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Demo solution with OpenJUMP Original polygons Buffer the polygons so much that they overlap and make a union. This can be done as a single operation with OpenJUMP. Flat end cap and mitre join with quite a high limit are good settings. The gaps between the polygons have disappeared but the union is too large. Use negative buffer for the union and ...
Buffer your lines by a small amount with the dissolve option set to All. Do not include any dissolve fields so that a single buffer feature is created. Then run the Multipart to Singlepart tool to break the buffer apart into the set of single part polygons that do not actually touch each other. The polygon with the largest area will cover the lines in ...
If you mean to have 1-4 adjacent color boxes at bottom-left, top-left, bottom-right, and top-right positions then I would do it by having one square symbol with points POINTS 0 0 0 1 1 1 1 0 0 0 END Then I would make four copies of the symbol with different ANCHORPOINTs as documented in http://www.mapserver.org/mapfile/symbol.html. ...
You may export to Shapefile with v.out.ogr Example from the doc: v.out.ogr input=lines type=line output=lines.shp
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