2020亞太數學建模競賽A題翻譯

激游標記陰影輪廓生成

Laser is an important invention in the 20th century, and it is called “the sharpest knife”, “the
most accurate ruler” and “the most unearthly light”. Laser has been increasingly applied to
industrial processing, which can be employed in various processing operations such as marking,
welding, drilling, cutting, heat treatment, and spray-coating. Remarkably featured by its fine
directionality, laser can be converged into tiny sized spots so as to achieve the high
centralization of energy; moreover, due to its sound monochromaticity, laser is easy to control.

激光是20世紀的一項重要發明，被稱為“最鋒利的刀”、“最精確的尺”和“最不可思議的光”，激光已越來越多地應用于工業加工，可用于各種加工操作，如標記、焊接、鉆孔、切割、熱處理和噴涂，激光的顯著特點是方向性好，可以匯聚成微小的光斑，實作能量的高度集中；此外，由于其良好的單色性，激光易于控制，

Laser marking means using laser to mark LOGO, characters, symbols, images, etc. on the
surface of products. It is a widely used processing method with its advantages of high
processing efficiency, non-contact operation, no consumables, slight influences on product
surface deformation, and firmness of marked content.

激游標記是指用激游標記LOGO、文字、符號、影像等，在產品表面，它具有加工效率高、非接觸操作、無耗材、對產品表面變形影響小、標記內容牢固等優點，是一種廣泛使用的加工方法，

The hatch tool of laser marking machine can be used to hatch specified 2D-compound curve
graph, and the setting of different hatch parameters have a great impact on the processing effects
of different materials. The direction parallel hatch and the contour parallel hatch are two basic
ways of hatching. The direction parallel hatch, also known as “zigzag” hatch, has paths being
moved along line segments which are parallel to an initially selected reference direction. Based
on this strategy a connected paths is obtained by linking these parallel segments so that they are
either all traversed from right to left (or left to right) or, alternately from left to right and from
right to left. Whereas the contour parallel hatch uses offset segments base the boundary curves
as smooth hatch path that similar to the boundary curve. Thus, the contour parallel hatch be
generated in a spiral-like fashion along curves that are at constant distances from the curve
boundary. Which type of hatch is applied in practice highly depending on mark materials and
the process effects on the particular machining task to be performed.

激光打標機的陰影工具可用于陰影指定的2D復合曲線圖，不同陰影引數的設定對不同材料的加工效果有很大影響，方向平行陰影和輪廓平行陰影是兩種基本的陰影方式，平行方向陰影線，也稱為“之字形”陰影線，其路徑沿著與初始選定的參考方向平行的線段移動，基于這種策略，通過連接這些平行的線段來獲得連接的路徑，使得它們或者全部從右向左(或者從左向右)穿過，或者從左向右和從右向左交替穿過，而輪廓平行陰影使用基于邊界曲線的偏移線段作為類似于邊界曲線的平滑陰影路徑，因此，輪廓平行陰影可以以螺旋形方式沿著距離曲線邊界恒定距離的曲線生成，哪種型別的開口在實際應用中高度依賴于標記材料和對要執行的特定加工任務的工藝影響，

The hatching entities must be closed curvilinear polygons, and multiple mutually-nested
contour objects may be filled by group-hatching. For the hatching process of figures, the
existing boundary contours shall be offseted inward or outward firstly according to edge
distance, before getting subject to the zigzag parallel or contour parallel hatch. The hatch curves
shall be even and regular, and be kept basically parallel to each other. Neither having omissions
of filling in an area, nor repeated filling of the area is allowed. The hatching by laser marking
shall generate hatched contours online in a real-time way. To meet the requirement of high-
efficiency laser marking, the hatch curves should stay parallel to the figures’ boundary lines,
distribute evenly to the greatest extent, and be generated automatically and quickly.
Efficiency is an important indicator for the generation of hatched figures.

