Understanding Hanfu aesthetics mathematically: Curves of a Robe

Source: http://tieba.baidu.com/f?kz=1039230216
Original Title: [Technical] Overview of Hanfu collar curves and lower hem curves and its drawing methods
By: Hu Jingming, Hunan Normal University
Translated by: Juni L. Yeung   

Translator’s disclaimer: The views expressed by the original author by no means represent the only authority on the issue, nor does TorGuqin or the translator unconditionally endorse the opinions expressed in this article. The following article is translated by TorGuqin for reference, discussion, and similar uses only.  The theories expressed in this article may not apply to certain designs or articles of clothing, and should not be taken as an all-encompassing rule to judge the make or reproduction of articles of clothing, modern or otherwise.  

Misconceptions of the Collar.

First, let us look at the first diagram (1.1). I intentionally drew this wrong (meaning the collar line) – because I found that many Hanfu diagrams are drawn like so, to the extend where even historical records are also drawn this way. This is an obvious and serious fault, as people ask whether the collar can be a straight line. In actuality, only a few artifacts prove such examples, and the majority of surviving articles have an arc. Regarding the worn effects of the collar with or without the curve, it will be explained later in this article. However, the most lethal mistake to point out is the turn on the collar (by the shoulders): if it is drawn as a sharp corner without a curve, it is definitely wrong. This is a matter of the craft: even if you spend a lot of effort putting the collar on, many creases will form in a radiating pattern out towards the front and sides from the turn.   

Since surving artifacts have been long-term exposed in the elements, particularly so with more distant ones, they are prone to warpage on the clothing’s surface, and archaeologists don’t dare to pull with force in the cleanup process, so we may be often visually misled by pictures of it. For example, this clothing (1.2) from Mashan Chu Grave No.1 from  Jiangling, the picture is presenting an illusion – there is no way the collar was made so big. To solve this problem, we can only hope that the archaeologists in question also have some understanding of couture, in order to prevent us from reading baffling reports on its cutting.   

But, I still have a way to prove that the turn on ancient articles of clothing are a curve rather than an angle. This photo (1.3) was taken in the Jingzhou Museum, and is a rare sight. The piece is from the Ming dynasty – the clothing itself is nothing special, but the way it was hung was something of useful reference. Usually museums lays clothing on a flat surface, and it is difficult to see this part of the clothing. This piece, however, was hung on display, and one could clearly see this region, hence is why I say this is a rare sight to behold.   

Collar Curves.

Now I will explain the basis and method of drawing the collar curve, with this short Ru top as example (2.1). First, we  convert this flat layout into a cutting piece diagram (2.2). Forgive me as I am unable to explain clearly how I converted from one to the other, but those who have made clothes before should understand these diagrams. The red lines denote folding lines for separating the front and back.For the sake of explaining, I removed some unnecessary lines (2.3).  

First, we mark out the size of the collar opening on the folding line. This depends on the wearer’s neck size; I use 7.5cm for my inner layer pieces, so I draw a 7.5cm radius circle with the pivot at the intersection of the back meridian seam and the shoulder line, and we can find the two spots (on the folding line, 3.4). This figure needs to be close to the human measurement, since if the opening is too big, the clothing outside cannot be worn neatly flat. I find that on the photos of some compatriots, their collars have been either pressed or pulled apart by their inner zhongyi. This is because the relations of the different sizes of the openings was not considered in advance. Also, I would like to point out that the two points we have just marked will not actually end up on the fold line. As for why, please read on.  

Shifting the collar position back.

Remove the assisting marks (3.1), measure and mark a position towards the back panel 1.5 to 2cm. This value is relatively constant, as moving this too far to the back would result in some special effects, explained later. Now, measure 4 to 6cm towards the front panel and mark it – this figure will matter in the depth and curve of the collar’s curve (3.2). If we shifted to far to the back, it will cause the collar to not fit snugly around the neck, such as this effect here (3.3), since the human neck is not flat, and does not protrude out from straight above the abdomen (3.4). This is something not many notice.Now we begin to draw the curve for the collar. First we draw a straight line that would become the stopping point of the front extended panel. The length of this line doesn’t matter, and the angle of this line can depend on your design. As this is a temporary assisting line, it will be removed later (4.1).  

Drawing the collar curve.

Method 1: Prioritize on calculating the depth of the collar.  

The depth of the collar determins how close the collar would fit: the deeper the neck, the more it’ll open by the chest. Normally, summer clothing can open up deeper, so that it’ll be cooler to wear. The other factor to consider is the design of the clothing itself, and certain designs are indeed quite low. What is important here is, the depth that is being drawn here is not the actual depth when worn, as we have to put on a collar strip later on, and the actual depth is calculated after adding the height of the collar itself. With this method, we first determine the measurements of the collar’s depth to fulfill our specifications, while the width and stopping position of the extending panel will be set relatively freehandedly. Then we draw another two assisting lines, forming this triangle (shaded) here as a limit zone: This means that when we draw our curve, the curve and the endpoint must not exceed this area. Now, draw the curve through these three points – if it is drawn by hand, these three points would do. If this were CAD-drawn, then you need at least 8 points to complete a good curve. Here, I drew an approximate demonstration, and didn’t find all the spots by the parameters (fig. 5.4), hence the curve isn’t perfectly smooth. This curve itself is extremely hard to draw, as it requires itself to be aesthetically pleasing yet ergonomic at the same time, demanding the designer’s experience and aesthetic touch.  

