Abstract: An apparatus and method for abrasively processing an article involves the use of an abrasive product provided with a machine discernable pattern representative of information of varying types. The pattern is read while the abrasive product moves relative to the article, and is used to control the movement of the abrasive product relative to the article. The pattern may include one or more of a machine discernable electrical characteristic, optical characteristic, topographic characteristic or magnetic characteristic. Reading the pattern may involve one or more of electrically, optically, mechanically or magnetically reading the machine discernable pattern provided on the abrasive product. The pattern may include one or more of indicia, protrusions, depressions, holes, voids, color or pigment variations, bar codes, magnetic transitions or periodic markings. The pattern may include one or more of indexing information, servo information, alignment information or abrasive product identification information.

Abstract: A physical and logical block search method and apparatus that also locates the end of data on a data tape written in a serpentine pattern. A physical address is decoded to determine the track location and physical block address of a physical block on a serpentine data pattern written on a data cartridge tape. The tape is manipulated in the forward and reverse direction depending on the location of the beginning of data on the track. The search algorithm exploits serpentine nature of the tape and the location of the physical blocks in each track to find the physical address. The logical address of a logical block is used to determine a target track number. A prediction is made as to the location of the target track. The prediction is verified by checking the block. If the logical block was not accurately predicted the method repredicts until the logical block is found. The end of tape is located using a binary search based on knowledge of the track assignment of the serpentine data pattern on the tape.