K9K | Similarity, Isometric and Isomorphic recognition

K9K | Searching 2 "K"s and put equivalent results in a group

Project Description |

Continuing the research of shape recognition, this test is to group found shapes which are symmetrically equivalent. Each column in the category presents the equivalent shapes. For example, the shapes in the first column, all the shapes are the rotations, reflections or diag-reflections of other shapes.

Fig.01 - 2 "K"s, page 1

Fig.01 - 2 "K"s, page 2

Expanding Sol Lewitt

Project Description |

This small project is inspired by Sol Lewitt, an American artist who introduced the complexity of geometry to art. One of his works, “no title, 1973”, reveals the possibilities of a simple geometry. This work is based on a square which contains 4 lines in it. Sol Lewitt simply shows all the configurations with these four lines: 1-line configuration, 2-line configuration, 3-line configuration and 4-line configuration. By manipulating the number of lines, he demonstrate how complex a simple geometry can be. Furthermore, this concept can be used in computational design to explore more potential of geometry. Sol Lewitt only reveals the complexity of line number changing, however, this geometry contain much more thing than we think. For instance, there are 28 configurations (or combinations) when the geometry is inquired for combinations of one T shape and one L shape shown as below.

No title, Sol Lewitt, 1973

T and L configurations in Sol Lewitt, T.C. Kurt Hong, 2017

Within these T-L configurations, it can be observed that each configuration can be a plan, section or elevation of a small house. In other words, this geometry actually provides us a large number of design candidates. This concept can also be seen in many architects’ plans. In Siza’s Museum of Contemporary Art Nadir Afonso shown as below, it can be observed there are some “underlying” geometries forming a geometry context. All the lines are part of this context. This context provides architect a source of design candidates. For instance, by removing some lines from geometry context, architects can create openings; by thickening some lines, architects can thus create walls; by trimming some lines, architects can thus create a interesting corner, etc. This geometry context is usually a combination of simple shapes such as rectangles, triangles, lines, squares just like the geometry that Sol Lewitt used. To explore more in Sol Lewitt’s geometry, we try different four-line configurations such as four-floating-line configurations, two-L configurations and other configurations shown as below.

Museum of Contemporary Art Nadir Afonso, Álvaro Siza, 2015

Two-L configurations in Sol Lewitt, page 1, T.C. Kurt Hong, 2017

Two-L configurations in Sol Lewitt, page 2, T.C. Kurt Hong, 2017

Two-L configurations in Sol Lewitt, page 3, T.C. Kurt Hong, 2017

Two-L configurations in Sol Lewitt, page 4, T.C. Kurt Hong, 2017

There are 46 results in four-locating-line configuration, and 258 results in two-L configuration. Each result can be used as a small plan to create space. In other words, this geometry can at least provide architects more than 300 Design candidates. The complexity of Sol Lewitt’s geometry actually can be much higher than 300 candidates if we ask for more configurations. Complexity is a critical element in design process. By introducing complexity, designers can thus create diversities to help them see more possible solutions, a mindful design category. Also, in Sol Lewitt’s works, the beauty of complexity is revealed.

Incomplete Open Cubes, Sol Lewitt, 1974

Incomplete Open Cubes, Sol Lewitt, 1974

Another term for complexity in Sol Lewitt’s work may be “variation”. Producing variations is also a critical step in design process. Incomplete open cubes show us that variations can be created by simply removing lines from a cube, or simply selecting lines from a cube. Removing things or selecting thing are two of the ways to create “combinations”, like the operations in geometry context while designing architectures. To wrap up, this project is to propose a computational methodology to create complexity and diversity. With a simple geometry context, architects can have a highly diverse category for design. By adopting this method, the potential of geometry can thus be revealed.

ARGO | Construction Lines

Construction line | What do users mean when they draw this?

In the second semester at GT, we tried to generalize the shape recognition for more applications. Instead of recognizing those predefined shapes such as triangles, quadrilaterals, pentagons, etc, we are aiming to expand the recognition to any shape, those shapes without names. This April, we completed the first prototype of the software on Rhino. Now it can recognize any embedded shape in a bigger shape. However, users may want more, for instance, two L shapes can be arranged in multiple (infinite) ways, but they may just want one specific way. Thus, to approximately position the shape relationships, we introduce the concept of construction lines to provide users more precise recognition. Here is a demo video link:

Fig.01 - Implementation of Construction Line option

Video.01 - Demo of Construction Line in ARGO

CourtSpace | Update

Project Updates |

To improve the previous version of CourtSpace, we looked into the grammars of the federal courthouse in Austin to make CourtSpace more robust, practical and real.

