Skip to main content

Stereographic Projection take 2

The first time we took on stereographic projection, I discussed how it reminded me of the little kid night lights that projected starry nights onto the ceiling. When attempting to replicate the starry night, I failed and turned it into a cloudy night projection. Because I was annoyed I couldn't make it work and because right after I finished my project last time, I came up with new ideas, I decided to repeat the stereographic projection example and make it better.

Last time, I used an array of clouds out of frustration because I could not get stars to work. My clouds were each made up of four circles and then I just multiplied them across an array. Well, that was boring. And while I still haven't been able to create the perfect star, I have decided to create a recognizable constellation rather than an array. Since I still couldn't figure out how to use the hull function properly with stars, I decided to create my constellation using lines. I thought this was a genius idea but when I was finished, I realized a piece of my final sphere would be missing, so I scratched that idea too. Eventually, I decided to plot the points where a star would be and hull them to a single point above.

The constellation I chose to replicate is the big dipper because it is a fairly recognizable constellation in my opinion but for those who don't know what it looks like, you can see a picture from azcentral.com below:
I was able to make improvements from my last example by plotting individual points in specific places on the grid to form a constellation rather than just forming an array of identical shapes. I couldn't find actual points of the stars in the constellation, so I just maneuvered the location of the points until it resembled the big dipper. The image below shows the constellation I created.
While the points are pentagons and not quite stars, you are still able to see the constellation form between all of the points! My final object will be a sphere and when a flashlight is shown through the top hole, a projection of the big dipper will appear on the wall. This design was more challenging than my first example and although there was probably a simpler way to code it, my example still runs and I think the print will turn out well.

Comments

Popular posts from this blog

The Approximation of a Solid of Revolution

Most math teachers I've had have been able to break down Calculus into two very broad categories: derivatives and integrals. What is truly amazing, is how much you can do with these two tools. By using integration, it is possible to approximate the shape of a 2-D function that is rotated around an axis. This solid created from the rotation is known as a solid of revolution. To explain this concept, we will take a look at the region bounded by the two functions: \[ f(x) = 2^{.25x} - 1 \] and \[ g(x) = e^{.25x} - 1 \] bounded at the line y = 1. This region is meant to represent a cross section of a small bowl. While it may not perfectly represent this practical object, the approximation will be quite textured, and will provide insight into how the process works. The region bounded by the two functions can be rotated around the y-axis to create a fully solid object. This is easy enough to talk about, but what exactly does this new solid look like? Is...

Solids of Revolution Revisited

Introduction In my previous blog post on solids of revolution, we looked at the object formed by rotating the area between \(f(x) = -\frac{1}{9}x^2+\frac{3}{4} \) and \( g(x)=\frac{1}{2}-\frac{1}{2}e^{-x} \) around the \( x \) axis and bounded by \( x = 0 \) and \( x = 1.5 \). When this solid is approximated using 10 washers, the resulting object looks like this: When I was looking back over the 3D prints I’d created for this course, I noticed that the print for this example was the least interesting of the bunch. Looking at the print now, I feel like the shape is rather uninteresting. The curve I chose has such a gradual slope that each of the washers are fairly similar in size and causes the overall shape to just look like a cylinder. Since calculating the changes in the radiuses of the washers is a big part of the washer method, I don’t think this slowly decreasing curve was the best choice to illustrate the concept. The reason I had done this o...

Finding the Center of Mass of a Toy Boat

Consider two people who visit the gym a substantial amount. One is a girl who loves to lift weights and bench press as much as she possibly can. The other is a guy who focuses much more on his legs, trying to break the world record for squat weight. It just so happens that these two are the same height and have the exact same weight, but the center of their weight is not in the same part of their body. This is because the girl has much more weight in the top half of her body and the boy has more weight in the bottom half. This difference in center of mass is a direct result of the different distributions of mass throughout both of their bodies. Moments and Mass There are two main components to finding the center of mass of an object. The first, unsurprisingly, is the mass of the whole object. In this case of the boat example, the mass will be uniform throughout the entire object. This is ideal a majority of the time as it drastically reduces the difficulty...