影線物體必須是閉合的曲線多邊形，多個相互嵌套的輪廓物件可以通過組影線填充，對于圖形的陰影化程序，現有的邊界輪廓應先根據邊緣距離向內或向外偏移，然后再進行鋸齒形平行或輪廓平行陰影化，陰影曲線應均勻、規則，并保持基本平行，既不允許遺漏某一區域的填充，也不允許重復填充該區域，通過激游標記的陰影應實時在線生成陰影輪廓，為了滿足高效激光打標的要求，陰影曲線應與圖形的邊界線保持平行，最大限度地均勻分布，并能自動快速生成，效率是陰影圖形生成的重要指標，

1. Realize the zigzag parallel and contour parallel hatch of the single-layer contour pattern in
   Attachment 1; and here, only the hatch in horizontal direction (0° degree) is considered for
   zigzag parallel hatch. Please realize the hatching under two groups of input parameters
   according to the coordinate points data of the figure in Attachment 1 (unit: mm):

1.實作附件1單層輪廓圖案的之字形平行和輪廓平行陰影；這里，只有水平方向(0度)的陰影被認為是鋸齒形平行陰影，請根據附件1中圖的坐標點資料(單位:mm)，實作兩組輸入引數下的范訓:

(1) Internal contraction of boundary distance 1mm, hatch line spacing 1mm;

(1)邊界距離內部收縮1毫米，影線間距1毫米；

(2) Internal contraction of boundary distance 0.1mm, hatch line spacing 0.1mm.
Under the two groups of parameters, calculate the total length of hatching lines of the hatched
curves subject of zigzag parallel and contour parallel hatch, and count the number of horizontal
lines of zigzag parallel hatch, and the number of circles of contour parallel hatch. Count the
average elapsed time (unit: ms) based on the multiple runs of hatching program, and calculate
the ratio of elapsed time for program running under conditions of parameter groups (2) and (1).

(2)邊界距離內縮0.1mm，影線間距0.1mm，在兩組引數下，計算鋸齒形平行影線和輪廓平行影線的影線主體的影線總長度，統計鋸齒形平行影線的水平線數，輪廓平行影線的圈數，根據范訓程式的多次運行計算平均運行時間(單位:毫秒)，并計算引陣列(2)和(1)條件下程式運行的運行時間比率，

2. Realize zigzag parallel and contour parallel hatch of the mutually nested multi-layer contour
   patterns in Attachment 2; and here, only the hatching in horizontal direction (0° degree) is
   considered for zigzag parallel hatch. Please realize the hatching under two groups of input
   parameters according to the coordinate points data of the figure in Attachment 2 (unit: mm):

2.實作附件2中相互嵌套的多層輪廓圖案的之字形平行和輪廓平行陰影；這里，對于鋸齒形平行陰影，只考慮水平方向(0度)的陰影，請根據附件2中圖的坐標點資料(單位:mm)，實作兩組輸入引數下的范訓:

(1) Internal contraction of boundary distance 1mm, hatch line spacing 1mm;

(1)邊界距離內部收縮1毫米，影線間距1毫米；

(2) Internal contraction of boundary distance 0.1mm, hatch line spacing 0.1mm.

(2)邊界距離內部收縮0.1毫米，影線間距0.1毫米

Under the two groups of parameters, calculate the total length of hatching lines of the hatched
curves subject to zigzag parallel and contour parallel hatch , and count the number of horizontal
lines of zigzag parallel hatch, and the number of circles of contour parallel hatch. Count the
average elapsed time (unit: ms) based on the multiple runs of hatching program, and calculate
the ratio of elapsed time for program running under conditions of parameter groups (2) and (1).

在兩組引數下，計算曲折平行和輪廓平行陰影的陰影曲線的陰影線總長度，計算曲折平行陰影的水平線數和輪廓平行陰影的圈數，根據范訓程式的多次運行計算平均運行時間(單位:毫秒)，并計算引陣列(2)和(1)條件下程式運行的運行時間比率，

3. The diameter of light spots is very small when generated from laser marking machine. The
   hatching line spacing of laser marking is generally 0.01mm-0.1mm. Laser marking generates a
   large number of contour lines data, and the contour lines of any shape have extremely high
   requirements on the running efficiency of programs. Please check the elapsed time of your
   hatching algorithm and analyze its performance to provide a strategy or direction for optimizing
   the performance and efficiency of the hatching algorithm, so that it can meet the efficiency
   requirement of actual industrial applications.

3.激光打標機產生的光斑直徑很小，激光打標的影線間距一般為0.01mm-0.1mm，激光打標產生大量的等高線資料，任何形狀的等高線對程式的運行效率都有極高的要求，請檢查您的范訓演算法的運行時間，并分析其性能，為優化范訓演算法的性能和效率提供策略或方向，使其能夠滿足實際工業應用的效率要求，