Scaling Your World Project
Summary
The purpose of the Scaling Your World project was to utilize newly learned math techniques to scale an object up or down. The proportions all needed to kept the same and all math needed to be done by hand. For instance, the object I chose to scale down was the USS Enterprise (NCC-1701)("NCC-1701. No bloody A, B, C, or D!"). The original ship was 289 metres, and I took the easy route, scaling my model down to one metre (Scaling Factor Of 1/289). The general ideal to be taken away is the effect of scaling an object as well as the nature of scaling (maintaining proportions, etc).
Benchmarks
Benchmark.1Benchmark 1’s topic was to get into groups and decide what we were going to scale up/down.
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Benchmark.2Benchmark 2’s goal was to ensure that we had the calculations done correctly to maintain the proportions of our design.
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Benchmark.3Benchmark 3, I did not finish on time*, but it was the point where we were supposed to turn in our final construction. *I did not finish this on time because my project was quite ambitious, and I was given an extension.
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Benchmark.4Benchmark 4 was a point where our DP posts were due (this page).
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Concepts Learned
CongruenceCongruence is the definition of relating two identical shape, in shape, size, and side proportions. Rigid transformations will not affect a shape’s congruency state.
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SimilaritySimilarity is the comparison between two shapes that have identical side proportion ratios, but have been scaled or have undergone any other non-movement transformations.
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Ratios And Proportions |
Proving Similarity |
Ratios and proportions, are the relationships between side lengths or between shape scaling. Ensuring that side length ratios and proportions are identical between two separate shapes is integral to determining whether it is congruent/identical. The ratios between shape sizes are also important for determining whether two shapes are identical or congruent. (Congruent Size Ratio = 1:1)
Dilation And Point Of DilationDilation is the act of scaling an object while maintaining its side length ratios. A dilated object would be classified as an identical shape and not a congruent one. Scale is measured by scale factors; for instance a shape scaled up by a factor of 2 would be scaled up 2/1 or a 2:1 relationship. A center of dilation is a point at which the shape scales from. This point, whether on the dilated shape or on the original, will be in the same location relative to the environment it was scaled in.
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Confirming that the side length proportions are the same, and therefore the angle proportions, will ensure that the two shapes are similar, however if you wanted to prove congruency, you must see to it that the actual side lengths are identical as well as the proportions.
Dilation's Affect On Area And PerimeterDilation has an obvious effect on perimeter and area, changing them drastically as you scale up/down. The equations that I developed in an earlier worksheet are as follows: Dilated Perimeter = Original Perimeter*Scale Factor and Dilated Area = Original Area*Scale Factor^2. I got these by analyzing data sets given to me on the worksheet and by comparing homebrewed examples.
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Connection To Scaling My World
My model Enterprise is a dilated model of the "Original", meaning it is of similar proportions, but is scaled down, so it is not congruent, but similar. My scale factor for the Enterprise is 1/289, bringing my model to a length of 1 metre. There was not a point of dilation involved because the model is individual from any x,y chart and is simply just dilated down.
Executing Benchmarks 1-4
For me, benchmark 1 was a mainly a breeze, because it would’ve been an oddity for me not to choose the Enterprise. The real problem was within which Enterprise to make (Enterprise NX-01, 1701, A, B, C, D, E, or the non-canon F). I decided on the Original Series’ NCC-1701 because it’s design was less curved and complex. Also it was a great deal smaller than it’s 685m descendant, the E. The second benchmark was relatively more difficult than the first benchmark. The math was pretty easy, the actual difficulty attributed to measuring the 1701’s features. Thankfully, the Star Trek fan base is ridiculously accurate when it comes to their fandom. I was able to acquire pixel perfect graphs detailing the ship I was planning to scale. The next benchmark was/is significantly more difficult than the rest, primarily due to material acquisition and processing. Apart of this processing phase was the creation of Illustrator files for the laser cutter. Let it be noted that this was a breeze, as I’m fluent in English and Illustrator. As of this date (9/13/16), the model is still under construction, (I needed to refit the nacelles), so I can't give a complete walkthrough of Benchmark 3’s ups and downs, but so far, so good, with the disc and (ugly) nacelles cut, with the neck, pylons, and engineering section underway. Throughout construction I will put in place some kind of documentation, both digitally, and in the physical sense.
Reflection
Although the project isn’t fully complete, I feel like I can give some instance of a reflection on the subject. For one, looking back, I wish I started earlier, as I could add more detail until the December due date. I put aside the purchasing of wood back a week or so, so that gave me a late start I never should have allowed myself to get. On another note, I wish I hadn’t chose a partner for this project, not out of spite for the partner, but in spite of myself taking over the project. Any failures I cause upon myself would echo into this partner’s grade. Whether the added pressure is an up or downside, I do not wish my procrastination habit’s consequences upon them. As far as the reflection for benchmark 3, I feel like it is going well, as construction is well relative to my Illustrator skills. So, in a general sense, I feel the project is going well, but I would have changed some configurations in the team aspect in benchmark 1.