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<H3><A name="HDRSTREAML" ></A>Streamline</H3>
<A NAME="IDX728"></A><A NAME="IDX729"></A>
<A NAME="IDX730"></A>
<P><STRONG>Category</STRONG>
<P>
<A HREF="refgu008.htm#HDRCATREL">Realization</A>
<P><STRONG>Function</STRONG>
<P>
Computes streamlines to represent the movement of particles through
static vector fields.
<P><STRONG>Syntax</STRONG>
<PRE>
<STRONG>line</STRONG> = Streamline(<STRONG>data, start, time, head, curl, flag, stepscale</STRONG>);
</PRE>
<P><STRONG>Inputs</STRONG>
<BR>
<TABLE BORDER>
<TR>
<TH ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">Name
</TH><TH ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">Type
</TH><TH ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">Default
</TH><TH ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">Description
</TH></TR><TR>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>data</STRONG></TT>
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">vector field
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">none
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">vector field
</TD></TR><TR>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>start</STRONG></TT>
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">vector list or geometric field
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">center of the first series member
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">starting point(s)
</TD></TR><TR>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>time</STRONG></TT>
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">scalar list
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">series start time(s)
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">starting time(s)
</TD></TR><TR>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>head</STRONG></TT>
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">integer
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">final series frame number
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">series time-step at which the
streamlines end
</TD></TR><TR>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>curl</STRONG></TT>
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">vector field
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">no curl
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">vorticity of vector field(s)
</TD></TR><TR>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>flag</STRONG></TT>
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">flag
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">input dependent
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">
0: curl not used
<BR>
1: curl used to generate twist of streamline(s)
<BR></TD></TR><TR>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%"><TT><STRONG>stepscale</STRONG></TT>
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">value
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="20%">0.1
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="40%">step length as a fraction of the
size of the connection
element
</TD></TR></TABLE>
<P><STRONG>Outputs</STRONG>
<BR>
<TABLE BORDER>
<TR>
<TH ALIGN="LEFT" VALIGN="TOP" WIDTH="25%">Name
</TH><TH ALIGN="LEFT" VALIGN="TOP" WIDTH="25%">Type
</TH><TH ALIGN="LEFT" VALIGN="TOP" WIDTH="50%">Description
</TH></TR><TR>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH="25%"><TT><STRONG>line</STRONG></TT>
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="25%">field or group
</TD><TD ALIGN="LEFT" VALIGN="TOP" WIDTH="50%">one or more streamlines
</TD></TR></TABLE>
<P><STRONG>Functional Details</STRONG>
<P>
This module traces the path of a particle through a static vector field
in discrete steps.
The visual form of this trace is a streamline, which starts at a
specified time and continues until the particle it represents
exits from the field or reaches a region of zero velocity.
<TABLE CELLPADDING="3">
<TR VALIGN="TOP"><TD><P><B><TT><STRONG>data</STRONG></TT>
</B></TD><TD><P>specifies a vector field.
Vector fields are limited to <I>n</I>-D vectors defined in
<I>n</I> space; for example, 2-D vectors on a 2-D sheet or
3-D vectors defined in a 3-D volume.
</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>start</STRONG></TT>
</B></TD><TD><P>specifies a set of positions at which streamlines originate.
It can be either a list of positions or a geometric field (e.g., the
output of a Grid module or even an isosurface).
</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>time</STRONG></TT>
</B></TD><TD><P>specifies a set of times at which streamlines begin to be
traced.
The units of time correspond to the units of the vector field.
That is, a particle travelling at a unit velocity moves one unit of
distance in one unit of time.
<P>
Both <TT><STRONG>time</STRONG></TT> and <TT><STRONG>start</STRONG></TT> can
contain
single or multiple elements.
If either parameter contains a single element, that element is
associated with each element of the other list.
If both parameters contain multiple elements, they must contain the
same number of elements, which are then matched in pairs.
<P>
You can use the time parameter to start different streamlines at
different times. Note that for the static vector fields used by
Streamline, a particle at a given location will trace the same
streamline, regardless of what time it is started.
</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>head</STRONG></TT>
</B></TD><TD><P>specifies an expiration time for streamlines that have not
otherwise terminated.
The streamline points are computed iteratively, and the spacing between
the points depends on the element size of the connections and the
stepscale.
