@article {18846,
	title = {Geometric algorithms for containment analysis of rotational parts},
	journal = {Computer-Aided Design},
	volume = {37},
	year = {2005},
	month = {2005/02//},
	pages = {213 - 230},
	abstract = {This paper describes a system and underlying algorithms to perform geometric containment analysis to determine if a newly designed rotational part can be manufactured from a part in an existing database of rotational parts. Only material removal of the database part is considered in order to obtain the newly designed part from the database part. The system uses a three-step algorithm to test for containment. The first step analyzes feasibility of containment using bounding cylinders. If the bounding cylinder of the query part is bigger than the part in the database, then the database part cannot contain the query part and it is eliminated from consideration. The second step analyzes feasibility of containment by ignoring off-axis features. Any part that fails to satisfy containment at this stage is eliminated from consideration. The third step analyzes the remaining parts from the database for feasibility of containment by including the off-axis features. Finally, the system rank-orders all the database parts that can contain the query part based on their volume differences with the query part. The system described in this paper can be used by designers and process planners to find an existing part that can be used as a stock to manufacture a newly designed part. This capability is expected to significantly reduce proliferation of parts, to improve manufacturing responsiveness, and to reduce the cost of new products.},
	keywords = {COMPUTER AIDED DESIGN, geometric reasoning, Part containment, Shape signatures, Shape similarity},
	isbn = {0010-4485},
	doi = {10.1016/j.cad.2004.06.007},
	url = {http://www.sciencedirect.com/science/article/pii/S0010448504001186},
	author = {Karnik,Mukul and Gupta, Satyandra K. and Magrab,Edward B.}
}
@article {18844,
	title = {Geometric algorithms for automated design of rotary-platen multi-shot molds},
	journal = {Computer-Aided Design},
	volume = {36},
	year = {2004},
	month = {2004/10//},
	pages = {1171 - 1187},
	abstract = {This paper describes algorithms for automated design of rotary-platen type of multi-shot molds for manufacturing multi-material objects. The approach behind our algorithms works in the following manner. First, we classify the given multi-material object into several basic types based on the relationships among different components in the object. For every basic type, we find a molding sequence based on the precedence constraints resulting due to accessibility and disassembly requirements. Then, starting from the last mold stage, we generate the mold pieces for every mold stage. We expect that algorithms described in this paper will provide the necessary foundations for automating the design of rotary-platen molds.},
	keywords = {geometric reasoning, mold design, Multi-shot molds},
	isbn = {0010-4485},
	doi = {10.1016/j.cad.2003.11.003},
	url = {http://www.sciencedirect.com/science/article/pii/S0010448503002331},
	author = {Li,Xuejun and Gupta, Satyandra K.}
}
@conference {18799,
	title = {A geometric algorithm for automated design of multi-stage molds for manufacturing multi-material objects},
	series = {SMA {\textquoteright}01},
	year = {2001},
	month = {2001///},
	pages = {278 - 288},
	publisher = {ACM},
	organization = {ACM},
	address = {New York, NY, USA},
	abstract = {This paper describes a geometric algorithm for automated design of multi-stage molds for manufacturing multi-material objects. In multi-stage molding process, the desired multi-material object is produced by carrying out multiple molding operations in a sequence, adding one material in the target object in each mold-stage. We model multi-material objects as an assembly of single-material components. Each mold-stage can only add one type of material. Therefore, we need a sequence of mold-stages such that (1) each mold-stage only adds one single-material component either fully or partially, and (2) the molding sequence completely produces the desired object. In other to find a feasible mold-stage sequence, our algorithm decomposes the multi-material object into a number of homogeneous components to find a feasible sequence of homogeneous components that can be added in sequence to produce the desired multi-material object. Our algorithm starts with the final object assembly and considers removing components either completely or partially from the object one-at-a-time such that it results in the previous state of the object assembly. If the component can be removed from the target object leaving the previous state of the object assembly a connected solid then we consider such decomposition a valid step in the stage sequence. This step is recursively repeated on new states of the object assembly, until the object assembly reaches a state where it only consists of one component. When an object-decomposition has been found that leads to a feasible stage sequence, the gross mold for each stage is computed and decomposed into two or more pieces to facilitate the molding operation. We expect that our algorithm will provide a step towards automating the design of multi-stage molds and therefore will help in reducing the mold design lead-time for multi-stage molds.},
	keywords = {geometric reasoning, mold design, spatial partitioning},
	isbn = {1-58113-366-9},
	doi = {10.1145/376957.376989},
	url = {http://doi.acm.org/10.1145/376957.376989},
	author = {Kumar,Malay and Gupta, Satyandra K.}
}
