This article's tone or style may not reflect the encyclopedic tone used on Wikipedia.(August 2014) |

**Collision detection** is the computational problem of detecting the intersection of two or more objects. Collision detection is a classic issue of computational geometry and has applications in various computing fields, primarily in computer graphics, computer games, computer simulations, robotics and computational physics. Collision detection algorithms can be divided into operating on 2D and 3D objects.^{ [1] }

- Overview
- Collision detection in computer simulation
- A posteriori (discrete) versus a priori (continuous)
- Optimization
- Exploiting temporal coherence
- Pairwise pruning
- Exact pairwise collision detection
- A priori pruning
- Spatial partitioning
- Bounding boxes
- Triangle centroid segments
- Video games
- Hitbox
- See also
- References
- External links

This article is written like a manual or guidebook.(March 2020) |

In physical simulation, experiments such as playing billiards, are conducted. The physics of bouncing billiard balls are well understood, under the umbrella of rigid body motion and elastic collisions. An initial description of the situation would be given, with a very precise physical description of the billiard table and balls, as well as initial positions of all the balls. Given a force applied to the cue ball (probably resulting from a player hitting the ball with their cue stick), we want to calculate the trajectories, precise motion and eventual resting places of all the balls with a computer program. A program to simulate this game would consist of several portions, one of which would be responsible for calculating the precise impacts between the billiard balls. This particular example also turns out to be ill conditioned: a small error in any calculation will cause drastic changes in the final position of the billiard balls.

Video games have similar requirements, with some crucial differences. While computer simulation needs to simulate real-world physics as precisely as possible, computer games need to simulate real-world physics in an *acceptable* way, in real time and robustly. Compromises are allowed, so long as the resulting simulation is satisfying to the game players.

Physical simulators differ in the way they react on a collision. Some use the softness of the material to calculate a force, which will resolve the collision in the following time steps like it is in reality. Due to the low softness of some materials this is very CPU intensive. Some simulators estimate the time of collision by linear interpolation, roll back the simulation, and calculate the collision by the more abstract methods of conservation laws.

Some iterate the linear interpolation (Newton's method) to calculate the time of collision with a much higher precision than the rest of the simulation. Collision detection utilizes time coherence to allow even finer time steps without much increasing CPU demand, such as in air traffic control.

After an inelastic collision, special states of sliding and resting can occur and, for example, the Open Dynamics Engine uses constraints to simulate them. Constraints avoid inertia and thus instability. Implementation of rest by means of a scene graph avoids drift.

In other words, physical simulators usually function one of two ways, where the collision is detected * a posteriori * (after the collision occurs) or * a priori * (before the collision occurs). In addition to the *a posteriori* and *a priori* distinction, almost all modern collision detection algorithms are broken into a hierarchy of algorithms. Often the terms "discrete" and "continuous" are used rather than *a posteriori* and *a priori*.

In the *a posteriori* case, the physical simulation is advanced by a small step, then checked to see if any objects are intersecting or visibly considered intersecting. At each simulation step, a list of all intersecting bodies is created, and the positions and trajectories of these objects are "fixed" to account for the collision. This method is called *a posteriori* because it typically misses the actual instant of collision, and only catches the collision after it has actually happened.

In the *a priori* methods, there is a collision detection algorithm which will be able to predict very precisely the trajectories of the physical bodies. The instants of collision are calculated with high precision, and the physical bodies never actually interpenetrate. This is called *a priori* because the collision detection algorithm calculates the instants of collision before it updates the configuration of the physical bodies.

The main benefits of the *a posteriori* methods are as follows. In this case, the collision detection algorithm need not be aware of the myriad of physical variables; a simple list of physical bodies is fed to the algorithm, and the program returns a list of intersecting bodies. The collision detection algorithm doesn't need to understand friction, elastic collisions, or worse, nonelastic collisions and deformable bodies. In addition, the *a posteriori* algorithms are in effect one dimension simpler than the *a priori* algorithms. An *a priori* algorithm must deal with the time variable, which is absent from the *a posteriori* problem.

On the other hand, *a posteriori* algorithms cause problems in the "fixing" step, where intersections (which aren't physically correct) need to be corrected. Moreover, if the discrete step is too large, the collision could go undetected, resulting in an object which passes through another if it is sufficiently fast or small.

The benefits of the *a priori* algorithms are increased fidelity and stability. It is difficult (but not completely impossible) to separate the physical simulation from the collision detection algorithm. However, in all but the simplest cases, the problem of determining ahead of time when two bodies will collide (given some initial data) has no closed form solution—a numerical root finder is usually involved.

Some objects are in *resting contact*, that is, in collision, but neither bouncing off, nor interpenetrating, such as a vase resting on a table. In all cases, resting contact requires special treatment: If two objects collide (*a posteriori*) or slide (*a priori*) and their relative motion is below a threshold, friction becomes stiction and both objects are arranged in the same branch of the scene graph.

