Related papers: Build Boy's Surface
This is an introductory article about the Boy surface. Boy found 1901 that $\mathbb{R}P^2$ can be immersed into $\mathbb{R}^3$, and published it. (The image of) the immersion is called the Boy surface after Boy's discovery. We have created…
We present a simple visual description of the topology of the space of three-dimensional rotations, requiring just intuition, imagination and no advanced math.
Building robots is an engaging activity that provides opportunities for hands-on learning. However, traditional robot-building kits are usually costly with limited functionality due to material and technology constraints. To improve the…
Three dimensional (3D) structures composed of planar surfaces can be build out of accessible materials using easier fabrication technique with shorter fabrication time. To better design 3D structures with planar surfaces, realistic models…
This paper proposes a method to design protective foam for packaging 3D objects. Users first load a 3D object and define a block-based design space by setting the block resolution and the size of each block. The system then constructs a…
In this paper, we provide assembly instructions for an easy to build experimental setup in order to gain practical experience with tomography. In view of this, this paper can be seen as a complementary work to excellent mathematical…
This article is a survey article that gives detailed constructions and illustrations of some of the standard examples of non-orientable surfaces that are embedded and immersed in 4-dimensional space. The illustrations depend upon their…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…
We develop a direct and elementary (calculus-free) exposition of the famous cubic surface of revolution x^3+y^3+z^3-3xyz=1.12 pages. We have added a second elementary proof that the surface is of revolution.
We address the problem of texturing flat surfaces by spray-painting through 3D printed stencils. We propose a system that (1) decomposes an image into alpha-blended layers; (2) computes a stippling given a transparency channel; (3)…
In the Euclidean unit three-ball, we construct compact, embedded, two-sided free boundary minimal surfaces with connected boundary and prescribed high genus, by a gluing construction tripling the equatorial disc. Aside from the equatorial…
Design prototyping involves creating mockups of products or concepts to gather feedback and iterate on ideas. While prototyping often requires specific parts of objects, such as when constructing a novel creature for a video game, existing…
For designing a wide range of everyday objects, the design process should be aware of both the human body and the underlying semantics of the design specification. However, these two objectives present significant challenges to the current…
In this paper, we give several simple methods for drawing a whole rational surface (without base points) as several Bezier patches. The first two methods apply to surfaces specified by triangular control nets and partition the real…
Shape fabrication from developable parts is the basis for arts such as papercraft and needlework, as well as modern architecture and CAD in general, and it has inspired much research. We observe that the assembly of complex 3D shapes…
A simple method of constructing the 3D surface of non-transparent micro-objects by extending the depth-of-field on the whole attainable surface is presented. The series of images of a sample are recorded by the sequential movement of the…
We construct a surface of general type with invariants \( \chi = K^2 = 1 \) and torsion group \( \Bbb{Z}/{2} \). We use a double plane construction by finding a plane curve with certain singularities, resolving these, and taking the double…
Drawing is a fun and intuitive way to create a character, accessible even to small children. However, animating 2D figure drawings is a much more challenging task, requiring specialized tools and skills. Bringing 2D figures to 3D so they…
This paper aims to develop the mathematical representation of a surface generated by elliptical arcs joining the sides of a regular polygon to a point lying vertically upward on the central axis of the polygon. The volume of the…
Developability refers to the process of creating a surface without any tearing or shearing from a two-dimensional plane. It finds practical applications in the fabrication industry. An essential characteristic of a developable 3D surface is…