【译文】如何设计容器折纸的cp图

静候轮回

在网上看到一篇关于如何设计容器折纸cp图的文章，现翻译给大家（按意思翻译的，不是逐句翻译），希望对大家有帮助，有英文好的同学可以再帖子下面加注你的翻译，欢迎交流。
在看译文之前先看一个折纸容器和它的cp图


上面的cp图有七部分组成，每一个小部分就是下面译文中提到的皱褶
下面是译文

一 Planning a Shape

The first step in the design process is choosing the shape for the origami form. Drawing the shape on a grid will make it easier to figure out the dimensions later. Here’s the shape I designed for this tutorial
一 预想一个容器的形状
设计的第一步就是要选择一个适合折纸的容器形状，将它画在网格图上，这样容易就是计算容器尺寸，下图就是我在本教程中设计的形状

Some hints for choosing a shape:
1.In general, the simpler the shape, the easier it will be to fold.
2. Convex curves (like the body of the bowl) are easier to fold than concave curves (like the neck of the bowl).
3. Curves that stay close to vertical are easier and don’t have to be nearly as precise as curves that are close to horizontal.

选择容器形状的一些要点
1 一般情况，形状越简单越好折
2 凸曲线（如碗体）比凹曲线（如碗的脖子）好折
3 接近垂直的曲线容易折，不必刻意地精确计算让曲线接近水平
二 Gore Number and WidthFirst we’re going to decide on a number of gores and on the width of each gore based on how big the final model will be. The width of the paper will be the circumference of the shape at its widest point, plus one extra gore for overlap.
For my design, each square in the pattern above will be 0.5 cm, so the radius of the largest circle is 5 cm. That means the circumference is (5 cm)(2)(3.14) = 31.4 cm, which I will round up to 32 cm. The circumference then divides evenly into 16 gores that are 2 cm wide. When we add one extra gore for overlap, that gives a total of 17 gores that are 2 cm wide, for a total width of 34 cm.
二 计算折叠容器需要的褶皱数量和宽度
首先我们先要计算折叠容器需要的褶皱数量和宽度，这将决定我们折出的容器的大小，纸张的宽度是容器最宽处的周长加上首尾相接时重叠的部分
在我的设计中，上图中每个方格是0.5cm，所以容器最宽处的半径是5cm，周长则是5*2*3.14＝31.4cm，我算作32cm，将这32cm均匀的分在16个褶皱里（每个褶皱我用2cm），在加上首尾相接处额外重叠的褶皱，一共是17个褶皱，每个褶皱宽2cm，所以纸张的宽度是34cm
三 Paper LengthThe next step is to calculate the length of the paper. Along the length of the paper, the paper will go from the center of the base to the top rim. We can estimate the length of the curve by converting it to a series of straight line segments.  Then we can use the Pythagorean Theorem to calculate the length of each line segment. If the height of the line segment is h and the width is w, then the length is √(h2 + w2).  To get the total length of the paper, we just add up the lengths of all the segments.
三 计算纸张的高度
下一步是计算纸张的高度，从容器的顶部到容器底部中心位置，我们各处的曲线按直线看待，按照勾股定理计算出各处的线段的长度，纸张的高度就是各处线段长度的和




For my design, the length of each line segment is shown in the picture above. The total length is 1.4 cm + 3.2 cm + 0.5 cm + 4.3 cm + 2.5 cm = 11.9 cm. Paired with the width we calculated above, the paper will be 34 cm wide x 11.9 cm tall.

在我的设计中，根据勾股定理计算的每个线段的长度如上图所示，总长度是1.4cm+3.2cm+0.5cm+4.3cm+2.5cm＝11.9cm，综合前面的计算，纸张的尺寸是长34cm，高11.9cm
四  Creating the Curved Form
The final step is to figure out the shape of the curved fold in each gore. Here we’ll use the same straight line approximation of the curve as we did above. At each end of each line segment, we can calculate how far the curve should be from the edge of the gore based on the radius of the form at that point. Where the radius is zero, the curve should be at the exact center of the gore at that point. Where the radius is at its maximum, the curve will touch one edge of the gore. Where the radius is half of its maximum, the curve will be halfway between the center of the gore and the edge, or a quarter of the way from one edge of the gore.
Here are the dimensions for my design:
四 设计折图的曲线形状
最后就是如何做出cp图中的曲线，（下图是做好的cp图的十七分之，可以看出若做出cp的曲线，应该先确定容器几个有代表性部位的宽度，也就是图中标有具体数值的横向线段的长度），下图中每个横线的长度都是根据容器不同部分的半径算出的，半径是零的地方，也就是容器底部，，该点我们设在皱褶的中点，半径最大的地方，和皱褶同宽。
下面是我的设计尺寸






Since my gores are 2 cm wide, the center of the gore is 1 cm from its left edge. At the very bottom edge, the radius is zero, so the curved fold is 1 cm from the edge. Because the radius at the widest point is 10 squares, each square corresponds to 0.1 cm. From those measurements, we can calculate the width at each point just by counting squares.
因为我们的皱褶是2厘米宽，皱褶的中点是从它的左边缘起1厘米处。在底部边缘，半径为零，所以cp曲线起自皱褶左起边缘1厘米处，也就是皱褶的中点。因为容器最宽的点的半径是5cm，对应于cp图中是2厘米。从这些测量数据，我们可以计算出在每个点在cp图上的宽度。（线段的在垂直方向的位置由步骤三算出的数值决定，然后将各个线段的右端相连，再复制出17份连在一起）。


At this point, we have figured out all of the dimensions that go into the crease pattern. The folded model from the design looks like this:
现在我们已经算出了所有形成cp曲线各点的尺寸，下面就是我们的成品图

碧海不惑

楼主加油！！

王军胜

支持,加油

soxgoon

请问原网址是哪儿？

金正昆

真是专业啊 。

静候轮回

soxgoon 发表于 2013-3-10 10:18
请问原网址是哪儿？

http://rebecca.gieseking.us/2013/03/tutorial-designing-pleated-forms-2/

tosummerny

倒是用过专门设计容器cp的软件~

hhh氢气球

谢谢楼主分享。有学者风范，加油！。得慢慢研读。

静候轮回

tosummerny 发表于 2013-3-10 13:52
倒是用过专门设计容器cp的软件~

啥软件？叫什么名字

tosummerny

海绵宝宝 发表于 2013-3-10 16:54
啥软件？叫什么名字

ori-revo