Ambiguous objects

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 to make a very simple burger. Then a burger will include an outer outline (the shape of the entire burger). From another angle, I want to see the mixed food in the burger, such as lettuce leaves and cheese. So in this case, we first make out the shape of the appearance we hope to get:

The equations of "bread" are (1-x^10)^5 and -(1-x^10)^5, which are the upper and lower half of "bread," respectively. "Lettuce" is a cos function, obtained by changing the value, the equation is 0.2*cos(900*x)+0.2, and the equation of "cheese" is (0.2-0.2^(x^10))^7. The overall look is good, so our goal is to make an object to see the outline of the burger from one direction and lettuce and cheese in the other direction. After the graphics are generated, we can get this shape:

It looked a little strange, it looked like a paw, and the outline of the hamburger was not visible. But this is normal because only through a specific angle can we really see the pattern we want, then by displaying the previous function pattern and the formed object at the same time, we can easily find the pattern we want.

This is what I want. It looks great, and its appearance is somewhat confusing, but from a specific angle, it can show people its special features.

Why I chose this: Just like the first picture, I want to make a crease and turn it into a straight line (or a curve that looks flat). This looks cool, so lettuce is transformed into bread Thoughts, and if there are too many creases on the other line, the overall look is not very coordinated. At this time, I suddenly thought of Hamburg, so I made a model like this.

Size:x: 62.71 y: 42 z: 47.26

Comments

Do Over: Integration Over a Region in a Plane

Throughout the semester we have covered a variety of topics and how their mathematical orientation applies to real world scenarios. One topic we discussed, and I would like to revisit, is integration over a region in a plane which involves calculating a double integral. Integrating functions of two variables allows us to calculate the volume under the function in a 3D space. You can see a more in depth description and my previous example in my blog post, https://ukyma391.blogspot.com/2021/09/integration-for-over-regions-in-plane_27.html . I want to revisit this topic because in my previous attempt my volume calculations were incorrect, and my print lacked structural stability. I believed this print and calculation was the topic I could most improve on and wanted to give it another chance. What needed Improvement? The function used previously was f(x) = cos(xy) bounded on [-3,3] x [-1,3]. After solving for the estimated and actual volume, it was difficult to represent in a print...

Minimal Surfaces

Minimum surfaces can be described in many equivalent ways. Today, we are going to focus on minimum surfaces by defining it using curvature. A surface is a minimum surface if and only if the mean curvature at every point is zero. This means that every point on the surface is a saddle point with equal and opposite curvature allowing the smallest surface area possible to form. Curvature helps define a minimal surface by looking at the normal vector. For a surface in R 3 , there is a tangent plane at each point. At each point in the surface, there is a normal vector perpendicular to the tangent plane. Then, we can intersect any plane that contains the normal vector with the surface to get a curve. Therefore, the mean curvature of a surface is defined by the following equation. Where theta is an angle from a starting plane that contains the normal vector. For this week’s project, we will be demonstrating minimum surfaces with a frame and soap bubbles! How It Works Minimum surfac...

Do Over: Ruled Surfaces

Why to choose this project to repeat For the do over project, I would like to choose the ruled surfaces. I don't think my last project was creative, and the 3D printed effect was not very satisfactory. In the previous attempts, all the lines are connected between a straight line and a circle. This connection structure is relatively uncomplicated. The printed model has too many lines, resulting in too dense line arrangement. The gaps between lines are too small, and the final effect is that all the lines are connected into a curved surface, which is far from the effect I expected. What to be improved In this do over project, I would like to improve in two aspects. Firstly, a different ruled surface is chosen. In the previous model, one curve is a unit circle on the \(x-y\) plane, and the ruled surface is a right circular conoid. In this do over project, it is replaced by two border lines. Each borderline is in the shape of an isosceles right triangl...

MA 391 Composition and Communication

Search This Blog