.
DATACF
This value is the simulation frame (see variable SF) at which the current data was created. This value may not be the same as the current simulation frame if this node is modifying existing data, rather than creating new data.
RELNAME
This value will be set only when data is being attached to a relationship (such as when Constraint Anchor DOP is connected to the second, third, of fourth inputs of a Constraint DOP).
In this case, this value is set to the name of the relationship the data to which the data is being attached.
RELOBJIDS
This value will be set only when data is being attached to a relationship (such as when Constraint Anchor DOP is connected to the second, third, of fourth inputs of a Constraint DOP).
In this case, this value is set to a string that is a space separated list of the object identifiers for all the Affected Objects of the relationship to which the data is being attached.
RELOBJNAMES
This value will be set only when data is being attached to a relationship (such as when Constraint Anchor DOP is connected to the second, third, of fourth inputs of a Constraint DOP).
In this case, this value is set to a string that is a space separated list of the names of all the Affected Objects of the relationship to which the data is being attached.
RELAFFOBJIDS
This value will be set only when data is being attached to a relationship (such as when Constraint Anchor DOP is connected to the second, third, of fourth inputs of a Constraint DOP).
In this case, this value is set to a string that is a space separated list of the object identifiers for all the Affector Objects of the relationship to which the data is being attached.
RELAFFOBJNAMES
This value will be set only when data is being attached to a relationship (such as when Constraint Anchor DOP is connected to the second, third, of fourth inputs of a Constraint DOP).
In this case, this value is set to a string that is a space separated list of the names of all the Affector Objects of the relationship to which the data is being attached.
ST
This value is the simulation time for which the node is being evaluated.
This value may not be equal to the current Houdini time
represented by the variable T, depending on the settings of the 
DOP
Network Offset Time and Time Scale
parameters.
This value is guaranteed to have a value of zero at the
start of a simulation, so when testing for the first timestep of a
simulation, it is best to use a test like $ST == 0 rather than
$T == 0 or $FF == 1.
SF
This value is the simulation frame (or more accurately, the simulation time step number) for which the node is being evaluated.
This value may not be equal to the current Houdini frame number
represented by the variable F, depending on the settings of the DOP
Network parameters. Instead, this value is equal to
the simulation time (ST) divided by the simulation timestep size
(TIMESTEP).
TIMESTEP
This value is the size of a simulation timestep. This value is useful to scale values that are expressed in units per second, but are applied on each timestep.
SFPS
This value is the inverse of the TIMESTEP value. It is the number of timesteps per second of simulation time.
SNOBJ
This is the number of objects in the simulation. For nodes that
create objects such as the 
Empty Object node,
this value will increase for each object that is evaluated.
A good way to guarantee unique object names is to use an expression
like object_$SNOBJ.
NOBJ
This value is the number of objects that will be evaluated by the current node during this timestep. This value will often be different from SNOBJ, as many nodes do not process all the objects in a simulation.
This value may return 0 if the node does not
process each object sequentially (such as the 
Group
DOP).
OBJ
This value is the index of the specific object being processed by the node. This value will always run from zero to NOBJ-1 in a given timestep. This value does not identify the current object within the simulation like OBJID or OBJNAME, just the object’s position in the current order of processing.
This value is useful for generating a
random number for each object, or simply splitting the objects into
two or more groups to be processed in different ways. This value
will be -1 if the node does not process objects sequentially (such
as the Group DOP).
OBJID
This is the unique object identifier for the object being processed. Every object is assigned an integer value that is unique among all objects in the simulation for all time. Even if an object is deleted, its identifier is never reused.
The object identifier can always be used to uniquely identify a given object. This makes this variable very useful in situations where each object needs to be treated differently. It can be used to produce a unique random number for each object, for example.
This value is also the best way
to look up information on an object using the dopfield expression
function. This value will be -1 if the node does not process objects
sequentially (such as the Group DOP).
ALLOBJIDS
This string contains a space separated list of the unique object identifiers for every object being processed by the current node.
ALLOBJNAMES
This string contains a space separated list of the names of every object being processed by the current node.
OBJCT
This value is the simulation time (see variable ST) at which the current object was created.
Therefore, to check if an object was created
on the current timestep, the expression $ST == $OBJCT should
always be used. This value will be zero if the node does not process
objects sequentially (such as the Group DOP).
OBJCF
This value is the simulation frame (see variable SF) at which the current object was created.
This value is equivalent to using the
dopsttoframe expression on the OBJCT variable. This value will be
zero if the node does not process objects sequentially (such as the
Group DOP).
OBJNAME
This is a string value containing the name of the object being processed.
Object names are not guaranteed to be unique within a simulation. However, if you name your objects carefully so that they are unique, the object name can be a much easier way to identify an object than the unique object identifier, OBJID.
The object name can
also be used to treat a number of similar objects (with the same
name) as a virtual group. If there are 20 objects named "myobject",
specifying strcmp($OBJNAME, "myobject") == 0 in the activation field
of a DOP will cause that DOP to operate only on those 20 objects. This
value will be the empty string if the node does not process objects
sequentially (such as the Group DOP).
DOPNET
This is a string value containing the full path of the current DOP Network. This value is most useful in DOP subnet digital assets where you want to know the path to the DOP Network that contains the node.
Note
Most dynamics nodes have local variables with the same names as the
node’s parameters. For example, in a 
Position node,
you could write the expression:
$tx + 0.1
…to make the object move 0.1 units along the X axis at each timestep.
