# Tagged Questions

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17k views

### How to check if 4 points form a square?

Assume I have 4 points (they are 2-dimension), which are different from each other, and I want to know whether they form a square. How to do it? (let the process be as simple as possible.)
1k views

### How to calculate figure rotation efficiently?

I have a Figure represented through a matrix of bytes (bitmap-like matrix). Example Figure is shown on the Picture 1. The goal is to find the best rotation angle of some given Figure. When Figure is ...
3k views

### How to compare features of two curves?

I need to compare two curves f(x) and g(x). They are in the same x range (say -30 to 30). f(x) may have some sharp peaks or smooth peaks and valleys. g(x) may have the same peaks and valleys. If so I ...
6k views

### Find the new coordinates using a starting point, a distance, and an angle

Okay, say I have a point coordinate. var coordinate = { x: 10, y: 20 }; Now I also have a distance and an angle. var distance = 20; var angle = 72; The problem I am trying to solve is, if I want ...
234 views

### How do graphics programmers deal with rendering vertices that don't change the image?

So, the title is a little awkward. I'll give some background, and then ask my question. Background: I work as a web GIS application developer, but in my spare time I've been playing with map ...
284 views

### Generate equally sized areas in polygon

I am looking for a pseudo code logic that would find n equally sized areas in a given polygon. No space should be between or outside the matched areas. First valid match of areas should be returned. ...
270 views

### Maximizing number of nested triangles

There is a finite set of points on a plane (about 1500 points in the current task). I need to construct triangles on those points such as each triangle lies completely inside one larger triangle: ...
1k views

### How to represent a geometric line programmatically?

I have been trying to design a library to do some simple geometric computations in an Euclidean space regardless of its dimension. While it is easy to represent points, vectors, hyperspheres and ...
378 views

### How to determine if set of ordered coordinates form a simple curve?

I hope it is the right place to ask this. I wasn't sure if it belongs to Stack Overflow or Computer Science. Eventually this seemed more suitable. Anyway, some background first: A closed curve, is ...
743 views

### Intersection of geometric entities

I was trying to design a small C++ geometric API for learning purposes, but came across a problem when dealing with intersections of geometric entities. For example, the intersection of a line and a ...
79 views

### How to generalize the planar case of the closest pair problem to d dimensions?

I'm trying to create a solution for the Closest pair problem using d-dimensional points. I've done a thorough search on google but it seems that there is no explanation for the d-dimensional case ...
146 views

### How do I find which line connected two squares?

In the Permissive Field of View algorithm, a destination square is visible from a source square if any unobstructed line can be drawn from the source square to the destination square. The algorithm ...
155 views

### Neighbourhood points (2d)

I have a 2d coordinates system with some points on it, like this one: Now I am looking for an algorithm (or just some approach) to find neighboured points. So, if you have the coordinates of one ...
1k views

### Area calculation of irregular shapes

Is there any algo that can help splitting irregular shape into regular shapes, and eventually calculate the area of the main object by summing the areas of those regular objects?
2k views

### Algorithm to calculate trajectories from vector field

I have a two-dimensional vector field, i.e., for each point (x, y) I have a vector (u, v), whereas u and v are functions of x and y. This vector field canonically defines a set of trajectories, i.e. ...
3k views

### Efficient method for finding closest point to a line segment from a set of points including line segment's vertices

Let's say I have a list of points (in my case, point objects in a Python implementation). I then have a line segment connecting two of these points. I want to know if there's a way to efficiently ...
220 views

### Method for determining if a line segment is an external edge of a Delauney triangulation?

I've created a Delauney triangulation of a set of points. Now I want to iterate over the triangulation and remove any line segments/edges on the exterior for which the following are true: The ...
730 views

### Find points whose pairwise distances approximate a given distance matrix

Problem. I have a symmetric distance matrix with entries between zero and one, like this one: D = ( 0.0 0.4 0.0 0.5 ) ( 0.4 0.0 0.2 1.0 ) ( 0.0 0.2 0.0 0.7 ) ( 0.5 1.0 0.7 0.0 ) I would ...
214 views

### Find a line that is closest to scattered points

I came across the below interview question on Glassdoor: A scatter graph of points on a page, draw a horizontal line across the page such the the perpendicular y distance to the line from all ...
309 views

### Trying to code the points on a circle [closed]

I am trying to understand this: I wrote a code for points on a circle of radius 1. Note that the first and last point intentionally coincide. do i=1,imax X(i,1) = COS(-2*4.0*ATAN(1.0)*(i-1)/(imax-1)...
405 views

### How to detect two moving shapes overlapped?

Given a list of circles with its coordinates (x and y) that are moving every second in different direction (South-East, South-West, North-East and North-West), and the circle will change direction if ...
229 views

### Selecting a point inside a non-convex polygon

There are a lot of algorithms which will tell you whether or not a given point is found inside a polygon. I'm looking to write an algorithm which, given a non-convex polygon, will return a point ...
65 views