Why do we need to draw this as a curve in the first place? Many will sure ask this, so I will explain it now. Japanese Kimono collars are straight cuts, hence their collars have a slight upward curve to them, sort of like the letter “r”, whereas Hanfu collars are required to be “y” shaped, or a downward-facing curve. These two collar types each have their own place for corresponding designs, and in any case I don’t think that Hanfu’s shape is suited with the upward-protruding collar used by the kimono. As for why straight collars have this effect, it is because the human body is a three-dimensional bucket-shaped figure, and when flat lines pass through this surface, it causes certain visual deformations.  

Collar making errata

 Still remember what I said about the limit zone? If we put our later part of the curve and endpoint outside this area, it will produce an effect like so (figure. 5.1, 5.2). This obviously is not desirable. However, I still want to say that we shouldn’t place it near the fringes of this limit zone either, as this won’t look good either, so this is the time to pick “the middle ground”. 

Method 2: Limit the endpoint for the front panels. This method requires us to accurately determine the endpoint of the front extending panel, and relatively the depth of the collar is more loosely regulated. First, we find our needed endpoint position. Similarly, we can use assisting lines to find a limit to the curve on the front central meridian and the limit zone at the end. 

Also, The extending lapel on some designs may be smaller than the one in front, therefore the curve will not be the same as the other one, but the drawing method is the same, hence I won’t repeat the details here.
Now we disucss the end stretch of the collar’s curve. This line can be done accordingly to the person: if the wearer’s body is thick, this line can be drawn straighter, while thinner wearers can have a bit more curve. Otherwise, the end stretch on the extending lapel may look like this (fig. 5.6). The reason of this skewing is also due to the 3-D nature of the human body. If the collar is relatively wider, the situation becomes different again. If the collar is wide, then reduce the curve of the cut by a bit. But come to speak of it again, it is also advisable not to make this curve too large, or the collar won’t be straight.


Lower hem curves.

Now we will discuss the method for drawing the bottom hem. Compared to the collaar, this is much simpler. Usually when we draw our diagrams to this stage, we will come across the problem of drawing the curve for the lower hem. Since the lower hem of the clothing needs to be hemmed (folding in the fuzzy edge in) or sutured aesthetically, we will need to create a smooth curve for both front and back. I know many people get stuck on here, as since this line isn’t straight but an ovuloid shape. Among this is a mathematical relation that not everyone may know, hence I will mention  how it is done.

First we mirror these two  lines to the left (fig. 6.1), with the axis of symmetry on the side seam. In actuality, we can assume this action as opening up the back’s central meridian and see the piece linked up from the sides. We will then discoover an obvious corner (fig. 6.3), and this is the source of the problem. Now we need to reasonably eliminate this corner: First, we divide the two bottom lines in half, and mark them accordingly. Then, we draw a line connecting these two points (fig.6.4), perpendicular to the side seam line. now draw a round curve through these three points, and remove the extra lines. Now draw the mirror image of the curve with the central meridian as axis of symmetry, and we’re done. If we extend this curve to the back panels (on the sides here) and it forms a smooth arc, that means that we were successful (see fig.7).

Lower hem errata and correct model.

If we didn’t draw the curve in accordance to mathematical theory, and use freehand instead, the following situation may occur (fig. 7.1). After we we connect them, we will find places that curve in or protrude outward, which cannot qualify for quality and aesthetic requirements. Therefore, it is necessary to obtain some essential know-how for drawing these lines.

Lastly, I would like to tell everyone that what I have given is a mathematical method, but that cannot be the only thing that we’re in pursuit of. We need to understand the theories behind these formulae, and develop a sense of aesthetics from it. Afterall, art cannot be made just by math itself – it needs a kind of spiritual matter. Just like our collar example from before, it creates grace without violating principles previously mentioned. This is a matter of discipline for the designer himself. Developing every fine detail to an aesthetically pleasing and unique degree is somethinng for us to continually think and pursue. I believe that making a piece of clothing, requires at least the mathematical theorems for its basic structure, but at its essence is a form of emotion, a masterpiece consists of heart-pouring work, as contrasted to an industrial product. Hanfu is beautiful, but not perfect. Let us endeavour ourselves to make it a better thing.

5 Comments (+add yours?)

  1. Charles Henry Wolfenbloode
    Apr 11, 2011 @ 15:00:25

    Bloody hell. Makes Western tailoring seem like a stroll in the park…


  2. chinese girl
    Apr 02, 2012 @ 16:04:26

    This seems really complicated. Is it possible for you to give step by step instructions on how to do this without a computer. I really want to be able to make one, but i don’t know how i can get the curves right on the hanfu. Its a very through explanation though, i just need help on how i can use that to actually make the hanfu.


    • Satsuki Shizuka 五月靜
      Apr 02, 2012 @ 17:01:09

      Hello CG:

      Hu suggested to “wing it” by plotting out (at least) 8 points of the projected arc onto the pattern, and to keep drafting/modifying it until it looks right. However, there is a more precise way when it comes to the bottom hem.

      Since we know that there is a length and axis of symmetry, we can simply replicate the angle of the bottom seam and axis on the other side, virtually extend the line with a long ruler (metre stick), find the midpoint, project the median line, and draw the arc from there. Humanity only had electronically/digitally assisted geometry for less than a century, but we’ve been doing this for aeons using rulers and compasses. Stationery.

      I’m sure this hands-on exercise will probably change your impression of mathematics, altogether.


  3. tsumaranagatta
    Jun 30, 2012 @ 04:46:50

    Thanks for linking to this page 🙂
    The design looks so simple yet all these nuances are really hard to master.


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