The feature-based multi-resolution models of a solid represent an object at different levels of detail (LOD), particularly in the unit of feature, according to a certain LOD criterion. The need of feature-based multi-resolution modeling is currently increasing for various engineering tasks, such as analysis, network-based collaborative design, virtual prototyping and manufacturing. To provide feature-based multi-resolution models, it is essential to generate a valid and unique solid model at each LOD after feature rearrangement. To meet this requirement, we propose the history-based selective Boolean operations that satisfy the commutative law between union and subtraction by considering the history of the Boolean operations for the features. Owing to the commutative properties, the feature-based multi-resolution modeling technique based on these operations guarantees the same resulting shape as the original, and provides a unique and reasonable shape at each intermediate LOD after arbitrary feature rearrangement.
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