Related papers: Build Boy's Surface
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
This work expands further our earlier poster presentation and integration of the OpenGL Slides Framework (OGLSF) - to make presentations with real-time animated graphics where each slide is a scene with tidgets - and physical based…
This note (which makes no claim to novelty) presents a proof of the separable rational connectedness of smooth cubic hypersurfaces, in any characteristic, by showing how to explicitly construct very free curves (of degree 3) on them. -----…
The theory of geometric structures on a surface with nonempty boundary can be developed by using a decomposition of such a surface into hexagons, in the same way as the theory of geometric structures on a surface without boundary is…
We suggest a geometric visualization of the process of constructing a triangle with prescribed bisectors that makes the existence of such a triangle geometrically evident.
Texture is an essential property of physical objects that affects aesthetics, usability, and functionality. However, designing and applying textures to 3D objects with existing tools remains difficult and time-consuming; it requires…
A surface with boundary is randomly generated by gluing polygons along some of their sides. We show that its genus and number of boundary components asymptotically follow a bivariate normal distribution.
We leverage increasingly popular three-dimensional neural representations in order to construct a unified and consistent explanation of a collection of uncalibrated images of the human face. Our approach utilizes Gaussian Splatting, since…
Consider a periodical (in two independent directions) tiling of the plane with polygons (faces). In this article we shall only give examples using squares, regular hexagons, equilateral triangles and parallelograms ("unions" of two…
Let X be a minimal complex surface of general type such that its image via the canonical map is a surface; we denote by d the degree of the canonical map. In this expository work, first of all we recall the known possibilities for the…
In this paper we survey with complete proofs some well--known, but hard to find, results about constructing closed embedded minimal surfaces in a closed 3-dimensional manifold via min--max arguments. This includes results of J. Pitts, F.…
We construct the first examples of rationally convex surfaces in the complex plane with hyperbolic complex tangencies. In fact, we give two very different types of rationally convex surfaces: those that admit analytic fillings by…
Surface topography refers to the geometric micro-structure of a surface and defines its tactile characteristics (typically in the sub-millimeter range). High-resolution 3D scanning techniques developed recently enable the 3D reconstruction…
We demonstrate a simple and cost-efficient scanning confocal microscope setup for use in advanced instructional physics laboratories. The setup is constructed from readily available commercial products, and the implementation of a…
Physically-based simulation is a powerful approach for 3D facial animation as the resulting deformations are governed by physical constraints, allowing to easily resolve self-collisions, respond to external forces and perform realistic…
We characterise which simplicial surfaces can be folded onto a triangle. We define a notion of folding that incorporates the non-intersection-properties of real materials. All of the surfaces foldable onto a triangle admit a…
We develop some design examples for approximating a target surface at the final rigidly folded state of a developable quadrilateral creased paper, which is folded with a 1-DOF rigid folding motion from the planar state. The final rigidly…
We give a criterion for certain generic nondegenerate surfaces in a fake weighted projective $3$-space to have Picard number $>1$. These algebraic surfaces are of general type. We do this by considering degenerations (along an edge),…
This paper presents PlanarSplatting, an ultra-fast and accurate surface reconstruction approach for multiview indoor images. We take the 3D planes as the main objective due to their compactness and structural expressiveness in indoor…
We present a simple construction of hat tilings. The construction can be carried out by superimposing a triangular grid on a specially colored image and reading off the orientation of the tiles. We show that our construction produces valid…