On-device research index

arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

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8 results for “form-finding”

Mathematics of stable tensegrity structuresmath.DS

New method stabilizes tensegrity structures suitable for engineering.

problem Tensegrity structures often have unstable modes unsuitable for engineering.

method Proposes a relationship between rods and strings for full-rank convexity.

result Designs a stable three-rod three-string tensegrity.

tensegrity engineering stability form-finding mathematics

2021-01-24abs ↗pdf ↗

On Elastic Geodesic Grids and Their Planar to Spatial Deploymentcs.GR

We introduce elastic geodesic grids for easy-to-fabricate, deployable structures.

problem Approximating freeform surfaces with deployable structures.

method Geodesic curves on target surfaces, kinematic mechanism, differential geometry.

result Elastic geodesic grids can approximate freeform surfaces easily and deployably.

geodesic grids elastic structures form-finding architecture freeform surfaces

2020-07-01abs ↗pdf ↗

Seifert surfaces in the four-ball and composition of binary quadratic formsmath.GT

New method uses binary quadratic forms to classify Seifert surfaces in 4-ball.

problem Classifying non-isotopic Seifert surfaces in 4-ball.

method Composition of binary quadratic forms and number-theoretic approach.

result Established a new connection between Bhargava cube and Gauss composition.

Seifert surfaces binary quadratic forms 4-ball Gauss composition Bhargava cube

2023-11-29abs ↗pdf ↗

Conformal Surface Splinesmath.DG

New boundary and point constraints for controlling conformal surfaces.

problem Controlling the geometry of surfaces defined by minimizers of conformal variational problems.

method Introducing new boundary conditions, point constraints, and flux constraints to control the metric and conformal scale factor.

result Introduces intuitive controls for exploring a subspace of conformal immersions.

conformal surfaces boundary conditions point constraints discrete conformal equivalence rigidity

2024-11-07abs ↗pdf ↗

Data-Driven Design: Exploring new Structural Forms using Machine Learning and Graphic Staticscs.LG

The aim of this research is to introduce a novel structural design process that allows architects and engineers to extend their typical design space horizon and thereby promoting the idea of creativity in structural design. The theoretical base of this work builds on the combination of structural form-finding and state…

2018-09-23abs ↗pdf ↗

The architectural application of shells whose boundaries subtend a constant solid anglemath.DG

The paper introduces surfaces with constant solid angle for designing shell structures.

problem Designing shell structures with balanced structural, spatial, aesthetic, and construction requirements.

method Proposes surfaces defined by constant solid angle at all points, using Gauss-Bonnet theorem and Newton's method.

result Constant solid angle surfaces enable control over boundary slope and span-to-height ratio, making them structurally viable.

shell structures surface geometry constant solid angle surface grids Airy stress function

2022-12-06abs ↗pdf ↗

A Nonlinear Extension of the Variable Projection (VarPro) Method for NURBS-based Conformal Surface Flatteningcs.CG

This study develops a NURBS-based method for conformal surface flattening without singularities.

problem Flatten surfaces conformally without singularities.

method NURBS-based approach with iterative refinement of input and flattening surfaces, leveraging nonlinear extension of VarPro.

result Developed a singularity-free NURBS-based method for conformal surface flattening.

NURBS Conformal surface flattening Variable projection Iterative refinement Nonlinear extension

2025-02-26abs ↗pdf ↗

Dynamics of Cayley Formsmath.DG

Investigates second-order conditions for Cayley forms in eight dimensions.

problem Natural conditions for Cayley forms in eight dimensions.

method Linear and non-linear completion of Lagrangians, parametrization of intrinsic torsion, construction of action functional.

result Two-parameter family of diffeomorphism-invariant Lagrangians, leading to Einstein equations.

Cayley forms Spin(7) structures Einstein equations Lagrangians Second-order PDEs

2024-03-25abs ↗pdf ↗