The alternative is to buffer your polygons by zero, but this probably will join polygons of different types together where you don't want it to happen, so dissolve (optionally follwed by multipart to single part) is safer. I very often use Connect and Delete as I don’t normally need the separate objects any longer. Automatic polygon decimation when objects move to the distance (read Cinefex about Avatar). If it is undesirable then simply split the feature up into its constituent polygons by using Vector->Geometry Tools->Multipart to Singlepart. If the polygons belong to different objects I think you’ll need to select those objects and use Mesh > Conversion > Connect Objects before you Optimize the resulting mesh. This may well result in a multipolygon (a single feature which has more than one part, like an archepelago), which might or might not be acceptable. If you select the 'Type' field (or other appropriate attribute in your case) as the attribute to dissolve on then all features of the same type will join together (internal boundaries will be dropped). Then in your example your polygons would all be type 'A' (and you could have some other polygons of type 'B' which you don't want to join with ones of type 'A'). So, let's say you have a field called 'Type' (for example). With the Merge option in ArcGIS, the polygons get merged with only one polygon, which isnt good for working. The new object is named after the first selected object and increments by 1. The meshes are combined as separate polygon shells into a new polygon mesh node. Select Mesh > Combine or click in the Modeling Toolkit. With dissolve you don't need to select anything first as it is all done from the attributes. To combine two or more polygon meshes into one mesh Select the meshes you want to combine into a single object. There's a couple of ways of going about this but you probably want to dissolve the features ( Vector->Geoprocessing Tools->Dissolve).
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