Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1410.3018

A mathematical design and evaluation of Bernstein-Bezier curves' shape features using the laws of technical aesthetics

Rifkat I. Nabiyev·Rushan Ziatdinov
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present some notes on the definition of mathematical design as well as on the methods of mathematical modeling which are used in the process of the artistic design of the environment and its components. For the first time in the field of geometric modeling, we perform an aesthetic analysis of planar Bernstein-Bezier curves from the standpoint of the laws of technical aesthetics. The shape features of the curve segments' geometry were evaluated using the following criteria: conciseness-integrity, expressiveness, proportional consistency, compositional balance, structural organization, imagery, rationality, dynamism, scale, flexibility and harmony. In the non-Russian literature, Bernstein-Bezier curves using a monotonic curvature function (i.e., a class A Bezier curve) are considered to be fair (i.e., beautiful) curves, but their aesthetic analysis has never been performed. The aesthetic analysis performed by the authors of this work means that this is no longer the case. To confirm the conclusions of the authors' research, a survey of the "aesthetic appropriateness" of certain Bernstein-Bezier curve segments was conducted among 240 children, aged 14-17. The results of this survey have shown themselves to be in full accordance with the authors' results.

Explore related subjects

cs.GR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Rifkat I. Nabiyev, Rushan Ziatdinov. 2014-10-11. A mathematical design and evaluation of Bernstein-Bezier curves' shape features using the laws of technical aesthetics. https://doi.org/10.13187/md.2014.2.6

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Constrained Program Generation for 3D Reaction Animation with a 0.8B Model

Visualizing a chemical reaction requires making its molecular changes visible while keeping the animation faithful to the stated chemistry. Equations, structural diagrams and molecular viewers provide complementary descriptions, but assembling an interactive three-dimensional explanation still requires specifying the changes and checking their consistency. We present ChemXRG, a domain-specific language (DSL) framework that addresses this gap by representing a reaction animation as an executable program. Persistent atom identifiers and explicit bond, charge and grouping operations connect the symbolic reaction to the displayed transformation. This shared representation lets generation, verification and rendering operate on the same account of what changes. Given known, atom-mapped reactant and product structures, reaction-grounded constraints fix input-determined facts and restrict action choices; execution checks validate the resulting transformation before geometry and frames are constructed. We implement this paradigm with a reaction-program corpus and ChemQwen, a trained 0.8B DSL generator. Paired and component evaluations show improved compiler acceptance and normalized full-program agreement under input-conditioned constraints, while identifying remaining failures that require execution checks. A public browser application demonstrates the connection from symbolic reaction descriptions to inspectable programs and interactive 3D animations.

cs.GR↗
arXiv2026

NaRPA: Navigation and Rendering Pipeline for Astronautics

This paper presents the applications of scientific ray-tracing in modeling and simulating light transport for space-borne image data generation. A ray-tracing engine, the Navigation and Rendering Pipeline for Astronautics (NaRPA), is introduced as a rendering framework to generate virtual datasets and support simulations for robust navigation pipelines. Sensor and environment models that enable the synthesis of space-to-space and ground-to-space virtual observations are presented. The work demonstrates the capabilities of simulating passive and active vision-based sensors using NaRPA to facilitate the design, testing, and verification of aerospace visual navigation algorithms. Additionally, the paper describes a velocimeter LiDAR model and its statistical validation with experimental data.

cs.GR↗
arXiv2026

VoroUDF: Meshing Unsigned Distance Fields with Voronoi Optimization

We present VoroUDF, an algorithm for reconstructing high-quality triangle meshes from Unsigned Distance Fields (UDFs). Our algorithm supports non-manifold geometry, sharp features, and open boundaries, without relying on error-prone inside/outside estimation, restrictive look-up tables nor topologically noisy optimization. Unlike fixed-grid approaches, our Voronoi-based formulation optimizes a set of movable seeds that travel freely along the iso-surface, jointly minimizing a tangent-plane fitting energy, driven by a fixed set of surface samples queried once from the UDF and its gradient, and a repulsion energy that keeps the seeds evenly distributed. It achieves significantly improved topological consistency and geometric fidelity compared to existing methods, while producing lightweight meshes suitable for downstream real-time and interactive applications.

cs.GR↗