Related papers: Build Boy's Surface
Computer animations often lack the subtle environmental changes that should occur due to the actions of the characters. Squealing car tires usually leave no skid marks, airplanes rarely leave jet trails in the sky, and most runners leave no…
3D Reconstruction of moving articulated objects without additional information about object structure is a challenging problem. Current methods overcome such challenges by employing category-specific skeletal models. Consequently, they do…
To study the preference of infants for contingency of movements and familiarity of faces during self-recognition task, we built, as an accurate and instantaneous imitator, a real-time face- swapper for videos. We present a non-constraint…
In this note we present a computational approach to the construction of ovoids of the Hermitian surface and show some related experimental results.
In this paper, we analyze the problem of constructing a surface pencil from a given spacelike (timelike) line of curvature. By using the Frenet frame of the given curve in Minkowski 3-space, we express the surface pencil as a linear…
We show that there are a finite number of possible pictures for a surface in a tetrahedron with local index $n$. Combined with previous results, this establishes that any topologically minimal surface can be transformed into one with a…
This is the first in a series of papers where we develop new structural elements on singular area minimizing hypersurfaces, the skin structures. They disclose previously unapproachable and largely unexpected geometric and analytic…
In this primer, we will describe a number of projects that can be completed with a 3D printer, particularly by mathematics professors and their students. For many of the projects, we will utilize Mathematica to design objects that…
Surfaces are typically represented as meshes, which can be extracted from volumetric fields via meshing or optimized directly as surface parameterizations. Volumetric representations occupy 3D space and have a large effective receptive…
The task of style transfer for 3D Gaussian splats has been explored in many previous works, but these require reconstructing or fine-tuning the splat while incorporating style information or optimizing a feature extraction network on the…
The design and fabrication of soft robot hands is still a time-consuming and difficult process. Advances in rapid prototyping have accelerated the fabrication process significantly while introducing new complexities into the design process.…
We discuss well known geometric constructions via paper-folding. The note is written primary for school students.
Recent advancements in Text-to-3D modeling have shown significant potential for the creation of 3D content. However, due to the complex geometric shapes of objects in the natural world, generating 3D content remains a challenging task.…
We construct embedded closed minimal surfaces in the round three-sphere, resembling two parallel copies of the Clifford torus, joined by m^2 small catenoidal bridges symmetrically arranged along a square lattice of points on the torus.
We introduce the concept of pseudo-trisections of smooth oriented compact 4-manifolds with boundary. The main feature of pseudo-trisections is that they have lower complexity than relative trisections for given 4-manifolds. We prove…
Given a unirational parameterization of a surface, we present a general algorithm to determine a birational parameterization without using parameterization algorithms. Additionally, if the surface is assumed to have a birational…
We present a technique for a complete 3D reconstruction of small objects moving in front of a textured background. It is a particular variation of multibody structure from motion, which specializes to two objects only. The scene is captured…
This paper proposes a simple and efficient method for the reconstruction and extraction of geometric parameters from 3D tubular objects. Our method constructs an image that accumulates surface normal information, then peaks within this…
The purpose of this short paper is to describe a project to manufacture a 3D-print of a pendant that includes a logo. The methods described in this paper involve processing the image of the logo through a Mathematica script. These methods…
The conchoid of a surface $F$ with respect to given fixed point $O$ is roughly speaking the surface obtained by increasing the radius function with respect to $O$ by a constant. This paper studies {\it conchoid surfaces of spheres} and…