# Tagged Questions

The study of computer algorithms which admit geometric descriptions, and geometric problems arising in association with such algorithms. The two major classes of problems are (a) efficient design of algorithms and data classes using geometric concepts and (b) representation and modelling of curves ...

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### Balanced, center-free set. [closed]

We say that a finite set $\mathcal{S}$ of points in the plane is balanced if, for any two different points $A$ and $B$ in $\mathcal{S}$, there is a point $C$ in $\mathcal{S}$ such that $AC=BC$. We say ...
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### Obtaining the four corner coordinates of a square from the center point.

I'm trying to get the corner coordinates of a Square (NOTE, always a square) problematically. (EX: With a formula) and I'm having a hard time adding this into my computer application. Here's an ...
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### Sum of distances of points in unit closed disk

Let $D$ be the closed unit disk in the plane, and let $p_1, p_2, \dots, p_n$ be fixed points in $D$. My question is, does there necessarily exist a point $p$ in $D$ such that the sum of the distances ...
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### 3D kinematic geometry problem motivated by chemistry

It is well known that six carbon atoms can form a ring called cyclohexane. Since the angle between bonds is $\cos^{-1}\left(\frac{-1}{3}\right)\approx 109^\circ$, the ring is not a planar hexagon. ...
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### Tetrahedron subdivision

What are all the possible subdivisions of the P3 tetrahedron (i.e. for each face, 3 vertices plus two points per edge, located at 1/3 and 2/3, and the centroïd of the face, so a total of 20 points for ...
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### How to find the closest line to two segments?

I have two segments in 2D space, defined by their endpoint x and y coordinates. How can I find a best-fit line using vector algebra (formally, that minimizes the integral of square-distance from it to ...
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### How to determine whether a point is inside a closed region or not?

Take the following parametric equation of an implicit curve as an example: $$\left\{\quad \begin{array}{rl} x=& 9 \sin 2 t+5 \sin 3 t \\ y=& 9 \cos 2 t-5 \cos 3 t \\ \end{array} \right.$$ ...
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### How to determine if some line segments are collinear

Let's say I have several Line Segments that are connected to each other and make a Polyline. How can I determine if they are ...
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### How do I place two points on two axis-aligned line segments such that they have given Euclidean distance l?

This is my problem: I am given two axis aligned line segments $l_1$ and $l_2$ of finite length and a distance $l$. How do I find points $p_1 \in l_1$ and $p_2 \in l_2$, such that $||p_1-p_2||_2 = l$? ...
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### Finding other two vertices when one vertex and each point on the triangle is known ?

I am working on some gesture recognition for my game. I am stuck on a problem. I have one vertex i.e the starting point and every point on the triangle, I also have the centroid. So how do I find the ...