Common Tangents to Four Unit Balls in R

An Enumerative Geometry Framework for Algorithmic Line Problems in $\mathbb R^3$

We investigate the enumerative geometry aspects of algorithmic line problems when the admissible bodies are balls or polytopes. For this purpose, we study the common tangent lines/transversals to k balls of arbitrary radii and 4− k lines in R3. In particular, we compute tight upper bounds for the maximum number of real common tangents/transversals in these cases. Our results extend the results ...

Common Tangents to Four Unit Balls in R3

Modeling the Operational Speed of Tangents and Curves in Four-lane Highways Based on Geometric and Roadside Factors

Operational speed is an index that represents drivers’ speeding behaviors and shows the comfort and safety levels they experience. Many models had been proposed to predict operational speed in tangent and curve segments of highways. Most of these works had used geometric, with few of them conducted using roadside variables to predict operational speed. Also, the operational speed study in multi...

Tangents of plurisubharmonic functions

Tangents of plurisubharmonic functions Local properties of plurisubharmonic functions are studied by means of the notion of tangent which describes the behavior of the function near a given point. We show that there are plurisubharmonic functions with several tangents, disproving a conjecture of Reese Harvey.

The Expected Number of 3D Visibility Events Is Linear

In this paper, we show that, amongst n uniformly distributed unit balls in R , the expected number of maximal non-occluded line segments tangent to four balls is linear, considerably improving the previously known upper bound. Using our techniques we show a linear bound on the expected size of the visibility complex, a data structure encoding the visibility information of a scene, providing evi...