Related papers: Hands-on Tropical Geometry
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…
3D Computer-Aided Design (CAD) users need to overcome several obstacles to benefit from the flexibility of programmatic interface tools. Besides the barriers of any programming language, users face challenges inherent to 3D spatial…
We prove a correspondence theorem for singular tropical surfaces in real three space, which recovers singular algebraic surfaces in an appropriate toric three-fold that tropicalize to a given singular tropical surface. Furthermore, we…
We continue, in this second article, the study of the the algebraic tools which play a role in tropical algebra. We especially examine here the polynomial algebras over idempotent semi-fields. this work is motivated by the development of…
We present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing…
We present applications of tropical geometry to some integrable piecewise-linear maps, based on the lecture given by one of the authors (R. I.) at the workshop "Tropical Geometry and Integrable Systems" (University of Glasgow, July 2011),…
Given a curve defined over an algebraically closed field which is complete with respect to a nontrivial valuation, we study its tropical Jacobian. This is done by first tropicalizing the curve, and then computing the Jacobian of the…
We introduce the notion of resultant of two planar curves in the tropical geometry framework. We prove that the tropicalization of the algebraic resultant can be used to compute the stable intersection of two tropical plane curves. It is…
We define arroids as an abstract axiom set encoding the intersection properties of arrangements of curves. The tropicalization of the complement of arrangement of curves meeting pairwise transversely is shown to be determined by the…
This paper presents Tabby, an interactive and explorable design tool for 3D printing textures. Tabby allows texture design with direct manipulation in the following workflow: 1) select a target surface, 2) sketch and manipulate a texture…
We present a flexible interactive 3D morpho-kinematical modeling application for astrophysics. Compared to other systems, our application reduces the restrictions on the physical assumptions, data type and amount that is required for a…
Given a tropical line $L$ and a smooth tropical surface $X$, we look at the position of $L$ on $X$. We introduce its primal and dual motif which are respectively a decorated graph and a subcomplex of the dual triangulation of $X$. They…
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…
We construct isoperimetric regions from separating hypersurfaces in closed manifolds. This yields isoperimetric boundaries exhibiting a wide variety of topological types and singular sets.
A new approach for 2D to 3D garment retexturing is proposed based on Gaussian mixture models and thin plate splines (TPS). An automatically segmented garment of an individual is matched to a new source garment and rendered, resulting in…
As an important optical component, lens is widely used in scientific inquiry and production. At present, lens manufacturing mainly relies on grinding, polishing and other methods. However, these methods often require expensive equipment and…
Polygon meshes are an efficient representation of 3D geometry, and are of central importance in computer graphics, robotics and games development. Existing learning-based approaches have avoided the challenges of working with 3D meshes,…
We study algebraic and combinatorial aspects of (classical) projections of $m$-dimensional tropical varieties onto $(m+1)$-dimensional planes. Building upon the work of Sturmfels, Tevelev, and Yu on tropical elimination as well as the work…
This paper proposes a tropical geometry-based edge detection framework that reformulates convolution and gradient computations using min-plus and max-plus algebra. The tropical formulation emphasizes dominant intensity variations,…
We present a new method for multimodal conditional 3D face geometry generation that allows user-friendly control over the output identity and expression via a number of different conditioning signals. Within a single model, we demonstrate…