I used the research tool "Regular Points" to produce a certain number of points within a polygon, but it forms a rectangular grid of points rather than only within the shape of the polygon. Since I need a certain number of points within the polygon, is there any way to do so without trial and error?
E.g. right now only 8 of the 25 points I want are within the polygon, but I want 25 points, so I could increase to 50 points and see how many then appear within the polygon
What QGIS is referring to in terms of the layer boundary is actually the envelope or bounding box of the geometry.
I've documented a solution which is probably the closest you will get to automating this is (short of filing a bug / feature request).
The process works based on the ratio between area of the two objects: the feature geometry and it's bounding box).
Check the following steps below:
Select the layer you want to work on.
Select the feature you wish to work on. Make sure nothing else is selected.
Run the following snippet within the Python Console.
layer = qgis.utils.iface.activeLayer()
features = layer.selectedFeatures()
feature = features[0]
geom = feature.geometry()
env_rect = geom.boundingBox()
env_geom = QgsGeometry.fromRect(env_rect)
env_geom.area() / geom.area()
Be sure to push enter as the last line will not automatically return.
Run the Regular Points tool again, but enter the number of points that you want inside the box multiplied by the output given by your script.
In my sample below, the result I received from the output was a value of ~2. I requested 20 dots to be output by the process where I actually only wanted 10. I was given 8 in return, which is fairly close. Depending on the actual shape you're using the results will vary.
If you were so inclined, you could automate (recursively) the Regular Points process modifying the variables until you arrived at your desired number.
You can easily do that just clipping: generate the regular grid of points just as you did and then use Vector>Geoprocessing tools>Clip, input the generated point grid and use the feature as clip mask.
A simplistic solution is suggested by the screenshot. You could extract the polygons into new layers with Vector -> Data Managment Tools -> Split vector layer, import them and then choose the layer with the feature (ID) you want as the input layer for the "Regular Points" sampler.
If you need to do this for only a handful of polygons, finding them and exporting them separately could be more efficient. Once you have one selected, right click on the layer name and choose Save Selection As ..., choose shapefile, fill out the rest and then repeat as before.
EDIT: Since you already have a single feature, I can't think of anything simpler but using a denser grid, intersecting it with the polygon again and finally removing all extraneus points (easiest through the attribute table, since you get both easy centering and total count).
Apply a definition query to your polygons (in 1.8 right click on the layer and choose Query). Then run the tool. Remove the query.
