3D visualization without a computer

Plan :

My first plan was plotting 2 pollutants across every states in the United States. But it’s not easy to find pollutant level that can represent state’s trend and data representation could be awkward at small sized (in terms of territory size) states like vermont, massachusetts, and so on. So, after several days of brainstorming and examining data at EPA site, I chose Carbon Monoxide(CO) and Nitrogen Dioxide(NO2) levels in five cities in the states. They are Los Angeles, Chicago, New York, Boston, and Philadelphia. And I’ll show comparison of the 13 year average and each year’s average of the 2 pollutants levels in those five cities. Please note that I’m going to focus on comparison between the five cities.

I’ll make tetrahedron for each city and pollutant. So each city will have 2 tetrahedrons each representing CO and NO2. The volume of tetrahedron is determined by 14 year (1993~2006) average of a pollutant. So a city with bigger tetrahedron means worse air compared to other cities. Each tetrahedron is painted with various colors showing each year average. The most recent(2006) data at the bottom and the oldest data at the top of a tetrahedron. The color range chosen here is nothing to do with national standard. Blue represents the lowest among the five cities and red means the highest.

Preparation :

hardboard, any thick paper (e.g. coated paper for watercolor), quick dry glue, cutter, protractor, ruler, colored pencil, plenty amount of time, patience, music(optional).

Procedure :

Since there are five cities and a tetrahedron is used for each city, they can form a pentagon. So the pentagon base should be drawn first. More precisely, the size of five isosceles triangles that make a pentagon must be chosen wisely cause it will eventually determine the size of finished product.

The pentagon drawing at the upper left, data I used from EPA site at the upper right. And tetrahedron drawing at the lower left.

Another important factor is the height of tetrahedron. The volume of tetrahedron should represent 13 year average of a pollutant level, and it’s the most important data in my product. I wanted the highest tetrahedron would be roughly 15 centimeter ( Los Angeles ). Since I know square measure of base of tetrahedron(S), and desired height(H), the volume(V) can be calculated. 13 year CO average of Los Angeles is 5.47.  S is 89 square centimeter.  H is 15 centimeter.  So V is (S*H)/2 =  667.5 cubic centimeter.  But actual data from LA is 5.47, so I need a constant value that should be applied to all five cities for each pollutant so that their 13 year average can be scaled up to volume of tetrahedron. In LA case, it’s roughly 122. The scale constant for NO2 is roughly 14254. In short, 13 year average * scale constant = volume of tetrahedron. And with this scale constant heights of each city’s tetrahedron can be calculated. H = (13y Avg * Scale) * 2/S

Math is done. All I need to now is calculate height for each city and pollutant and draw, cut, paint, and assemble.

Tetrahedron drawing and cutting.

Now color choice for each range of value is needed because I’m going to paint them so that each year’s average also can be shown. I picked minimum and maximum value among all five city data for each pollutant. And the range is lying between those min. and max.

The data range and its matching color.

Now drawing 10 triangular pyramids, cutting them, painting them. But everything has an end. It also is almost done. And the gluing wasn’t easy and it was the hardest part. It needs patience. You apply adhesive, carefully fold the joints, and hold it for one or two minute. And repair them two or three times. Then finally, 10 tetrahedrons. 5 cities, 2 pollutants per city, 14 data points for each city and pollutant. Total 140 data points.

And the final “real” 3D visualization.