# Questions tagged [triangulation]

For questons about triangulation, that is a) the subdivision of the plane or other topological spaces into triangles (or, more generally, simplices) or b) the methods used in surveying for locating points by measuring angles and accessible lengths of triangles

464 questions
Filter by
Sorted by
Tagged with
1 vote
19 views

### Delaunay Triangulation but in 3D

I guess this is the right place to ask this question. Let me tell you why did I ask this question, so I have a pointcloud data that I want to calculate it's volume, I know that pointcloud lib has ...
• 11
34 views

### Existence of smooth triangulation for Riemannian 2-manifold

Most proofs that I can find of the Gauss-Bonnet Theorem for a compact Riemannian $2$-manifold $M$ always start with the assumption that $M$ has a smooth triangulation, i.e. a triangulation where the ...
• 4,615
48 views

### A certain proof method for Ky Fan's sphere covering theorem

Ky Fan's theorem (1952) for sphere covering states the following: Let $A_1, A_2,\dots,A_m$ be an antipodal-free (which means $A_i\cap (-A_i)=\varnothing$) closed (can be open, let's go with closed ...
• 1,802
47 views

### Finding all empty triangles of a plane

I have a set of $N$ points ${(x_i,y_i)}_{i=1,...,N}$. I am looking for an efficient algorithm to find the set of all empty triangles (i.e., that do not contain any points). The brute-force method that ...
30 views

### How to triagulate multiple sound locations

Other people posed the question of how to triangulate sound from multiple locations. Approximate (but as accurate as it can) location of sound Sound Triangulation My question is how to seperate ...
1 vote
19 views

• 596
1 vote
110 views

### Non-delaunay triangulation of a set of points and its convex hull boundary

I have a set of n random points on a 2D plane, and its convex hull boundary. Some points lie interior to the convex hull boundary. I want to triangulate this in a non-delaunay random fashion, such ...
• 63
60 views

### Rotating matrices to display data from radar onto a HUD

I'm trying to write a code (in-game scripts) that takes data from radar (distance, azimuth, elevation) and displays points on a HUD in front of the player. Yesterday, I've managed to visualize radar ...
39 views

212 views

### Lifting triangulation by branched covering map

Let $X, Y$ be compact connected manifolds of the same dimension, and let $f : X \to Y$ be a branched covering with finitely many branch points. (For example, $f$ could be a holomorphic function ...
• 2,625
77 views

### A single-color path in a two-color triangulated square

Take any triangulation of a square (= a partition into triangles such that any two triangles are either disjoint or intersect in a common face). Suppose that there are no triangulation vertices on the ...
• 10.8k
1 vote
29 views

### Triangulation of the complement VS Complement of the triangulation

Consider a triangulable space $X$ in the $n$-sphere $S^n$ whose complement $X^c=S^n\backslash X$ is also triangulable: there exists finite simplicial complexes $T_X$ and $T_{X^c}$ whose geometric ...
• 13
98 views

### How do you find an unknown point via the known location of other points and the angle of the unknown point when facing the known points?

Based on this previous question, but slightly different: Find a point using multilateration or triangulation Suppose we have 3 points in a 3d coordinate system with the following locations. A=(100,0,0)...
1 vote
28 views

### Isolate downward-facing faces of a convex hull

long time fan / first time poster here! My question: is there an efficient algorithm for isolating just the downward-facing faces of a 3D convex hull? In two dimensions, if one draws a line from the ...
67 views

### Theorem 5, Section 6.4 of Hoffman’s Linear Algebra

Let $V$ be a finite-dimensional vector space over the field $F$ and let $T$ be a linear operator on $V$. Then $T$ is triangulable if and only if the minimal polynomial for $T$ is a product of linear ...
• 4,227
### Ratio of largest to smallest distance in a set of six points is $\ge \sqrt 3$?
Here is problem A1 of 25th Putnam 1964. Let $A_1, A_2, A_3, A_4, A_5, A_6$ be distinct points in the plane. Let $D$ be the longest distance between any pair, and $d$ the shortest distance. Show that \$...