Inca Reconstruction Using Shape Grammar

Course Project for CS888 - Computer Graphics for Architecture

---

Project Objective

Incan buildings have relatively simple and regular structures. It is possible to describe such buildings using several shape grammar rules. The purpose of this project is to demonstrate the feasibility of using shape grammar as a tool to recreate simple Inca sites.

Implementation Details

• The program is written using PyOpenGL and PyQt4. It is only tested on Ubuntu Hardy. The source code can be found here. To run the program, extract the files from the archive and run ./inca.py. You must have PyOpenGL and PyQt4 installed to run the program.
  
  
• The following shape grammar rules are used to generate an Incan house. The elements with all lowercase letters are terminals. The ones with all uppercase letters indicate different types. The rest are non-terminals.
  House -> Facades Roof
  Facades -> Facade{FRONT, BACK, SIDE}
  Facade[FRONT] -> pillar (30% probability)
  Facade[FRONT] -> RegularFacade (70% probability)
  Facade[BACK] -> RegularFacade
  Facade[SIDE] -> RegularFacade (35% probability)
  Facade[SIDE] -> side_wall (65% probability)
  Roof[Side facade is regular] -> rectangular_roof
  Roof[Side facade is triangular] -> sharp_roof
  RegularFacade -> wall+
  RegularFacade -> wall (window | door)* wall
  RegularFacade -> wall window* door window* wall
  RegularFacade -> wall (window door)+ window wall
  
  A set of parameters is associated with the house to determine its appearance. The parameters can be individually modified from GUI for each house. When the parameters specified by the user exceed the size of the house, the sizes of windows and doors are adjusted in order to maintain the desired number of windows and doors.
  
  
• Only simple Incan walls are supported by the system. Incan walls with niches are not included. There is no shape grammar rule for the Incan walls, since their locations are quite ad hoc. Users must specify where to create those walls and they are not included in random generation.
  
  
• When a site plan is provided, there is no rule for generating stairs and terraces. When a site is generated randomly, there are a couple of rules that govern the generation.
  Plan -> LeftTerraces stairs RightTerraces (stairs | e)
  LeftTerraces -> terrace terrace+
  RightTerraces -> TerraceWithHouse TerraceWithHouse TerraceWithHouse+
  TerraceWithHouse -> terrace House House
  TerraceWithHouse -> terrace House House House
  TerraceWithHouse -> terrace House House House House
  
  The choices of rules depend on probability. The location and the orientation of the stairs, the partitions of the terraces, the number of houses, and the orientation of the houses all depend on probability as well (within a certain range, of course). Those rules are definitely not enough if we want to generate a realistic Inca site randomly, but they suffice as a rough demonstration of the idea.
  
  
• The rules above are all hard-coded, which imposes a limitation on the possible tasks that the system can handle.
  
  
• Users can load plan images in the program to create houses, walls, and terraces. All the plan images are from [1], the book I used when I went to Machu Picchu for the first time.

Results

Discussions

Shape grammars in computation are a specific class of production systems that generate geometric shapes [2]. It is able to create new design based on the architectural rules summarized by designers and architects. In Xkipche's case [3], the rules were summarized by archaeologists. Like the Puuc buildings in Xkipche, Incan buildings have consistent designs that make them suitable for shape grammar modeling.

Compared to Puuc buildings, Incan houses have less decorations and less components in the facades. The variation in the rules mainly comes from the different number of doors and windows. It is also possible to have different types of front and side facade and the roof form can change as well, which slightly increases the complexity of the rules. Inca architecture has two other main elements besides its houses: Incan walls and terraces. They play a very important role in city construction therefore it is necessary to include them in the shape grammar rule base. However, since I don't have enough information on how the Incas placed the wall inside their villages or cities, I choose to let the user model the walls manually instead of devising a formal representation of the wall placement.

I believe that modeling using shape grammar is probably more time consuming compared to traditional modeling methods such as CAD. It is difficult to design rules for complicated shapes, and the results may or may not be satisfactory. For example, in the Xkipche paper, a large amount of additional rules were created for the decorations with repetitive patterns. When the pattern is less repetitive, shape grammar is not quite capable of modeling those decorations. The Incan buildings in this project have simple shapes, and it is easy to extract shape grammar rules. However, if we consider the time spent on building the system to interpret the rules, manual modeling can still outperform shape grammar.

One big advantage of shape grammar is the possibility of generating new designs. The random generation mode in the project tries to demonstrate this idea. If we encode our knowledge of city planning into shape grammar rules, then it is easy for a person without that domain knowledge to generate a sensible design using the system. This may not have any practical use in archaeology, but can be useful in modern urban planning.

Reference

[1] Ruth M. Wright, The Machu Picchu Guidebook: A Self-Guided Tour
[2] Shape Grammar, Wikipedia, http://en.wikipedia.org/wiki/Shape_grammar
[3] P. Müller et al., "Procedural 3D Reconstruction of Puuc Buildings in Xkipche," Proc. Eurographics Symp. Virtual Reality, Archaeology and Cultural Heritage (VAST 06), Eurographics, 2006, pp. 139–146.