Closed space?filling curves with controlled orientation for 3D printing

Dynamic Partitioning of Non-Uniform Structured Workloads with Spacefilling Curves

We discuss Inverse Spaceelling Partitioning (ISP), a partitioning strategy for non-uniform scientiic computations running on distributed memory MIMD parallel computers. We consider the case of a dynamic workload distributed on a uniform mesh, and compare ISP against Orthogonal Recursive Bisection (ORB) and a Median of Medians variant of ORB, ORB-MM. We present two results. First, ISP and ORB-MM...

Retailing with 3D Printing

Spacefilling Curves and Phases of the Loewner Equation

Similar to the well-known phases of SLE, the Loewner differential equation with Lip(1/2) driving terms is known to have a phase transition at norm 4, when traces change from simple to non-simple curves. We establish the deterministic analog of the second phase transition of SLE, where traces change to space-filling curves: There is a constant C > 4 such that a Loewner driving term whose trace i...

Geodesics Between 3D Closed Curves Using Path-Straightening

In order to analyze shapes of continuous curves in R, we parameterize them by arc-length and represent them as curves on a unit two-sphere. We identify the subset denoting the closed curves, and study its differential geometry. To compute geodesics between any two such curves, we connect them with an arbitrary path, and then iteratively straighten this path using the gradient of an energy assoc...

Autocomplete Textures for 3D Printing

Texture is an essential property of physical objects that affects aesthetics, usability, and functionality. However, designing and applying textures to 3D objects with existing tools remains difficult and time-consuming; it requires proficient 3D modeling skills. To address this, we investigated an auto-completion approach for efficient texture creation that automates the tedious, repetitive pr...