Fig.01 - Grammars of Austin Courthouse

Fig.02 - Scheme of Austin Courthouse

Fig.03 - Alternative of Austin Courthouse

Fig.04 - "Two" Austin Courthouse

Fig.05 - Alternative of Austin Courthouse

Fig.06 - "Three" Austin Courthouse

Fig.07 - Alternative of Austin Courthouse 

Fig.08 - "Ring" of Austin Courthouse

Smart 3D Atlantta

Project Description | Smart 3D Atlanta

Smart 3D Atalanta is a project aimed to create a 3D model platform for urban researchers to develop applications with city data. In this project, we choose City of Atlanta as the first implementation. The city model of Atlanta is imported into the Cesium geographic platform which is an open-source platform developed on Bing map. Each building in City of Atlanta is loaded into the platform individually as an entity. Thus, the data visualization can happen in building scale for users' further applications. The data used in this test is directly from Google Place API, MARTA, City of Atlanta and other data providers.

Smart 3D Atlanta now is available on the web sever of DBL (Digital Building Lab), School of Architecture, Georgia Tech. Here is the link:

https://dcom.arch.gatech.edu/kurthello/apps/atlanta/index.html

Fig.01 - Screen shot of Smart 3D Atlanta (Radius coloring)

In this web service, the building will be highlighted when user moves cursor on the building. When user clicks on the building, the information (picture, address and name) from Google Place API will be shown in a info box. Also, there is a menu on the left hand side for user to switch to different color mode (data), show/hide the buildings, buses and stops.

Fig.02 - Screen shot of Smart 3D Atlanta (Heatmap)

In the implementation, the data of bus routes are from MARTA real-timely and each bus has its information. If the bus is late, it turns to red. In other words, users can monitor MARTA buses real-timely. The screen shot below shows the implementation.

Fig.03 - Screen shot of Smart 3D Atlanta (buses)

In this 3D city model, each bus stop can be shown/hidden. The buses and stops are also can be highlighted when users move mouse on them, and click it for more details.

Fig.04 - Screen shot of Smart 3D Atlanta (bus stops)

Fig.05 - Screen shot of Smart 3D Atlanta (building information)

Small 4-wall Architectures

Project Description |

Small 4-wall architecture is a conceptual project inspired by Louis I. Kahn. In Louis I. Kahn's plans, the simple geometries such as squares, triangles, rectangles are composed as a geometric context. And, some lines are eliminated and some lines are kept to create openings, circulations and spaces. This project is aimed to explore the compositions of 4 lines by using ARGO. In each plan shown here, there are 4 lines with various compositions, for example, one L-shape (2 lines) plus one Cross-shape (2 lines), one T-shape (2 lines) plus two floating lines, or 4 floating lines.

Fig.01 - Louis I. Kahn, Dominican Sisters’ Convent, First Floor Plan, Media, Pennsylvania, 1965-1968

4-line figures and 4-wall architectures |

To explore the possibilities of 4-line compositions, ARGO is used in this test. In the beginning, some simple geometries are placed together to form the context. Then, the user can draw any 4-line shape and input the shape to ARGO and it will list out all the isomorphic results. Some compositions have a lot of topological results (more than 1900), some compositions only have less than 8 topological results. By selecting some interesting results and thickening the lines to form the walls, small architectures with 4 walls are presented.

Fig.02 Compositions of L-shape and T-shape (Context: Two Squares, One Triangle)

Fig.03 Compositions of X-shape and T-shape (Context: Two Squares, One Triangle)

Fig.04 Compositions of J-shape (Context: Two Squares, One Triangle)

Fig.05 Compositions of C-shape/Z-shape and One floating line (Context: Two Squares, One Triangle)

 Fig.06 - Compositions of L-shape and T-shape (Context: Two Triangles)

  Fig.07 - Compositions of L-shape and two floating lines (Context: Two Triangles)

  Fig.08 - Compositions of 4 floating lines (Context: One Triangle and One Square)

  Fig.09 - Compositions of two L-shapes (Context: Two Squares)

 Fig.10 - Compositions of L-shape and T-shape (Context: Two Squares)

 Fig.11 - All compositions of L-shape and T-shape (Context: Two Squares)

Fig.12 - Small 4-wall Architecture example