### Which algorithm to find the shortest (nodes count) path that encompasses all polygons inside a larger polygon?

Inside a large polygon (say the USA boundaries) I need to find the shortest path that will encompass smaller polygons (say the following cities: Kansas city, St Louis, Memphis, Oklahoma City) By ...
172 views

### How to find out if a tile is being covered by a polygon?

Given a (intersecting) polygon, I'd like find out which tiles are being covered by the polygon. Example: Details: Tiles are square, 1 unit wide/high The grid begins in (0,0) The corners of the ...
632 views

### Number of parallel lines in a given set of lines [closed]

I am given N lines, i.e, I am given a,b,c for N lines. And each line is of the form ax + by + c = 0. I need to find out the maximum number of lines that are parallel to each other. For this, first I ...
43 views

### Polygon simplification that encloses original set of points

I have been trying to implement an optimization for 2D sprite rendering to fight the problem of limited fillrate on mobile devices. The idea is to render textured polygons instead of quads that will ...
50 views

### Project a piece of image cut by N-vertex shape to a different N-vertex shape

I have an N-vertex shape that I cut out from an image, and I want to project it onto another shape with the same amount of vertices, but different. So, the image will get changed inside the projection....
259 views

### Generate complex (non-convex) polyhedron UV mapping

I need to find an approach to the problem of generating texture maps for non-convex polyhedrons without using a design tool like Maya. Specifically, I am mapping simulation results data onto a 3D ...
589 views

### Drawing a biggest possible circle inside a polygon - JSXGRAPH

I manage to create a circle inside triangle with this code, but circle inside other polygons are not maximum size: var p1 = board.create("point", [0.0, 2.0]); var p2 = board.create("point", [2.0, 1.0]...
657 views

### Calculate Ellipse based on 4 points

I need to move an object based on 100 images rotating. The object needs to move in a path that is forming an ellipse when I'm rotating the image based on my gestures. I have 4 points, 2 pairs of ...
99 views

### tiling algorithm for maximum size of equal-sized tiles

I'm trying to fit an arbitrary number of HD videos on screen so that they all have equal size, maximizing the size of the videos, with no scrollbars appearing. Given N number of tiles of equal ...
169 views

### Algorithm to “de-rasterize” a voxel image of a polyhedron

Rasterizing a polygon in this question consists of creating an array of binary pixels that "represent" the polygon. The reverse of this process is easy to approximate in linear time to the perimeter ...
779 views

### 2 closest points between 2 rectangles

On a 2D plane, I have 2 rectangles. I want to find the closest pair of points (one on each rectangle), which are closest to each other. By points I mean the corners of the rectangles. And no, they do ...
46 views

### Graph grouping with criteria

I start with a list of adjacent tetrahedra, where there are tight seals to one another along faces for two tetrahedra that are adjacent. The vertices belonging to these faces for both tetrahedra are ...
77 views

### How to synchronize segments in polylines?

My input are two polylines -- I had one polyline and I computed offset of it, similarly to polygons. Here is the useful post: http://stackoverflow.com/questions/1109536/an-algorithm-for-inflating-...
87 views

### distribute rectangles in order to do not overlap

I've a series of labels and icons inside the screen. A label is on the right of corresponding icon. I must perform a sort of declutter: when two or more labels overlap each other (or a label with an ...
274 views

### Algorithm for sweeping a 2d shape along a curve?

I am trying to create a graphics application where the user can use an arbitrary shape as a "brush", which will be swept along the drawing path. The shape may be transformed along the path (rotated, ...
76 views

### Adding a minimum rectangle overlap threshold

I have a function that works perfectly for detecting whether or not r1 overlaps with r2: boolean overlaps( Rectangle r1, Rectangle r2 ) { return r1.x < r2.x + r2.width && r1.x + r1....
363 views

### How to compute barycentric coordinates in a systematic and efficient way?

As part of a ray tracer implementation, I need to compute the barycentric coordinates in a triangle in 3D in order to decide if a ray hits the triangle or not. In theory this could be done by simply ...
655 views

### projective geometry: how do I turn a projection of a rectangle in 3D into a 2D view

So the problem is that I have a 3D projection of a rectangle that I want to turn into 2D. That is I have a photo of a sheet of paper laying on a table which I want to transform into a 2D view of that ...
21 views

### Find whether or not current location is near other locations with given radii

tl;dr: "Am I, with any given location, inside of any number of circles with varying radii" Assume you have a database full of locations (coordinates) with arbitrary radii. Now the user enters and ...
111 views

### How can I map a number of points of a polygon to matching points of a larger rectangle?

Suppose I have 2D polygon image and a larger 2D rectangle image and that I have a collection of points for each that I want to align. For Example the polygon has point collection: [PA(a, b), PB(c, d)...
98 views

### Finding all Triangular Hulls in a 2D Point Cloud

My question: Given a set of 2D points, enumerate all triples of points such that no other points is inside the triangle formed by those 3 points. I'm looking for something better than this: // The ...