MA 391 Composition and Communication

Introduction You have probably seen an optical illusion before. They are known to play tricks with our brain. We will be using ambiguous objects to create an optical illusion. In our illusion we will create an object that looks different from two different angles. In the picture below we can see a quick example of an optical illusion. We can see there are two different shapes that are created. The one on the bottom is made up of squares, but that same model has a reflection of circles. From the single model we are able to see two very different shapes. Ambiguous Object Example To create an optical illusion in 3-dimensions we can use almost any shape we want. For this optical illusion the two shapes that I have chosen are a heart and an infinity sign. To create the heart, I have used the equations below and can be seen in the image beside it. \begin{align*} x(t)&= \sin(t)^3 \\ y(t)&= \cos(t)+\cos(t)^4 \\ z(t)...

In the second dimension, two different curves could never be portrayed as one curve yet still be observed separately. If one has a different \(y\) value at a certain \(x\), then there's no way they can be portrayed as one curve. This changes when you add another dimension, though. In the second dimension, the only way perspective can change is by rotating the plane, translating the plane, or making the plane smaller. These perspective changes don't make the curve any different though. A perspective change in the third dimension, however, can make a curve look drastically different. A circle in the \(xy\) plane looks like a circle when looking in the \(z\) direction. When looking in the \(x\) or \(y\) direction, though, a circle would look like a straight line. This kind of property enables us to make one curve look like two different curves depending on the perspective. The two perspectives we will be observing our curve from are orthogonal to the \(yz\) plane...

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...

How an ambiguous object works Ambiguous objects are exactly what they sound like - ambiguous! Imagine you and your friend are out on a hike and find an ambiguous object in the wild. You decide to stand on opposite sides of it (and 45 degrees up in the air). You and your friend look something like this from where you are floating: Your friend says they see a circle from where they're standing, but you disagree. You see a square! How is that possible? You are standing along the y-axis, and the lines from your eyes to the curves of the object are perpendicular to the vectors \(\langle 0,1,1 \rangle\) and \(\langle 0,-1,1 \rangle\). The equation through \((x,f(x),0)\) and parallel to \(\langle 0,1,1 \rangle\) is \(r_{A} (s) = (x,f(x)+s,s)\). The equation through \((x,g(x),0)\) and parallel to \(\langle 0,-1,1 \rangle\) is \(r_{B} (t) = (x,g(x)-t,t)\). This is when you are observer A and your friend is observer B. We can find the point of intersection...

Ambiguous objects are visual information that makes people feel different from different directions and angles. Even though they are the same objects, they will still allow the observer to draw different conclusions. Ambiguous objects often have two different characteristics to induce observers to draw two different conclusions. So in simple terms, different angles look different. So when applied to three-dimensional graphics, we can create a certain object, making it look different from diagonally forward and diagonally behind. This is the theme of this time. Oh roar, the picture shows two different angles through the mirror. It looks directly that the top of the object is a rhombus. However, through the refraction of the mirror, we can know that its shape looks round, but in fact, from From other angles, it should be neither a circle nor a diamond, so let's try to make a similar object so that it can see different shapes from different angles. Then I try...

Ambiguous objects are objects that create an optical illusion to the human eye by exploiting the similarities between two objects. Ambiguity can occur between two dimensional images or shapes but can also appear in three dimensional objects. For example, you've probably seen sometime of ambiguous, optical illusion as an image in a psychology class at some point. The image below (from an article on https://www.nature.com/articles/s41598-018-31129-7) shows you an old woman, as well as a young woman depending on how you view the image. Do you see it? You are only able to see one image at a time because the artist draws one feature that doubles as a different feature in the other image. For example, in the above image, the jaw line of the young woman doubles as the chin of the old lady. Do you see it now? It's a pretty good trick for your mind. Ambiguous objects in three dimensions can be even harder to spot sometimes, but they are cons...

Have you ever had your mind blown by some sort of obstacle illusion? Where, when you look at some object one way, you see one shape and by slightly changing your point of view you see something completely different? This idea of constructing what feels to be an impossible shape was our task for this week! The goal is that by having two observers looking down at the object at different spots, they will see two completely different shapes. Below you will find an example of an ambiguous object so you can begin to get some sort of familiarity of what all is going on throughout the rest of this post! As you can see, when looking directly at the object from one direction you see one shape, but when changing your point of view, you see something else. While the concept of funny shapes that appear to be different may seem simple, since we are able to see many examples of them on the internet, they are fairly difficult to construct. I will begin by showing you the shape I...