EFFECTIVE COORDINATE OPERATIONS IN GEOSPATIAL SOFTWARE: CHAINING AFFINE TRANSFORMATIONS FOR OPTIMIZED MAP PROJECTION, EFFICIENT ACCESS TO N-DIMENSIONAL DATA, AND FLEXIBLE DISPLAY
Affine transforms, whose advantages are well known in computer graphics, offer great power for geospatial software in georeferencing operations, in the efficient manipulation of imagery or modeling grids, and in the operations for map display. Affine transforms can be concatenated using matrix multiplications reducing chains of linear operations to single transformations. Affine transforms are usually invertible enabling both forward conversions and backwards resampling through the same pathway. Also, affine operations can often be hardware optimized.
This talk will demonstrate the benefits of affine transforms by showing their use in the Geotoolkit.org software library. We will show how to use affine transforms to express:
axis reordering, flipping and unit conversion,
linear projections, and optimized re-projection,
changes in dimension, from n+m to n or back, and
an operation sequence from data coordinates to display output
Based on simple examples, the talk will show how to create and use these affine transformations. The talk will then explain how these mathematical relationships, drawn from the ISO and OGC abstract data model, form the core of the Geotoolkit.org API. Finally, the talk will discuss the extraction of the key parameters from imagery metadata, their storage in a relational database, and their use in an efficient system for the access to large satellite imagery files or to mosaics and pyramids of such images.
Martin Desruisseaux - Geomatys
Adrian Custer - Geomatys