Questions tagged [collision-detection]

Use this tag for questions about detecting the intersection of two or more objects.

97 questions
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Can a chain of solid round links be twisted without getting shorter?

Two linked tori If I have two linked tori of equal size with $r_{\rm major} >> r_{\rm minor}$ that are tangent at one point, can one of the toruses be slightly rotated around the line through ...
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Determining circle-line intersection on sphere

There are two sets of coordinates (latitude/longitude) that form a line along the surface area of the Earth. There is a third coordinate, along with a radius, that denotes a circular region somewhere ...
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Approximating a probability threshold for hash collisions

First off: I know this is on the verge of being subjective and i'll try my best to make it as specific as possible. I am in a situation where I need to generate a fixed number of hashes (k), say 10,...
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How to determine the position and time of intersection of a moving cone and basic shapes in a 3D environment?

I created a Simulink model in which two objects are moving in a 3D environment (objets have six degrees-of-freedom). The main object has the characteristics of a cone and the second object has the ...
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Collision course of 2 objects

i've tried the question in another Q&A website but nobody could really helped me there so i will try it in here. I want to calculate the point where 2 objects hit each other. More detailled: ...
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How to find the value of the projection of an angle onto a plane?

Consider a triangle (T) in 3D space of given vertices A, B, and C. A given ray (R) (assumed to be in the direction of the x-axis) hits the triangle at one of its vertices - say A. Let $\theta$ be ...
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Recursive integral in elastic collision modelled on springs

I am writing a simulator for elastic collisions; however, I would like an elegant solution to the time-continuous problem, rather than the time-discrete problem. As I was solving the elastic ...
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How to calculate the area and volume of a random 3d shape knowing only its coordinates?

Given a set of 3d points which make up an vector object of any shape (with any number of points), without the edges being known, how can the object's edges be found/detected so that the object's ...
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Finding pixel inside rotation rectangular around a point

I would like to determine that pixels are inside a rotated rectangle around the center of the circle. Let: say I have a circle radius R at the center ( x0, y0 ) Given: theta as the degree of rotation ...
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prevent time collision in N Course initiation for M Student

Hypothesis: we have n courses and m students. we decide to initiate a sample course program named ...
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Given 2 constant acceleration model with initial position in 2D, how can I compute the when will the two object be closest to each other?

The motion model is defined by Initial position $\vec{x}$ in 2d space Initial timestamp $t$ Initial velocity $\vec{v}$ of $x,y$ direction a constant acceleration $\vec{a}$ of $x,y$ direction How ...
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Axis aligned torus collision detection

I am looking to detect the collision (test for intersection) of axis aligned torus and other axis aligned shapes: Torus and box. Torus and cylinder. Torus and another torus. There exist algorithms ...
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Particle collisions in the plane

A particle, moving at a speed of $v$ and an angle of $\theta$ (taking $0^\circ$ to be the positive $x$-axis) collides with a fixed slope with a gradient of $m$. How are $v$ and $\theta$ affected? ...
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Probability of picking the same choices

I have a system where there are 5 players. At each of times $t$ and $t+1$, each of players 2 to 5 generates $0$ or $1$, where the probability to get $1$ is $p$. If a player gets at least one $1$, then ...
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How do I detect if a circle overlaps with a polygon or not?

I have a polygon on earth described by a set of latitude and longitude points. I have following list of points that construct my polygon: ...
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2D CSG: Finding difference between intersection of two polygons

Originally, I have two polygons that do not intersect, call them A and B. I now translate polygon A with a translation vector $V$ such that $A\land B \neq \phi$. I now want to find a factor $\alpha$ ...
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Collision detection of rotating circles around fixed point in 2D

Recently I have learned how to predict the time of collision between two circles moving linearly. Positions of $P$ and $Q$ after time $t$ are: $P(t) = P_0 + vPt$ $Q(t) = Q_0 + vQt$ The goal was to ...
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Line Segment vs Circle Swept Collision Detection Algorithm

Notice: Implementation Can be found on GitHub. Search the username MonkeyToiletLadder for the repository. It has passed all test cases I have given it. It's pretty fast with the most expensive ...
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Where can I find implementation code for the algorithm

I am trying to build a computer simulation for collision of 2 ellipsoids that translate and rotate with very high speed. (accuracy is more important then running speed) is the article: An Algebraic ...
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Ellipsoids - test for collision

I would like to be able to find two ellipsoid for collision. I have found a paper which describes an algorithm in which they use Lagrange multipliers and Cramer's rule to find the collision. However I ...
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What's a simple algorithm for orthogonally separating two colliding rectangles using these primitive functions?

Suppose there are two colliding rectangles $R_0$, and $R_1$, and I'd like to separate them by only moving $R_1$. In the degenerate case that $R_1$'s center is equal to $R_0$'s and that they are ...
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How to find vector components of velocities of two balls after elastic collision, using angle-free representation

You have two balls of equal masses: Ball 1 and Ball 2. You are given the initial vector velocities (i.e velocity represented as a vector, with x and y components) as well as the initial x and y ...
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Inelastic Collision Response

It comes to mind that the coefficient of restitution (CR) for collision response only models the separating velocity in the normal direction. Thus, for $CR=0$, the separating velocity of two colliding ...
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Point-Ellipse collision test.

O.k, so basically i am writing some C++ program and I've encountered some problem. i need to check if a given Point $P$ is inside Ellipse or not. So lets say points $(X_0,Y_0),(X_1,Y_1),P_0,P_1$ ...
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Calculate if circle intersects a rectangle

In Euclidean 2D space I have a circle $A$ with radius $r$ and center $c(x_c,y_c)$, and a rectangle $B$ with height $h$, width $w$ which topleft corner is positioned at $d(x_d,y_d)$. The rectangle is ...
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Predicting when and where 2 points with non-constant velocity will collide

I am trying to estimate when and where 2 objects will collide with non-constant velocites which also have thrust and friction considerations. This for a physics simulation I am working on where I have ...
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Converting an equation into a quadratic polynomial in terms of time

I was trying to do some collision detection between discs for a physics simulation program I was doing. I had arrived at the equation: Object1Coordinate + (time$\cdot$Object1Velocity) = ...
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Circle collision offset

Just to clear some things i know how to detect collision i do not want a bounce effect since i am not working with velocity so lets say i have 2 circles C1 and C2. C1 can not be moved, and is ...
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Constrained optimization problem using Largange multipliers: ellipsoid collision detection and response

This one is purely for the mathematics so the result is far less important than the method itself. My task is to implement a fast and efficient ellipsoid collision detection and response algorithm. ...
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Applying drag to a collision prediction formula

I feel like this question might be below the minds of Math StackExchange, but I'll try anyway. (I can understand Math generally, but I'm probably not the caliber of people here.) I've been working on ...
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Convex shape in ellipsoid containment test

Supposed you to want find out if an ellipsoid fully contains a convex shape. In the picture below I have drawn two situations. The left shape is overlapping with the ellipsoid, and the right shape is ...
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Scaling intersecting circles that are locked to individual rays

I have two circles that intersect and I need to find the scalar value where they are only touching at one point. Each circle is locked to a point on it's circumference and can only scale relative to ...