K9K | System of Shape

System of Shape | Classification system for shapes

How to differentiate two shapes? Where is the difference between two shapes? While we are talking about a shape, we are talking about a specific shape, or the class of shape? When we say "triangle", we mean a specific triangle, or shapes with the features of triangle? How do we classify shapes? In what levels? With what features? Based on what features we are able to say "Hey! These two shapes are different" ? Do we have a system to classify shapes? I know we have a system to classify nature, but how about shapes? What if we want to classify shapes, what system we can use? Based on what criteria? Eyes? Maths? Anything else? Can we ask someone to draw a shape we want, for instance: "Please draw a shape, this shape has three lines, six vertices. Two lines are jointed together with a vertex and the other line has an intersection with one line and has another intersection with another line. One intersection is a T-like intersection and the other is a X-like intersection." Can she/he draws a shape for us based on this description?

Here are two shapes we may think they are different. However, both shapes have three lines, an "L" and a floating line. Both shapes have three construction lines and these three construction lines have the same configuration. Briefly, they have the same structure (they are isomorphic) and they have the same underlying lines (construction lines). So, why they are different? The difference is the spatial relationship. The way the "L" and the floating line are arranged. Thus, here is a question: what kind of features we need to differentiate them or what information (data) we need? Good news is, we already found the features! Here are some examples:

Figure 01 - Differentiating the shapes with different spatial relationship

Another example we are interested in is "K" and "Ψ". These two shapes have the same structure (yes, they are isomorphic again) and they both have the same number of edges (lines), vertices including endpoints and intersections. The adjacency relationships among vertices are the same. So, again, why they are different? One more time, the simple answer is spatial relationship. We can view these two shapes as a composition with three lines with an arrangement that two "legs" connecting to one "spine". The difference is how these two legs are arranged. Are both legs in the same "side" like a "K"? Or, are these two legs are in different sides like a "Ψ"? What features we need to differentiate them? Or, how do we make the descriptions for these two shapes (to distinguish them)? Fortunately, we already found the features! Here are some tests:

Figure 02 - Differentiating "K" and "Ψ"

This kind of discussion can be also on "N" and "C". "N" and "C" are isomorphic, both shapes are a polygon with three line segments. Both shapes are a "continuous" polygon and the spatial difference is how these three segments are arranged. The features we used to differentiate "N" and "C" are the same as we used to differentiate "K" and "Ψ". Here are some tests:

Figure 03 - Differentiating "N" and "C"

Let's take a look at one more example: "Z" and "S". Again, these two shapes are isomorphic. Both shapes are continuous polygon with five line segments and the spatial relationship are very similar. But, in some level (what are the levels? we have other levels?), they are viewed as different shapes. So, the feature we used to differentiate these two shapes is the configuration of construction lines. Construction lines can be seen as the "guide lines" for the lines in a shape, we can say that construction lines are a part of spatial relationships. So, there are four intersections of construction lines in "Z" and six intersections of construction lines in "S". That's how we differentiate them. Here are some tests:

Figure 04 - Differentiating "Z" and "S"

For a long time, I thought dealing with an issue of shape recognition. It turns out I am dealing with an issue of shape classification, just like Carl Linnaeus did. "Recognition" is based on certain features which are already known, for example, when we show a frog picture to Google, Google will give me an answer: "Hey! This is a image of a frog!" But, if I show it an image of a creature which is just discovered (it is even without a name), then Google will say "Uh...it looks like a frog, but I don't know what kind of frog it is." However, if I put this creature into Carl Linnaeus's system, this system will give me a name, a new name. This is a question of classification, instead of a question of recognition. I spent a lot of time to figure out that I am actually working on a classification problem, not a recognition problem.

Let's go back to my research. If I draw a shape which is totally new, never exists before and never has a name, how we can name it? What features I should use to classify it? What kind of system I should follow? One more question: WHY DO I NEED TO NAME IT? My answer is simple:  ONCE WE NAME IT, WE CAN USE IT!

Merry Christmas!

Project Description | Folding Christmas tree from K9K!

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