Sample Part B to be Nested.
Minkowski Sum   (heavy line) of Sample Parts (light and dashed lines).

Optimal Material Utilization for  Various Translations Between Polygons A and B.
Conclusions
    In the stamping operation, production costs are dominated by material costs, so even tiny per-part gains in material utilization are worth pursing. This paper has presented a new algorithm for creating optimal strip layouts for pairs of parts nested together. This algorithm takes advantage of the Minkowski sum calculation to both find feasible relative positions between the pairs of parts, and to determine the optimal orientation and strip width for the strip layout.
When evaluating combinations of layouts, it should be kept in mind that all permutations should be considered. For example, the strip layout process for the sample parts in this paper would consider strip layouts for A alone, A paired with itself, B alone, B paired with itself, and A and B paired together. The designer would then consider total raw material costs, tooling construction costs and press operating costs since blanking parts together requires larger tools and presses and changes production rates.
    There are opportunities to extend this algorithm, as well. One obvious extension is to include optimization over relative rotations between the pairs of parts, i.e., changing the orientation of part B relative to A on the strip. A second opportunity is to study the utilization function more deeply.
摘要：在冲压生产中，生产成本受材料利用率影响最大，材料支出占整个生产成本的 75%。本文将介绍一种新的计算方法用于实现双工件在冲压排样设计中 的最佳规划方法， 以便提高材料利用率。这种计算方法可以预示在带料中结构废 料的位置及形状， 以及工艺废料的位置和最佳宽度。例如将两个相同的工件中的 其中一个旋转 180°,或是将两个不同的工件嵌套在一起。这种计算方法适合与 冲模设计 CAE 系统结合使用。
 关键字：冲压，模具设计，最佳化，材料利用率，明可夫斯基和，设计工具
绪论
在冲压生产中， 能够快速生产不同复杂程度的薄片金属零件，特别是在大产 量的情况下，能够高强度生产。生产过程效率高，其中材料成本占据整个冲压生 产成本的 75% [1]。但材料不能被完全利用到零件上，因为零件不规则的外形必须被包含在带料内。冲压生产的排样设计直接决定废料的大小。很明显，使用最理想的排样设计对于提高公司的竞争力是至关重要的。 冲压模具英文参考文献和中文翻译(4):http://www.751com.cn/fanyi/lunwen_29993.html