ARC 4303A | Updates

The section grammar is included in the Penn paper (Li forthcoming), which you can download here (text, images). The grammar is shown in figure 6, but don’t overlook the constraints on rule application, on page 6.
If you think there are stylistically correct designs that the grammar is not producing, you can “loosen” the grammar by changing the rules or the constraints on rule application (or both).
How do you know whether there are designs as mentioned in (2) above? We assume that:
- Columns can be located only below the ends of rafters (excluding the eaves rafters);
- A column is either there or not there; and
- There is always a column in the front wall and one in the back wall.
Therefore, since we are dealing only with 6-rafter buildings, we have 7 possible locations for a column. With 2 positions always “filled,” there are 2 ^ 5 = 2 × 2 × 2 × 2 × 2 = 32 combinations of columns. Your grammar may generate fewer than 32 sections, so you may want to consider the remainder of the 32 as candidates for (2) above.
If, because it is producing unstylistic designs, you want to “tighten” the grammar, you can change either the rules or the constraints or both.
How do you know whether the designs produced by the grammar are stylistically correct or not? Short answer: You don’t. Long answer: If your only information is the corpus of 18 sections, then all you know for sure is that those 18 sections are stylistically correct. Everything else is speculation. What we are trying to do is speculate in a way that both is precise and provides the 3 benefits mentioned by Stiny and Mitchell.
Don’t forget the descriptions. In particular, since a design consists of a section and a description, two designs with the same section but different descriptions are not the same design. Take for example the design D, with the description “a 6-rafter building, centrally divided, with 3 columns,” and the design E with the description “a 6-rafter building, a 3-rafter beam abutting a 3-rafter beam, with 3 columns.” D and E have the same section, but different descriptions. Therefore they are different designs. One may be in the style, and the other not. One may be grammatical, and the other not.

Monday 22 September 2003

I am wonder about how we define a design is legal or illegal. For a given design. If we can creat it with only one rule of the grammar which contains more than one rules. Is this design legal or not?
…
For the square grammar. Does all the dots which have the same positions with any of the squares have to be erased? Is it the rule?
- Dots first. The dots in the square grammar are for controlling the application of the rules only. They are not part of the final design. So when you’ve finished adding squares, you should erase all the dots. The dots are like the construction lines when you make a drawing. You need them to make the drawing, but you don’t necessarily want to see them in the final drawing. So you might erase them, or even make an entirely new drawing by tracing over the old one.
But I am still confused by the assignment. If I choose the sqaure grammars. Call it grammar A. It also has two rules, rule 1 and 2. So I add rule 3 to creat grammar B.Now I can easily produce a design by grammar A. Precisely speaking, I produce it by applying rule 1 and 2 successively to the initial design.

Now, here is the question. Is this design legal or illegal in grammar B? Probably, I consider it to be legal because I can say I produce it by grammar B although I didn’t apply the rule 3. But it is my choice to apply rule 3 or not.

If my discussion above is right,how can I create a design that is legal in grammar A but illegal in grammar B?

You have already answered the question. Your problem is that you have assumed that there is a design that satisfies the requirements of the question. If there is no such design, say so and explain why.

Wednesday 17 September 2003

Dennis Leung pointed out a mistake in figure 4 of my Penn paper (Li forthcoming). After the 6th and 7th applications of rule 1, a dot should be added inside one of the existing squares. He is absolutely right. The derivation shows what I expected to happen, but I didn’t check carefully. My mistake. So, something to think about: what rules would give the derivation shown?

Tuesday 16 September 2003

The automated grammar for ting tang sections is available.
- View in the browser (SWF)
- Download the projector (Mac, 828 KB)
- Download the projector (PC, 708 KB)

Sunday 14 September 2003

The complete and final version of Li (forthcoming) is now available. Download the text and images (PDF, 254 and 241 KB).

Saturday 6 September 2003

“I am writing to ask whether we are going to draw the roof section(s) of 殿堂 or 廳堂, because I find that they have different 舉折之制.”
- For the roof sections, you can draw either. Just make sure you specify all your assumptions (e.g., what building type, number of rafters, length of rafters, tile type...).
- For the building sections, do ting tang.

Thursday 4 September 2003

A subassembly is an assembly that is part of a larger assembly. An assembly is a set of manufactured parts assembled to make a completed product, especially a machine (adapted from the American heritage dictionary). In the context of the assignment, the complete building is the assembly; building sections and roof sections are two kinds of subassemblies. So, do tasks 1, 2, and 3 for building sections. Then do tasks 1, 2, and 3 for roof sections. Finally, answer the last question.
For building sections, it is sufficient to draw line diagrams (like the one I drew on the whiteboard). All we need to see are the salient features (number and location of columns, beams, rafters, etc.). We do not need to see bracket sets.
For roof sections, please draw to scale. Actually, you will find it easier to do so, because it is a graphic method of calculation.
To make a PDF file on a Mac, you simply prepare to print the document. But instead of sending the document to the printer, you save it as a PDF file. In OS X, this feature is built into the system. In OS 9, you need first to install a piece of software from Adobe (I don’t remember the name). I don’t know how to do it on a PC, but I’m sure it’s similar.
A sharp-eyed student has asked a number of questions about the 18 ting tang sections and their descriptions. I should explain in more detail.
- p. 313, above. This is dian tang, so it is not one of the 18 ting tang sections.
- p. 315, above. “Bing rufu 並乳伏” means “two rufu touching.” In other words, “qian bing rufu, hou bing rufu 前並乳伏，後並乳伏.”
- p. 315, below. “Qian hou ge 前後各” means “in both front and back.” “Ge” is optional. Compare with p. 315, above.
- p. 316, below. “Dui 對” means “abutting.” In other words, there is no unspecified bay between the two beams. Compare p. 315, above and below.
- p. 318, below. The description should be “bajia chuan wu, qian hou zhaqian rufu, yong liu zhu 八架椽屋前後劄牽乳伏, an 8-rafter building, 1- and 2-rafter beam in front and in back, with 6 columns.”
- p. 320, above. The description should be “liujia chuan wu, qian hou rufu, yong si zhu 六架椽屋前後乳伏用四柱, a 6-rafter building, a 2-rafter beam in front and in back, with 4 columns.”
- p. 320, below left. The description should be “sijia chuan wu, zhaqian dui sanchuan fu, yong san zhu 四架椽屋劄牽對三椽伏, a 4-rafter building, a 1-rafter beam abutting a 3-rafter beam, with 3 columns.”
- p. 321, right. The description should be “sijia chuan wu, qian hou zhaqian, yong si zhu 四架椽屋前後劄牽用四柱, a 4-rafter building, a 1-rafter beam in front and in back, with 4 columns.”
- p. 321, left. The description should be “sijia chuan wu, tong yan, yong er zhu 四架椽屋通檐用二柱, a 4-rafter building, clear span, with 2 columns.”