BLENDC - Transfinite Interpolation

BLENDC is a collection of routines for "blending" data, that is, creating interpolated values based on a set of given data. BLENDC can handle input data that is 1, 2, or 3 dimensional. In the general, 3D case, the data can depend on smoothly varying space parameters (R,S,T) or on tabular indices (I,J,K). The data may be given at the corners, edges, or faces of the unit cube. In the (R,S,T) case, BLENDC can supply an interpolated value at any point in the cube. In the (I,J,K) case, BLENDC will fill in tabular values for all intermediate indices.

In the simplest case, where BLENDC is only given data values at the endpoints of a line segment, the 4 corners of a square, or the 8 corners of a cube, BLENDC is equivalent to linear, bilinear or trilinear finite element interpolation of the data. However, in the more interesting cases where BLENDC is given, say, a formula for the data along the sides of the square, or the edges of the cube, the interpolation is called "transfinite", since in theory it samples the input data at more than a finite number of points.

Reference 1:

W N Gordon and Charles A Hall,
Construction of Curvilinear Coordinate Systems and Application to Mesh Generation,
International Journal of Numerical Methods in Engineering,
Volume 7, pages 461-477, 1973.

Reference 2:

Joe Thompson, Bharat Soni, Nigel Weatherill,
Handbook of Grid Generation,
CRC Press, 1999.

A FORTRAN version of some of these routines is available as BLEND. Interesting examples of the use of transfinite interpolation are in TILER_2D and TILER_3D.

Files you may copy include:

• blendc.c, the source code;
• blendc.h, the include file;
• blendc_prb.c, the calling program;
• blendc_prb.out, the sample output.

The list of routines includes:

• BLEND_0D1 extends scalar data at endpoints to a line.
• BLEND_1D1 extends scalar data along the boundary into a square.
• BLEND_2D1 extends scalar data along the surface into a cube.
• BLEND_I_0D1 extends indexed scalar data at endpoints along a line.
• BLEND_IJ_0D1 extends indexed scalar data at corners into a table.
• BLEND_IJ_1D1 extends indexed scalar data along edges into a table.
• BLEND_IJK_0D1 extends indexed scalar data along corners into a cubic table.
• BLEND_IJK_1D1 extends indexed scalar data along "edges" into a cubic table.
• BLEND_IJK_2D1 extends indexed scalar data along faces into a cubic table.
• BLEND_R_0DN extends vector data at endpoints into a line.
• BLEND_RS_0DN extends vector data at corners into a square.
• BLEND_RS_1DN extends vector data along sides into a square.
• BLEND_RST_0DN extends vector data at corners into a cube.
• BLEND_RST_1DN extends vector data on edges into a cube.
• BLEND_RST_2DN extends vector data on faces into a cube.

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