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I'm playing with the heat map plugin with QGIS. I've run through QGIS tutorial: http://docs.qgis.org/html/en/docs/user_manual/plugins/plugins_heatmap.html,
using the airports data set as explained and I reproduced tutorial results. I have a 600,000+ data set (five years worth) of police calls from Philadelphia, which I've reduces to 185 points (a day) for testing. The Meta data for both sets is below although I've used both the dbf file and saved shp file as input.

For larger Radius settings (above about 0.1) I get a rainbow bulls Eye centered on but many time lager than my data set range. For smaller Radius settings I get a uniform single color covering the data set range and transparent holes opening over (but not centered on) each data point.

I get just what I should with the Alaska data set.

General:

Storage type of this layer: ESRI Shapefile
Source for this layer: C:\Users\Gallery of Tools\Documents\GIS DataBase\Alaska\shapefiles\airports.shp
Geometry type of the features in this layer: Point
The number of features in this layer: 76
Editing capabilities of this layer: Add Features, Delete Features, Change Attribute Values, Add Attributes, Delete Attributes, Create Spatial Index, Fast Access to Features at ID, Change Geometries
Extents:
In layer spatial reference system units : xMin,yMin -4480198.52,1433525.80 : xMax,yMax 4615124.98,6502586.83
Layer Spatial Reference System:
+proj=lcc +lat_1=40.96666666666667 +lat_2=39.93333333333333 +lat_0=39.33333333333334 +lon_0=-77.75 +x_0=600000 +y_0=0 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=us-ft +no_defs


General:
Storage type of this layer: ESRI Shapefile
Source for this layer: C:\Users\Gallery of Tools\Recovered from the Dell600GB\Image Catalog\EngravingsNMaps\Philadelphia\Police Incident\PoliceIncJune302012.dbf
Geometry type of the features in this layer: Point
The number of features in this layer: 185
Editing capabilities of this layer: Add Features, Delete Features, Change Attribute Values, Add Attributes, Delete Attributes, Create Spatial Index, Fast Access to Features at ID, Change Geometries
Extents:
In layer spatial reference system units : xMin,yMin -75.2515,39.9047 : xMax,yMax -74.9594,40.1226
Layer Spatial Reference System:
+proj=lcc +lat_1=40.96666666666667 +lat_2=39.93333333333333 +lat_0=39.33333333333334 +lon_0=-77.75 +x_0=600000 +y_0=0 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=us-ft +no_defs

P.S. And another thing. When I change the Radius setting, the cell size changes automatically. Is this supposed to happen?

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Please add information about which tutorial you are trying to follow and edit the title to a full sentence. The end of the title is missing. –  underdark Feb 18 '13 at 9:35
    
Judging from your metadata it seems like the projection information of your police incident dataset was changed incorrectly. Extents indicate that point coordinates are in geographic WGS84 (latitute/longitude) and not projected. If you use a radius of 1000000 as shown in the tutorial, you're actually telling the plugin to use 1000000 degrees(!) which makes no sense. –  underdark Feb 18 '13 at 18:03
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