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Sounds like QGIS API could be what you're looking for. It's written in C++ and Qt-based. API docs are here: http://doc.qgis.org/. This API enables you to load all kinds of geodata for your background …

Nicklas has already pointed out the most popular open source packages. If you are interested in a closer coupling of desktop and server GIS, you might want to have a closer look at QGIS. Similar to t …

Travelling Salesman is supported by pgRouting: http://www.pgrouting.org/docs/1.x/index.html, so no need to implement something yourself if you alread have PostGIS at hand.

There are commercial QGIS extensions/addons for use cases such as water and electricity utility management, e.g. by German developers norBIT who are also heavily involved in QGIS development.

3D City DB offers multiple open tools, including a database: The 3D City Database has been realized as Oracle Spatial/Locator and PostgreSQL/PostGIS database schema, supporting following key featu …

GeoApt Data Browser looks quite promising, but I haven't yet managed to make it run on Windows. The big advantage over wxGIS Catalog for me would be that you can access the dataset's metadata. Update …

In QGIS you can use "Extract nodes" to first get the corner points of your polygons. Then, using "Export/Add geometry columns" you can add x and y coordinates to those points. The results will be four …

I ended up converting the polygons to a raster and sampling it at the point positions. Since my polygons didn't overlap and high accuracy wasn't necessary (polygons represented land-use classes and th …

QGIS Mobile for Android supports WMS. It's a port of QGIS Desktop created during this years Google Summer of Code. Currently, it's only recommended for use on Android tablets since there is no dedicat …

You cannot change the query used in RT SQL Layer plugin. But you can try to only use a general query in RT and refine it in Layer Properties - General - Query builder. The part in Query builder can be …

You could just hard-code your features into Javascript like in this OpenLayers example: http://openlayers.org/dev/examples/vector-features.html. No need to bother about further data storage. Of course …

QGIS "Point Sampling Tool" should be the plugin you're looking for. Here's a detailed description of how to use it: http://pvanb.wordpress.com/2010/02/15/sampling-raster-values-at-point-locations-in …

The opencv project provides detailed instructions: https://github.com/opencv/opencv/wiki/How_to_contribute

There is also QGIS Server (WMS). Read "QGIS Server – A WMS Server for the masses" for more information. I've compiled a small feature comparison between Geoserver and UMN Mapserver. MapFish is a goo …

RT Sql Layer plugin can do what you want (but it's not a console). You can use python console too: 'PostGIS ’select’ statement as vector layer in QGIS'