- Short Description of the Program
- Delaunay Triangulation
- Program Structure
- File Format
- Grid to Grid Interpolation
- Short Tutorial

enables 2D and 3D presentations of data given*XY-Function*

on unstructured grids of XY-points.- The mathematical approach is based on the DELAUNAY triangulation.
- For this test version the number of points is restricted to 2000.
- The values and XY-coordinates can be read or saved with text files or they can manually be added one by one.
- 2D-Images with arbitrary numbers of contour lines and arbitrary colors can be generated.
- 3D-images (by using OpenGL) of functions can be drawn and rotated to get a better spatial impression of the data.
- Interpolated values of the function belonging to arbitrary coordinates are displayed simultaneously with the mouse movement.
- Interpolations of a complete function belonging to other, arbitrary grids of points are supported.
requires OpenGL 1.1 (contained in Win 98/ME/NT) to present 3D-images.**XY-Function**

Here a function was determined at 102 points given within the range: -1 < x,y < 1.

To represent this data as a continuous function the XY-plane may be divided into triangles by using the DELAUNAY triangulation:

The following conditions should be fulfilled at this:

- The variation in the area of the triangles should not be too large.
- The aspect ratio of triangles should be as close to 1 as possible. The aspect ratio is defined as the ratio of the circumradius of the triangle to twice its inradius. Hence the aspect ratio of an equilateral triangle is exactly 1.
- The ratio of the largest to the smallest edge/angle of each triangle should be close to 1.
- The ratio of the area of the largest/smallest triangle to all the immediate neighbours should not be drastically low/high.

The triangulation is also usefull for applications of OpenGL or Direct3D which can calculate 3D presentations of 2D-functions based on meshes of triangles.

- Load a function as text file (cfg. File Format, for example load file1.txt),
- Save the function as text file,
- Delete all XY-points and the corresponding values,
- Copy the actual picture to clipboard,
- Grid to grid interpolation,
- Example: Generates random points of a GAUSS distribution as long as the button is pressed,
- Open this help file.

**2D-Parameter Register**

**XY-Range:**

The edit fields are used for setting the default XY-range of the 2D-Image.**Show:**

With the check boxes You can switch on the drawing of points, trajectory etc. or the elements of designation (numeration of points, iso colors...). Be carefully with the coloration mode, it works slow!**IsoColors:**

The number of contour lines and the colors of the maximum and minimum line can be choosen here. For color change click on the corresponding field.**Design:**

Here you can change the used font and the title of the 2D-Image. Furthermore the number of auxiliary lines may be set here.**Regular Grid:**

A regular grid can be generated with arbitrary x- and y-steps with respect to the actual default range. The grid may be saved and can be used as a target grid for a grid to grid interpolation (button 5).**Data Table**

The table shows the numbered XY-coordinates and function values which can not be edited in this test version of the program. By marking the check boxes*Points*and*Numbers*on the*Show*sheet all numbered points will be drawn into the 2D-Image.**2D Image Field**

The visible range of the function may be enlarged and scaled-down (zoomed) by mouse dragging (with the left mouse button) from above on the left to down on the right. Inverse mouse dragging from down on the right to above on the left restores the default XY-range.

The values and XY-coordinates can be added manually one by one with a click of the right mouse button on the corresponding position of the 2D-image field.

The distance to the 3D-Image of the function may be changed with the trackbar

3D: direction of the Z-axis and the turn angle about the Z-axis.

For the input file for the

The result is decribed in a message box:

... points were read in,

... values were interpolated correctly,

... values were estimated roughly,

... values could not be estimated.

The interpolated values will be inserted in the grid file:

There are four examples named file1.txt ... file4.txt, you can load and view. Before loading a new file You should delete the old data by pressing the

- Load an example file and set the mode register on
*3D (OpenGL),* - Testing the effect of setting the
*Focal Length, Turn around Z*and*Show Axis*elements, - Rotate the 3D-Image by tilting the Z-Axis (mouse dragg).

- Load an example file and set the mode register on
*2D (Contour Lines)*, - Testing the effect of setting the parameter registers
*XY-Range, Show, Iso-Colors*and*Design*, - The visible range of the function may be zoomed by mouse dragging (with the left mouse button) from above on the left to down on the right. Inverse mouse dragging from down on the right to above on the left restores the choosen
*XY-Range*.

- Set mode register on
*2D (Contour Lines),* - Choose a initial file or press the
*Delete*button 3 to generate a new data set. - Add a new data point with a click of the right mouse button on the corresponding position of the
*2D-Image*field.

As long as the

Set the

- Generate a XY-function by pressing the
*Example*button 6 for a short time, - Save this function
*Save*button 2, - Generate and save a regular grid of points with X steps= 10,Y steps= 10 (i.e. 11 * 11 points, ) - the
*XY-rang*e should be unchanged at this, - Reload the function and press the
*Interpolation*button 5, - Choose the generated grid, the corresponding file will be modified as described above (cfg. Grid to Grid Interpolation).