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We present an algorithm for detecting basepoints of linear series of curves in the plane. Moreover, we give an algorithm for constructing a linear series of curves in the plane for given basepoints. The underlying method of these algorithms…
We utilise the two principles of decoupling introduced in [arXiv:2407.16108] to prove decoupling for two types of surfaces exhibiting radial symmetry. The first type are surfaces of revolution in $\mathbb R^n$ generated by smooth surfaces…
We introduce a method for learning to generate the surface of 3D shapes. Our approach represents a 3D shape as a collection of parametric surface elements and, in contrast to methods generating voxel grids or point clouds, naturally infers…
We show that the oscillatory driving of crystal surfaces can induce pattern formation or smoothening. The driving force can be of quite different origin such as a pulsed laser beam, an electric field, or elasticity. Depending on driving…
A surface is considered flexible if it allows a continuous deformation that preserves both metric and smoothness. We introduce a novel construction method, called 'base + crinkle,' for generating a broad class of non-self-intersecting…
Segregation patterns of size-bidisperse particle mixtures in a fully-three-dimensional flow produced by alternately rotating a spherical tumbler about two perpendicular axes are studied over a range of particle sizes and volume ratios using…
In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original surface can have non-trivial genus and…
We derive parametrizations of the Delaunay constant mean curvature surfaces of revolution that follow directly from parametrizations of the conics that generate these surfaces via the corresponding roulette. This uniform treatment exploits…
Additive manufacturing builds physical objects by accumulating layers upon layers of solidified material. This process is typically done with horizontal planar layers. However, fused filament printers have the capability to extrude material…
Molecular building blocks interacting at the nanoscale organize spontaneously into stable mono- layers that display intriguing long-range ordering motifs on the surface of atomic substrates. The patterning process, if appropriately…
The generalized winding number is an essential part of the geometry processing toolkit, allowing to quantify how much a given point is inside a surface, even when the surface has boundaries and noise. We propose a new universal method to…
Crumpled paper or drapery patterns are everyday examples of how elastic sheets can respond to external forcing. In this Letter, we study experimentally a novel sort of forcing. We consider a circular flexible plate clamped at its center and…
From the striped coats of zebras to the ripples in windblown sand, the natural world abounds with locally banded patterns. Such patterns have been of great interest throughout history, and, in the last twenty years, scientists in a wide…
Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…
In this paper, we study the special curves and ruled surfaces on helix hypersurface whose tangent planes make a constant angle with a fixed direction in Euclidean n-space Besides, we observe some special ruled surfaces in and give…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve has attracted much interest. In the present paper, we propose a new method to construct a surface…
Stripe patterns are ubiquitous in nature and everyday life. While the synthesis of these patterns has been thoroughly studied in the literature, their potential to control the mechanics of structured materials remains largely unexplored. In…
We present a method for the digital fabrication of surfaces whose appearance varies based on viewing direction. The surfaces are constructed from a mesh of bars arranged in a self-occluding colored heightfield that creates the desired…
There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles…
In this paper, we present a new computer-controlled weaving technology that enables the fabrication of woven structures in the shape of given 3D surfaces by using threads in non-traditional materials with high bending-stiffness, allowing…