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

Finding an object's center of mass using integration

Thinking about center of mass As a kid, I would sit in class and balance my pencil on my finger. What I didn't know then was that I was finding the pencil's center of mass. An object's center of mass is a point where the average weight of the object lies. In other words, the weighted position vectors of the object at this point sum to zero (source: https://www.dictionary.com/browse/center-of-mass ). The exact location of this point can be found using calculus. First, it is important to understand the moment . The moment for a two-dimensional object is given with respect to both the x- and y-axes. It is a physical characteristic of the object a certain distance from these axes. It's easiest to think about the axes as reference points for where the characteristic acts; in this case, where the mass is distributed. When computing these moments, the hardest concept to grasp is that the moment with respect to y, for example, is given by the x-coordinat...

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...

Ambiguous Objects

Introduction Ambiguous objects are very unique images or objects that create ambiguity. Ambiguity is a vague meaning of a phrase, statement, image, etc., is not explicitly defined. Ambiguous objects can be either two-dimensional or three-dimensional. For our topic today, we will be understanding how ambiguous objects work through understanding exploitation of graphical similarities between two functions of a curve. Ambiguous objects may be more commonly known as optical illusions. Some of the more commonly known optical illusions are the Rubin vase, the rabbit-duck illusion, and the Kanizsa Triangle. The image above is an example of the Kanizsa Triangle optical illusion. The spatially separated fragments give the impression of a triangle! These are just some examples of optical illusions that have been created. However, those optical illusions are two-dimensional. Now that we have a brief introduction with some common forms of ambiguous objects, we can furth...

MA 391 Composition and Communication

Search This Blog