# Questions tagged [nearest]

Questions on the usage of Nearest and creating a custom distance function for it; also on NearestNeighborGraph, RegionNearest, GeoNearest and related concepts.

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### Why does Nearest not return both equally distant values?

Define the following three vectors: a = {0., 0., 0.}; b = {-0.5, 0.4330127018922193, 0.25}; c = {-0.5, 0., 0.}; Note that the distance from a to c is the ...
86 views

### How to find the shortest distance between two regions?

I need to find the shortest distance between the two regions and the two points of the shortest distance, but the following code cannot achieve this requirement: ...
120 views

### Furthest point from nearby objects, packing a sphere on a region interior

Suppose I have a boundary $\partial\Omega$ of a region $\Omega\subset \mathbb{R}^3$ and within this are some compact objects $B_i\subset\Omega$. They could be points, lines, polygons, complex 3D ...
43 views

### How to get a NearestNeighborGraph[] for a given radius with periodic boundaries?

I'm wondering if there's a way to use NearestNeighborGraph with periodic boundaries, using all nearest neighbors within some radius. I am aware of similar custom ...
141 views

### Position of Nearest in sublist

I want to get the position of nearest value or the position of the value in a certain range. When I have the list, such as ...
36 views

### Nearest Region of a Point-cloud

For a given examplary set of points p(2D) with known NearestFunction nf ...
358 views

### Drawing lines between nearest neighbor points

I am reading a file with 4 columns (índex and 3 coordinates) and I want to plot spheres at these positions: ...
55 views

### NearestTo causes a kernel crash when applied to a list of SparseArrays [closed]

Nearest and NearestTo cause a kernel crash on Mathematica 12.0.0 for Mac OS X. (running on OS X 10.11.6) when operating on a list of SparseArray vectors. Here's my minimal breaking example: ...
64 views

### How to Create an Efficient Step Function from Data

I have list of rules from where a DateListStepPlot can be created to visualize the problem: ...
262 views

### Find the smallest and largest distance between two points distributed in 3D space

Suppose I have some 3D points, e.g. {{0, 0, 1}, {0, 0, 1.3}, {0, 1, 0}, {1.2, 0, 0}}. Now I want to find the smallest and largest distance between two points. A ...
228 views

### Efficient multicolor search

I'm hoping someone can help me improve the following fun code-snippet, which takes a target color and searches through a set of images to find the ones that most closely match: ...
26 views

### Ordering a list of elements as shortest euclidean distance between two points [duplicate]

I've got a list of points: ...
233 views

### Speeding up Nearest with multiple distance thresholds

Consider the following example of using Nearest: ...
392 views

### Is there a built-in function I can use to measure the similarity of two trees?

This is a higher level question, and I don't expect a full answer, but maybe a nudge in the right direction would help, or maybe there is a built in Mathematica function that does something very ...
230 views

### How to use Nearest as a lookup function?

I have data1 and a target point targetPts, and want to find the closest point from the data. As you can see from below, the 29th ...
157 views

### How to connect all points in a graph generated by a set of given vertexes?

I am trying to construct a tree by looking at the nearest neighbors (or just approximately nearest for higher efficient) of a set of given vertexes. I first try this:- ...
90 views

### Estimating Lyapunov exponent from a time series problem [duplicate]

I am trying to use this code for estimating L.e.: ...
232 views

### Find the element in a list of triples which has z-coordinate nearest a specified value

Here is my list coordinate {x,y,z} ...
635 views

### Finding the x-value corresponding to a y-value found using Nearest [closed]

I have a large 2d array of infinite precision named "data" of x values and y values. I am using Nearest to find the y-value closest to a specified number, say 0....
113 views

### Getting Distances from Nearest Function [closed]

I am fairly new to mathematica. I am trying to find a way to mock python's KDTree.query function in mathematica. Basically I have 9 vectors (each length two). I want to know the three closest vectors ...
218 views

### Forming tracks of coordinates depending on distance

I have a list that consists of certain number of coordinates sub-lists (here 8). (The following data are only an example to describe my problem.) ...
110 views

### Define a 3D surface for input in Region function

I am looking for the shortest distance from a 3D surface to a random point, and also for the exact point on the surface. These are the definitions and visualization. ...
319 views

