2020亚太数学建模竞赛A题翻译

激光标记阴影轮廓生成

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世纪的一项重要发明，被称为“最锋利的刀”、“最精确的尺”和“最不可思议的光”。激光已越来越多地应用于工业加工，可用于各种加工操作，如标记、焊接、钻孔、切割、热处理和喷涂。激光的显著特点是方向性好，可以汇聚成微小的光斑，实现能量的高度集中；此外，由于其良好的单色性，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.

激光标记是指用激光标记LOGO、文字、符号、图像等。在产品表面。它具有加工效率高、非接触操作、无耗材、对产品表面变形影响小、标记内容牢固等优点，是一种广泛使用的加工方法。

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.

激光打标机的阴影工具可用于阴影指定的2D复合曲线图，不同阴影参数的设置对不同材料的加工效果有很大影响。方向平行阴影和轮廓平行阴影是两种基本的阴影方式。平行方向阴影线，也称为“之字形”阴影线，其路径沿着与初始选定的参考方向平行的线段移动。基于这种策略，通过连接这些平行的线段来获得连接的路径，使得它们或者全部从右向左(或者从左向右)穿过，或者从左向右和从右向左交替穿过。而轮廓平行阴影使用基于边界曲线的偏移线段作为类似于边界曲线的平滑阴影路径。因此，轮廓平行阴影可以以螺旋形方式沿着距离曲线边界恒定距离的曲线生成。哪种类型的开口在实际应用中高度依赖于标记材料和对要执行的特定加工任务的工艺影响。

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.

影线实体必须是闭合的曲线多边形，多个相互嵌套的轮廓对象可以通过组影线填充。对于图形的阴影化过程，现有的边界轮廓应先根据边缘距离向内或向外偏移，然后再进行锯齿形平行或轮廓平行阴影化。阴影曲线应均匀、规则，并保持基本平行。既不允许遗漏某一区域的填充，也不允许重复填充该区域。通过激光标记的阴影应实时在线生成阴影轮廓。为了满足高效激光打标的要求，阴影曲线应与图形的边界线保持平行，最大限度地均匀分布，并能自动快速生成。效率是阴影图形生成的重要指标。

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.实现附件1单层轮廓图案的之字形平行和轮廓平行阴影；这里，只有水平方向(0度)的阴影被认为是锯齿形平行阴影。请根据附件1中图的坐标点数据(单位:mm)，实现两组输入参数下的孵化:

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

(1)边界距离内部收缩1毫米，影线间距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)边界距离内缩0.1mm，影线间距0.1mm，在两组参数下，计算锯齿形平行影线和轮廓平行影线的影线主体的影线总长度，统计锯齿形平行影线的水平线数，轮廓平行影线的圈数。根据孵化程序的多次运行计算平均运行时间(单位:毫秒)，并计算参数组(2)和(1)条件下程序运行的运行时间比率。

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.实现附件2中相互嵌套的多层轮廓图案的之字形平行和轮廓平行阴影；这里，对于锯齿形平行阴影，只考虑水平方向(0度)的阴影。请根据附件2中图的坐标点数据(单位:mm)，实现两组输入参数下的孵化:

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

(1)边界距离内部收缩1毫米，影线间距1毫米；

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

(2)边界距离内部收缩0.1毫米，影线间距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).

在两组参数下，计算曲折平行和轮廓平行阴影的阴影曲线的阴影线总长度，计算曲折平行阴影的水平线数和轮廓平行阴影的圈数。根据孵化程序的多次运行计算平均运行时间(单位:毫秒)，并计算参数组(2)和(1)条件下程序运行的运行时间比率。

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.激光打标机产生的光斑直径很小。激光打标的影线间距一般为0.01mm-0.1mm，激光打标产生大量的等高线数据，任何形状的等高线对程序的运行效率都有极高的要求。请检查您的孵化算法的运行时间，并分析其性能，为优化孵化算法的性能和效率提供策略或方向，使其能够满足实际工业应用的效率要求。

标签：竞赛,平行,建模,阴影,contour,2020,hatching,hatch,parallel
来源： https://blog.csdn.net/h201601060805/article/details/110188610