Design Document for FINITE

FINITE

AUTHOR: Lowell Johnson

Functional Summary:

Creates a geometric or radiometric mapping grid using the finite element method (triangulation) for surface fitting.

Comments:

None

Background:

FINITE was created to generate a LAS grid from predefined control points. The control points define the transformation between input and output image coordinates or radiometric amplitudes at those points.

Rather than fitting all of the control points with a single polynomial "best fit" transform, the finite element method is used to allow for a more flexible fit. A triangular mesh is generated from the control points. A first degree polynomial transform is associated with each triangle such that the transforms are continuous across triangle boundaries.

Requirements:

Scope/Limitations:

Overall design:



The above figure shows a generic image space (bounded by the thick black line) containing a set of tie points. Four corner control points, well outside the image, are generated so that the entire image region will have a defined transformation. A mesh of triangles (Delaunay triangulation) is then generated using the tie/control points as vertices.

Flow diagram:

Postscript version available here


Algorithm:


ALGORITHM REFERENCES:

Finite Element Surface Interpolation, June Thormosdgard

What is Dirichlet Tessellation?

Testing criteria: