# Questions tagged [geometry]

This challenge is intended to be solved by using, manipulating, or creating shapes or other geometric structures.

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### Write a function that returns an iterable object of all valid points 4-directionally adjacent to (x, y)

A very common need in algorithms classes and computer science in general is to iterate 4-directionally over a grid or matrix (such as in BFS or DFS). This seems to often result in a lot of clunky and ...
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### Random point on a sphere

The Challenge Write a program or function that takes no input and outputs a 3-dimensional vector of length $1$ in a theoretically uniform random direction. This is equivalent to a random point on ...
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### ​Plane​ ​Blow​up​

The Blow-up is a powerful tool in algebraic geometry. It allows the removal of singularities from algebraic sets while preserving the rest of their structure. If you're not familiar with any of that ...
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### Count the number of triangles

Given a list of positive integers, find the number of triangles we can form such that their side lengths are represented by three distinct entries of the input list. (Inspiration comes from CR.) ...
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### Billiard balls collision

Given the 2-dimensional positions and velocities of a pair of billiard balls right before impact, calculate their velocities after a perfectly elastic collision. The balls are assumed to be ideal ...
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### The Knight's estate

And then the King said: You fought bravely, Knight, and your deed will not be forgotten for centuries. For your valor I grant you this castle and the lands around it. Things rush me, and I can not ...
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### Construct a pentagon avoiding compass use

Rules You will start with only two elements: Points $A$ and $B$ such that $A \neq B$. These points occupy a plane that is infinite in all directions. At any step in the process you may do any ...
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### Counting generalized polyominoes

This challenge will have you count pseudo-polyforms on the snub square tiling. I think that this sequence does not yet exist on the OEIS, so this challenge exists to compute as many terms as possible ...
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### Golf the smallest circle!

The problem: Given a non-empty set of points in the Cartesian plane, find the smallest circle that encloses them all (Wikipedia link). This problem is trivial if the number of points is three or ...
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### Partition and Restructure

Given two contiguous shapes of the same area, determine the optimal way to divide the first shape into a minimum number of contiguous segments such that they can be rearranged to form the second shape....
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### Expand a hexagon

Given an ASCII art hexagon as input, output one whose sides are all one unit longer. ...
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### Dihedral group D4 composition with custom labels

The dihedral group $D_4$ is the symmetry group of the square, that is the moves that transform a square to itself via rotations and reflections. It consists of 8 elements: rotations by 0, 90, 180, ...
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### Area of a 2D convex hull

You are given an array/list/vector of pairs of integers representing cartesian coordinates $(x, y)$ of points on a 2D Euclidean plane; all coordinates are between $−10^4$ and $10^4$, duplicates ...
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### Can this container hold this much liquid?

Can this container hold this much liquid? Challenge Synopsis As you most likely know, liquids have an indefinite shape and a definite volume. As such, they always take the shape of their container. ...
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### How lit is this room? 🔥 pt. 1

Related to this question. A room is defined to be a (not necessarily convex) non-intersecting polygon, expressed as an ordered list of 2-dimensional coordinates. A sufficiently bright lightbulb is ...
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### Covering a Skyline with brush strokes

Given a non-negative integer skyline height list, answer how many uninterrupted 1-unit-high horizontal brush strokes are needed to cover it. [1,3,2,1,2,1,5,3,3,4,2]...
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### Count the Closed Polygons

Input: An NxM grid or multi-line string (or other reasonable input-format), containing only printable ASCII (unicode range ...
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### Hilbertize an image

For a computer vision app I want to do a mapping of an image, in such a way that every pixel fit hilbert curve, instead of conventional layout. So task could be as follows: Task description Given ...
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### Partitioning the grid into triangles

Goal The goal of this challenge is to produce a function of n which computes the number of ways to partition the n X 1 grid into ...
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### Drawing the Peano curve

Introduction In geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890. Peano's curve is a surjective, continuous function from the unit ...
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### Is this quadrilateral cyclic?

In mathematics, a cyclic quadrilateral is one whose vertices all lie on the same circle. In other words, every vertex is on the circumcircle of the other three. For more information, see the MathWorld ...
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### Smallest Integer Disk

This challenge is about finding the smallest disk that contains some given points. This is made somewhat trickier, however, by the fact that in this challenge, the disk's coordinates and radius must ...
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### Number of circles packed into a rectangle [closed]

Calculate the maximum number of circles of radius r that can fit in a rectangle with width x and height ...
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### Find a way to determine to which fibonacci squares a given coordinate belongs [closed]

Given a random coordinate (x,y), determine in which square (squares are referenced by their sidelength) it is (or the borders of which squares). The squares are drawn in a counter clockwise direction,...
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### Drawing convex polyiamonds

