Related papers: Hands-on Tropical Geometry
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…
Cylindrical algebraic decomposition (CAD) is an important tool, both for quantifier elimination over the reals and a range of other applications. Traditionally, a CAD is built through a process of projection and lifting to move the problem…
A tropical complete intersection curve C in R^(n+1) is a transversal intersection of n smooth tropical hypersurfaces. We give a formula for the number of vertices of C given by the degrees of the tropical hypersurfaces. We also compute the…
In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces.…
Representing a 3D shape with a set of primitives can aid perception of structure, improve robotic object manipulation, and enable editing, stylization, and compression of 3D shapes. Existing methods either use simple parametric primitives…
The generation of industrial Computer-Aided Design (CAD) models from user requests and specifications is crucial to enhancing efficiency in modern manufacturing. Traditional methods of CAD generation rely heavily on manual inputs and…
Ruled surface is widely used in engineering design such as parting surface design of injection mold and checking surface design of checking fixture, which are usually generated by offsetting 3D curves. However, in 3D curve offset, there…
Tropical geometry is sensitive to embeddings of algebraic varieties inside toric varieties. The purpose of this paper is to advertise tropical modifications as a tool to locally repair bad embeddings of plane curves, allowing the…
We study the notion of singular tropical hypersurfaces of any dimension. We characterize the singular points in terms of tropical Euler derivatives and we give an algorithm to compute all singular points. We also describe non-transversal…
This paper introduces a method for learning to generate line drawings from 3D models. Our architecture incorporates a differentiable module operating on geometric features of the 3D model, and an image-based module operating on view-based…
Crochet provides a superior method for the production of two-dimensional surfaces from one-dimensional material. Compared to any of the other known processes to generate constant flat, spherical or hyperbolic shapes, it is the most flexible…
In this survey, we discuss linear series on tropical curves and their relation to classical algebraic geometry, describe the main techniques of the subject, and survey some of the recent major developments in the field, with an emphasis on…
In this paper, we present TEXTure, a novel method for text-guided generation, editing, and transfer of textures for 3D shapes. Leveraging a pretrained depth-to-image diffusion model, TEXTure applies an iterative scheme that paints a 3D…
We enumerate complex curves on toric surfaces of any given degree and genus, having a single cusp and nodes as their singularities, and matching appropriately many point constraints. The solution is obtained via tropical enumerative…
We describe a new method for computing tropical linear spaces and more general duals of polyhedral subdivisions. It is based on Ganter's algorithm (1984) for finite closure systems.
In the context of additive manufacturing we present a novel technique for direct slicing of a dilated or eroded volume, where the input volume boundary is a triangle mesh. Rather than computing a 3D model of the boundary of the dilated or…
In this paper we develop a combinatorial abstraction of tropical linear programming. This generalizes the search for a feasible point of a system of min-plus-inequalities. It is based on the polyhedral properties of triangulations of the…
In this paper we present a practical approach for generating an occlusion-free textured 3D map of urban facades by the synergistic use of terrestrial images, 3D point clouds and area-based information. Particularly in dense urban…
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…
Duality of curves is one of the important aspects of the ``classical'' algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using…