['The', 'algorithms', 'of', 'topological', 'operations', 'between', 'open', 'shapes', 'and', 'closed', 'geometry', 'objects', 'are', 'presented', 'and', 'the', 'theoretical', 'proof', 'for', 'the', 'correctness', 'and', 'completeness', 'of', 'the', 'algorithms', 'is', 'performed', '.']