### Nearest non-collinear/non-coplanar points

This is a long post. Most of it is just an introduction so the question itself is understandable. The question is in bold. Just skip to it if you want to hear the point. Everything below the question ...
85 views

### How can I get get index and distance in Nearest functions in Low Version [closed]

Nearest[{"I'm", "sorry", "Dave"} -> All, "David"] {<|"Element" -> "Dave", "Index" -> 3, "Distance" -> 2|>} However, in a WolframScript.wl file, ...
383 views

### Opposite of Nearest?

There is an useful function Nearest in Mathematica, which finds the element in the aggregate given as its 1st argument that is nearest to its 2nd argument. It is ...
109 views

### A question for Nearest [closed]

Assume that I want to get nearest 10 points of a thousand random points in a given area to original point in three-dimensional coordinate system. Does anyone know how the ...
192 views

### Using Nearest with periodic boundary conditions of a list

Take the list e = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} I want to get the nearest points but with a wraparound condition. So lets say I want to find the 5 nearest ...
285 views

### How to rapidly find the nearest pairs of points in different clusters

Background For speed up this question or this question,I have such need. Current try: Suppose I have $3$ clusters of points: ...
164 views

### How to find the index of a facet of a boundary mesh region closest to a given point?

Using the RegionNearest[] function, it is possible to calculate the point, $p_{mesh}$, on a mesh region that is nearest to some input point, $p_{input}$. My ...
735 views

### Better way to use Nearest

I'm trying to write a snippet of code that, given an input value (value), checks a list of arbitrary length (data) for the ...
173 views

### Finding Nearest Element to a line in a 2 dimensional Array

I have a 2-dimensional list of data of $x$ and $y$ coordinates. I am looking for a way to get the element of the list which has the closest $y$ value to a given $y$ value. I tried using ...
230 views

In the following example Nearest finds the nearest values between list1 and list2 and ...
698 views

### Remove 2D points where nearest neighbor exceeds certain distance

I have the following 2D points: ...
427 views

### Mean distance beween nearest 2 coordinates

I have as an example the following 2d-coordinates: ...
327 views

### Tracing 2d coordinates by using Nearest function

In 5 digital images I have determined the 2d coordinates of detected objects. The resulting coordinate list can be downloaded from here: http://pastebin.com/7bE0CEJ5 ...
216 views

### Why won't DiscretizeRegion work with a custom distance function?

I am trying (in 10.0) to create a region from a list of data points. I have created myDistance to use as the boolean test for whether or not a point should be included in the region ...
231 views

### Draw lines between all neighbours

I have seen this question, but what I want is a bit different. I have a set of data (blue points) and I would like to end up with something like this: , i.e. joining each site with all its (nearest)...
246 views

### precision and speed inefficiency issues of Nearest function with sqrt expression [closed]

Recently, Nearest has been attacked for many bugs. Some are already fixed. I am going to show some issues when Nearest applied ...
688 views

### How to get Nearest lower value?

Nearestgives me the closest value to my reference, but what if I am always looking for the closest value, which is lower than my reference? ...
227 views

### Why does Nearest not support Sqrt?

Bug introduced in 10.0.2 and fixed in 10.3.0 Simple examples with two points nf1=Nearest[{{0, 0}, {Sqrt, Sqrt}}] nf1[{0, 0}, {All, 2.1}] gives ...
760 views

### Cannot get nearest neighbors from Nearest

Bug introduced in 10 and fixed in 10.3 There still persists the failure to return 30.72 (another bug according to Daniel Lichtblau but from the developer's point of view it may be a feature). ...
393 views

### Using an ellipse as a threshold for Nearest function

The Nearest function can receive as a threshold parameter a radius to look for elements inside that. From the documentation: ...
813 views

### Find nearest distance of an interior point from perimeter

By definition, the interior point is a point inside an arbitrary region like this: In picture above, $y$ is an interior point of region. My question is how to find the distance of an interior point ...
2k views

### efficient way to give nearest neighbour and next nearest neighbour of every point in a point set

Suppose we have a point set, the points are labeled 1,2,3,....n. And p[i] is the coordinate of the point. Now I want the label of nearest and next nearest point (...