What is a pseudodisk?

Question

I'm reading a paper on computational geometry and the term pseudodisk popped up. A simple googling doesn't provide me with any mathematical definitions.

Could anyone please explain to me the definition of a pseudodisk?

Edit: For more context: "It has been proved that for geometric objects with finite VC dimension d, there exist $\epsilon$-nets of size $O(\frac{d}{\epsilon}\log\frac{1}{\epsilon})$. $\epsilon$-nets of size $O(\frac{1}{\epsilon})$ exist for halfspaces in $\mathbb{R^2}$ and $\mathbb{R^3}$ and pseudo-disks in $\mathbb{R^2}$." Let me know if this is not enough.

Thanks in advance!

Please give some of the context you found that word in. – hmakholm left over Monica Mar 01 '17 at 18:13 — hmakholm left over Monica, Mar 01 '17 at 18:13
Possible duplicate of What is a pseudodisk? – Mr.Wizard Mar 01 '17 at 23:13 — Mr.Wizard, Mar 01 '17 at 23:13

score 1 · Answer 1 · answered Mar 02 '17 at 06:49

1

I could find this reference and short explanation, but nothing detailed: "A set of objects is a collection of pseudo-disks, if the boundary of every pair of them intersects at most twice." Chan and Sariel

answered Mar 02 '17 at 06:49

gue

328

score 1 · Answer 2 · answered Jul 13 '20 at 18:20

1

Consider two planar objects $o_1$ and $o_2$, each bounded by a simple closed curve. Intuitively, the pair $o_1,o_2$ is called a pair of pseudo-disks if their boundaries $\partial o_1$ and $\partial o_2$ intersect in at most two points.

answered Jul 13 '20 at 18:20

peng yu

1,271

What is a pseudodisk?

2 Answers2