Description OEIS sequence A096004 gives the Number of convex triangular polyominoes [polyiamonds] containing n cells. It begins: ...
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### Intersection Point of Two Line Segments

Given two line segments, determine if the line segments intersect and if so, where. In the case that the two given line segments are co-linear and overlap, determine the midpoint of the overlapping ...
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### Draw a times table (also called modular multiplication circle) of a number $n$ with $k$ vertices

Not to be confused with this question. You need to draw a times table (also known as Cremona's method for cardioid generation) as shown in this video. The number $n$ and $k$ will be the inputs. ...
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### Two dozen kissing number approximations

Given a number from 1 to 24, output the kissing number to the best of current knowledge (some numbers will have more than one acceptable output). Knowledge of geometry is not essential as the outputs ...
1 vote
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### Rounded Rectangles

Challenge Given an integer greater or equal to 4, n, print a rounded rectangle of as close as possible (with a gap of 1) sides and a perimeter of n characters. Rules n is always 4 or greater, ...
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### Smallest region of the plane that contains all free n-ominoes

On Math Stack Exchange, I asked a question about the smallest region that can contain all free n-ominos. I'd like to add this sequence to the On-Line Encyclopedia of Integer Sequences once I have ...
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### Find the longest uninterrupted arc in N dimensions

See similar question for 2D case: Find the longest uninterrupted arc The challenge here is to find the longest uninterruped great circle arc around a unit hypersphere in N dimensions, with a random ...
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### Find the longest uninterrupted arc

The challenge here is to find the longest uninterruped arc around a unit circle with a random amount of points distributed in random positions around it. Here is a diagram to assist my explanation: ...
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### Triangular Lattice Points close to the Origin

Background A triangular grid is a grid formed by tiling the plane regularly with equilateral triangles of side length 1. The picture below is an example of a triangular grid. A triangular lattice ...
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### Area enclosed by perimeter loop

Find the area of a region of unit cells given its perimeter loop as a sequence of 90-degree turns. For example, take the three-cell region XX X whose perimeter ...
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### Will you be my Weaver?

I've been recently playing through 'The Weaver' and I think it presents an interesting challenge for code-golf. Premise: The Weaver is a game wherein you are given a number of ribbons coming from 2 ...
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### Diamond creator +

Challenge : Given an integer n as input. Create a diamond that is 2x the given number n. Input : Input is integer ...
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### Circle intersection area

Description : Given x and y positions of two circles along with their radii, output the area ...
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### Distance between two points on the Moon

Given latitude/longitude of two points on the Moon (lat1, lon1) and (lat2, lon2), compute the distance between the two points in ...
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### Largest rectangle in 2d array

Input The board: A 2D container (matrix, list of lists, etc.) of letters like: ...
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### Join up the rooms

So, here's a map of, let's say, a dungeon... ########## # ##### # ##### ########## ########## ########## ########## #### ## #### ## ########## Let's ...
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### Euler-Poincaré-Characteristic of Polyhedra

Given a triangulation of the surface of a polyhedron p, calculate its Euler-Poincaré-Characteristic χ(p) = V-E+F, where ...
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### Sparse Protractor

Given some positive integer n, design a protractor with the fewest number of marks that lets you measure all angles that are an integral multiple of ...
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### Stereographic projection of polyhedra

You will create a program that generates the stereographic projection of polyhedra. In particular, to keep things simple, we'll only focus on n-chamfered dodecahedron. Given a natural number ...
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### Code Golf Simulated Golf

Given a list of hole yardages, green sizes, a slice angle and a max distance, compute a golf score. Assumptions Earth is flat All greens are circular Slice angle will be between -45 and 45 degrees ...
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### Solve a Rubik's Cube

Your challenge is to write a program to solve a 3x3x3 Rubik's Cube. This challenge is based on this one from 2013, rewritten to adhere to current community standards, and reposted with the original ...
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### Integer triangles with perimeter less than n

Definition An "integer triangle" is one with integer coordinates. For example the following triangle is an integer triangle: ...
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### ​L​o​o​p​ ​I​t​

Note: The title of this question should be "Loop It", but because title needs to be at least 15 characters, there are some invisible spaces. This note is such that the challenge can be ...
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### Maximum Area of a Polygon with Vertices of a Polygon [closed]

Rules Given a list of integer coordinates, l, with a length of at least 4, and an integer n such that n is smaller than the length of l (but at least 3), return the largest area of an n-sided polygon ...
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### Find the smallest triangle encompassing the specified polygon

Input: An integer N which represents the polygon's vertices and a list of their x and y coordinates. Expected output: The smallest difference possible between the area of the(not necessarily convex) ...
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Your task is to program a mathematical function $s$, that takes a nonempty finite set $A$ of points in the 2D plane, and outputs an uncircularity score $s(A)$ that satisfies following properties:...