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Unformatted text preview: we solve the system of equations once for each of the cases (two or three solutions), and denote the resulting transformations Ti = (tix,tiy,θi). An infinitesimal change in a single parameter pj either results in one of Ti being the correct solution, or leaves all solutions correct. In the latter case, ∂T/∂pj = ∂T1/∂pj = ∂T2/pj = ∂T3/∂pj. In the former case, we determine which of the solutions is correct (checking distance relations) for an infinitesimal increase and decrease of pj. We then compute the left-hand and right-hand derivatives: ∂T+/∂pj = ∂Ti+/∂pj, and ∂T-/∂pj = ∂Ti-/∂pj, where Ti+ (Ti-) is the correct solution for an increase (decrease) in pj, and ∂T+/∂pj (∂T-/∂pj) is the right-hand (left-hand) derivative of a Ti. 2.3. Relative positions of parts in an assembly We now describe how to model the relative position of parts in the entire assembly. Previous work by Latombe et al. [Latombe et al., 1997] introduces the relation graph to describe the relative position constraints...
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- Spring '10
- The Land