TILER_3D
3D Transfinite Interpolation

TILER_3D is an executable C++ program, using double precision arithmetic, which carries out transfinite interpolation to "tile" a 3D box that has already been subdivided into sub-boxes.

A simple "tile pattern" of a tetrahedron is used, and the resulting object is written out as an ASCII TRI graphics file.

The ASCII TRI graphics file can be easily converted to other 3D formats, such as IV or STLA. In particular, if the STLA format is used, then the object can be read into MATLAB and displayed, using the STLA_DISPLAY program.

Related Data and Programs:

BLEND is a C++ library of routines which carry out the blending demonstrated by TILER_3D.

IV is a data directory which contains a description and examples of the IV (Inventor) 3D graphics format.

IVCON is an executable C++ program which can convert the TRI file output by TILER_3D into various other formats.

IVREAD is an executable FORTRAN90 program which can convert the TRI file output by TILER_3D into various other formats.

STLA is a data directory which contains a description and examples of the ASCII STL (stereolithography) 3D graphics format.

STLA_DISPLAY is a MATLAB program which reads in an ASCII STL file and displays the 3D graphics image it describes.

TILER_2D is an executable FORTRAN90 program which is a 2D version of TILER_3D.

TILER_3D a FORTRAN90 version

TRIA is a data directory which contains a description and examples of TRIA, the ASCII TRIANGLE 3D graphics format.

Reference:

• William Gordon, Charles Hall,
  Construction of Curvilinear Coordinate Systems and Application to Mesh Generation,
  International Journal of Numerical Methods in Engineering,
  Volume 7, pages 461-477, 1973.
• Joe Thompson, Bharat Soni, Nigel Weatherill,
  Handbook of Grid Generation,
  CRC Press, 1999.

Source Code:

• tiler_3d.C, the source code;
• tiler_3d.csh, commands to compile and load the source code;

Examples and Tests:

• tiler_3d.tri, the output ASCII TRI graphics file;
• tiler_3d.iv, a copy of the graphics file converted to IV format;
• tiler_3d.stla, a copy of the graphics file converted to STLA format;
• tiler_3d.png, a PNG image of a snapshot of the STLA file, as displayed by STLA_DISPLAY.

List of Routines:

• TILER_3D illustrates the use of 3D blending.
• BOUNDARY_3D returns the (X,Y,Z) coordinates of a point (U,V,W).
• SUB_BOX_TILER_3D "tiles" a 3D sub-box with a given pattern.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.