單一多邊形的優(yōu)化排樣問題

摘要

本文首先介紹1種單1多邊形在矩形板材上的排樣算法。以常見排樣方式中最典型的對頭雙排為例分析板材2維排樣的整體優(yōu)化問題，結(jié)合余料的利用，建立2維排樣整體優(yōu)化的合理數(shù)學(xué)模型。利用改進(jìn)的平行線分割1步平移排樣算法，結(jié)合沖裁件外輪廓曲線，分析計算模型中的未知排樣參數(shù)，并給出了與整體優(yōu)化模型相匹配的整體優(yōu)化排樣算法。算法能夠根據(jù)板材和沖裁件的圖形信息快速、自動地確定板材2維排樣整體優(yōu)化的排樣參數(shù)，由此得到1個在板材上排放最多可沖裁0件的優(yōu)化排樣方案。
    在單1多邊形排樣算法研究的基礎(chǔ)上，結(jié)合計算機圖形學(xué)知識，進(jìn)1步提出1種基于掃描區(qū)間幾何表示方法的啟發(fā)式定位算法。排樣對象用等距掃描區(qū)間進(jìn)行表示，利用啟發(fā)式算法可以把復(fù)雜的多邊形判交與定位問題轉(zhuǎn)化為掃描區(qū)間之間的x坐標(biāo)值的簡單判斷，算法的計算復(fù)雜度與排樣多邊形的幾何形狀無關(guān)。在排樣多邊形的排樣次序和旋轉(zhuǎn)角度已經(jīng)確定的情況下，利用該算法可以自動、高效地實現(xiàn)多邊形在板料上緊密排列。

關(guān)鍵詞: 排樣；單1沖裁件；沖裁步距；自動排樣優(yōu)化；嵌套排樣；啟發(fā)式算法。

Abstract

This article first introduces one kind of sole polygon on the rectangular plate platoon type algorithm. Take the common platoon quadrat in the formula most typical enemy two-row as the example analysis plate two-dimensional platoon type whole optimization question, unifies Yu Liao the use, establishes reasonable mathematical model which the two-dimensional platoon type whole optimizes. Divides using the improvement parallel line one step displaces evenly the type algorithm, outside the union blanking outline curve, in the analysis computation model unknown platoon type parameter, and gave the whole which matched with the whole optimization model to optimize the row of type algorithm. The algorithm can according to the plate and the blanking graph information fast, determined automatically the plate two-dimensional platoon type whole optimizes the platoon type parameter, obtains one to discharge most much from this on the plate may the blanking components optimized row of type plan.
In the sole polygon row of type algorithm research foundation, unifies the computer graphics knowledge, further proposes one kind based on the scanning sector geometry expression method heuristic localization algorithm. The row of type object carries on the expression with the equal-space scanning sector, uses the heuristic algorithm to be possible to sentence the complex polygon delivers the localization question to transform as the scanning sector between x coordinate figure simple judgment, the algorithm computation order of complexity has nothing to do with with the row of type polygon geometry shape. Already determined in the row of type polygon platoon type order and the degrees rotation in the situation, used this algorithm to be possible automatic, to realize the polygon to be closely packed highly effective on the sheet.

Key word : Row of type; Sole blanking; Blanking step of distance; Automatic platoon type optimization; Nesting row of type; Heuristic algorithm.

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