If this maximum is reached, a warning is produced and the streamline
is terminated.
The maximum number of streamline points is 25,000.
</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>curl</STRONG></TT>
</B></TD><TD><P>causes Streamline to produce normals and binormals components
that represent the vorticity of the vector field.
<A HREF="refgu049.htm#HDRDIVCURL">DivCurl</A>).
In that case, the default value for <TT><STRONG>flag</STRONG></TT>
is 1.
The "normals" and "binormals" components of the resulting
streamlines rotate according to the vorticity of the vector
field.
This information is either interpolated from the vector field passed
in as the <TT><STRONG>curl</STRONG></TT> parameter or is computed
internally.
</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>flag</STRONG></TT>
</B></TD><TD><P>specifies whether or not the twist specified by
<TT><STRONG>curl</STRONG></TT> is enabled.
A setting of 0 (zero) disables the twist.
<P>
However, if <TT><STRONG>curl</STRONG></TT> is not specified, the default
value for <TT><STRONG>flag</STRONG></TT> is 0, and no twist is
produced.
In that case you have the option of setting <TT><STRONG>flag</STRONG></TT>
to 1, which causes Streamline to compute the curl internally.
</TD></TR><TR VALIGN="TOP"><TD><P><B><TT><STRONG>stepscale</STRONG></TT>
</B></TD><TD><P>specifies the accuracy of the interpolation.
Streamline traces the path of a particle through the vector field in
discrete steps.
These steps are determined by interpolating a vector from the vector
field at the current end of the streamline and appending a new
segment that extends the streamline in the direction of the
vector.
<P>
The length of the new segment is determined by two factors.
First, the length of the projection of the segment along the edges of
the cells of the prior and subsequent vector fields in which the
starting point of the segment is found does not exceed a
proportion (specified by the <TT><STRONG>stepscale</STRONG></TT>
parameter) of the length of the edge.
Second, if grid is irregular, the segment is truncated at the boundary
of the element in which it begins.
This allows the segment length to be determined anew for the next
element.
<P>
Thus the <TT><STRONG>stepscale</STRONG></TT> parameter offers the user control
over the accuracy of the streamline.
If <TT><STRONG>stepscale</STRONG></TT> is a small value (perhaps in the range
of 0.01 to 0.05), the resulting streamline contains a relatively
large number of segments that closely trace small variations
in the vector field.
If <TT><STRONG>stepscale</STRONG></TT> is assigned a large number (0.5 to 1),
the steps are larger and less accurate, but require less execution
time.
Note, however, that since the step is determined as a proportion of the
size of the grid cell in which it is contained, the segments are
small in areas in which the grid elements are small, and
proportionally larger in areas in which the grid
elements are large.
</TD></TR></TABLE>
<P>
Streamlines trace particles through time.
Associated with the streamline is a "time" component that
indicates, for each position of the streamline, the time at
which the particle reached that position.
The initial value in this component, therefore, is equal to the
starting time for that stream, which is by default the first
series position, or settable by the user using the
<TT><STRONG>time</STRONG></TT> parameter.
The final value in the time component is equal to (1) the time at which
the particle exits from the vector field or (2) the time specified
by the <TT><STRONG>head</STRONG></TT> parameter.
<P>
The output streamlines also contain a "data" component that
indicates the velocity of the data field at each position
in the streamline.
<P><STRONG>Components</STRONG>
<P>
Creates new
"positions,"
"connections,"
"data,"
"time," and
"colors"
components.
If the flag argument is set, "normals" and "binormals"
components are also created.
<P><STRONG>Example Visual Programs</STRONG>
<PRE>
Interop.net
InvalidData.net
RubberTube.net
Streamline.net
ThunderStreamlines.net
</PRE>
<P><STRONG>See Also</STRONG>
<P>
<A HREF="refgu049.htm#HDRDIVCURL">DivCurl</A>,
<A HREF="refgu068.htm#HDRGLYPH">Glyph</A>,
<A HREF="refgu122.htm#HDRRIBBON">Ribbon</A>,
<A HREF="refgu148.htm#HDRSTREAKL">Streakline</A>,
<A HREF="refgu163.htm#HDRTUBE">Tube</A>
<P>
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