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# Fast Streamline Generation Method

IP.com Disclosure Number: IPCOM000104069D
Original Publication Date: 1993-Mar-01
Included in the Prior Art Database: 2005-Mar-18
Document File: 4 page(s) / 100K

IBM

## Related People

Doi, A: AUTHOR [+2]

## Abstract

A stream line can be defined by the solutions of the differential equation dX / ds = V (1) where V is the vector field to be visualized and is assumed to be a function of the position vector X.

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 42% of the total text.

Fast Streamline Generation Method

A stream line can be defined by the solutions of the
differential equation
dX / ds = V                                                       (1)
where V is the vector field to be visualized and is assumed to be a
function of the position vector X.

The stream line can be obtained by starting with an initial
pointand integrating the vector field.  This integration is usually
approximately executed by dividing the domain of the integration
intosegments, whose number is increased until the exit point
converges.

Fig. 1 shows a flow chart of an overview of the proposed
method.  The stream line generation algorithms assume that a grid
structure is subdivided  into tetrahedral cells.  Stream lines are
generated in tetrahedral cells, and the iteration of this process
yields the whole stream line.  Kaneda has proposed a similar
algorithm based on tetrahedral cell subdivision [1].
-----------------------------------------------
|  Determination of All Grid Points   |
-----------------------------------------------
|
-----------------------------------------------
|     Subdivision of Grid Space          |
|     into Tetrahedral Cells                |
-----------------------------------------------
|                                         Figure 1.
Flow Chart of the Proposed Method
-----------------------------------------------
|     Search for a Tetrahedral Cell      |
|     Containing a Starting Point        |
-----------------------------------------------
|----------------------------------------|
-----------------------------------------------         |
|      Generation of Stream Lines       |         |
|      in the Tetrahedral Cell              |         |
|      -  Parametric Stream Line         |         |
----------------------------------------------          |
|                                           |
------------------------------------------------         |
|     Traverse to Next Tetrahedral Cell  |        |
------------------------------------------------         |

|----------------------------------------|

Since a tetrahedral cell is a basic primitive for filling an
arbitrary 3D space and has started to be used in 3D FEM analysis, the
algorithm we give is applicable to unstructured grid data.  A method
of subdividing regular or rectilinear grid into tetrahedral-cells is
described in [2], and Koyamada has proposed a practical method for
un-structured grid [3].

Following is a method using an adju...