Hints: ImageMagick
Cropping Images
When you crop an image, the output depends on where the co-ordinate frame of the image is defined. If an image has been cropped previously, it probably still has the old co-ordinate frame and recropping probably won't give the output you want. It's easiest, therefore, if you reset the coordinate frame with '+repage' before cropping:
convert input.png +repage input2.png
convert input2.png -crop wxh+x+y output.png
convert input2.png -crop wxh+x+y output.png
Converting Vectors to Bitmaps
When converting a vector graphic to bitmap, -density is the option to control the resolution (in dots per inch). NB: it needs to come before the input file, not after.