The obvious approaches to collision detection for multiple objects are very slow. Checking every object against every other object will, of course, work, but is too inefficient to be used when the number of objects is at all large. Checking objects with complex geometry against each other in the obvious way, by checking each face against each other face, is itself quite slow. Thus, considerable research has been applied to speed up the problem.^{ [2] }

This article may be too technical for most readers to understand.(March 2020) |

This article's tone or style may not reflect the encyclopedic tone used on Wikipedia.(March 2020) |

In many applications, the configuration of physical bodies from one time step to the next changes very little. Many of the objects may not move at all. Algorithms have been designed so that the calculations done in a preceding time step can be reused in the current time step, resulting in faster completion of the calculation.

At the coarse level of collision detection, the objective is to find pairs of objects which might potentially intersect. Those pairs will require further analysis. An early high performance algorithm for this was developed by Ming C. Lin at the University of California, Berkeley , who suggested using axis-aligned bounding boxes for all *n* bodies in the scene.

Each box is represented by the product of three intervals (i.e., a box would be ). A common algorithm for collision detection of bounding boxes is sweep and prune. Observe that two such boxes, and intersect if, and only if, intersects , intersects and intersects . It is supposed that, from one time step to the next, if and intersect, then it is very likely that at the next time step they will still intersect. Likewise, if they did not intersect in the previous time step, then they are very likely to continue not to.

So we reduce the problem to that of tracking, from frame to frame, which intervals do intersect. We have three lists of intervals (one for each axis) and all lists are the same length (since each list has length , the number of bounding boxes.) In each list, each interval is allowed to intersect all other intervals in the list. So for each list, we will have an matrix of zeroes and ones: is 1 if intervals and intersect, and 0 if they do not intersect.

By our assumption, the matrix associated to a list of intervals will remain essentially unchanged from one time step to the next. To exploit this, the list of intervals is actually maintained as a list of labeled endpoints. Each element of the list has the coordinate of an endpoint of an interval, as well as a unique integer identifying that interval. Then, we sort the list by coordinates, and update the matrix as we go. It's not so hard to believe that this algorithm will work relatively quickly if indeed the configuration of bounding boxes does not change significantly from one time step to the next.

In the case of deformable bodies such as cloth simulation, it may not be possible to use a more specific pairwise pruning algorithm as discussed below, and an *n*-body pruning algorithm is the best that can be done.

If an upper bound can be placed on the velocity of the physical bodies in a scene, then pairs of objects can be pruned based on their initial distance and the size of the time step.

This article may be too technical for most readers to understand.(March 2020) |

This article's tone or style may not reflect the encyclopedic tone used on Wikipedia.(March 2020) |

Once we've selected a pair of physical bodies for further investigation, we need to check for collisions more carefully. However, in many applications, individual objects (if they are not too deformable) are described by a set of smaller primitives, mainly triangles. So now, we have two sets of triangles, and (for simplicity, we will assume that each set has the same number of triangles.)

The obvious thing to do is to check all triangles against all triangles for collisions, but this involves comparisons, which is highly inefficient. If possible, it is desirable to use a pruning algorithm to reduce the number of pairs of triangles we need to check.

The most widely used family of algorithms is known as the *hierarchical bounding volumes* method. As a preprocessing step, for each object (in our example, and ) we will calculate a hierarchy of bounding volumes. Then, at each time step, when we need to check for collisions between and , the hierarchical bounding volumes are used to reduce the number of pairs of triangles under consideration. For simplicity, we will give an example using bounding spheres, although it has been noted that spheres are undesirable in many cases.^{[ citation needed ]}

If is a set of triangles, we can precalculate a bounding sphere . There are many ways of choosing , we only assume that is a sphere that completely contains and is as small as possible.

Ahead of time, we can compute and . Clearly, if these two spheres do not intersect (and that is very easy to test), then neither do and . This is not much better than an *n*-body pruning algorithm, however.

If is a set of triangles, then we can split it into two halves and . We can do this to and , and we can calculate (ahead of time) the bounding spheres and . The hope here is that these bounding spheres are much smaller than and . And, if, for instance, and do not intersect, then there is no sense in checking any triangle in against any triangle in .

As a precomputation, we can take each physical body (represented by a set of triangles) and recursively decompose it into a binary tree, where each node represents a set of triangles, and its two children represent and . At each node in the tree, we can precompute the bounding sphere .

When the time comes for testing a pair of objects for collision, their bounding sphere tree can be used to eliminate many pairs of triangles.

Many variants of the algorithms are obtained by choosing something other than a sphere for . If one chooses axis-aligned bounding boxes, one gets AABBTrees. Oriented bounding box trees are called OBBTrees. Some trees are easier to update if the underlying object changes. Some trees can accommodate higher order primitives such as splines instead of simple triangles.

Once we're done pruning, we are left with a number of candidate pairs to check for exact collision detection.

A basic observation is that for any two convex objects which are disjoint, one can find a plane in space so that one object lies completely on one side of that plane, and the other object lies on the opposite side of that plane. This allows the development of very fast collision detection algorithms for convex objects.

Early work in this area involved "separating plane" methods. Two triangles collide essentially only when they can not be separated by a plane going through three vertices. That is, if the triangles are and where each is a vector in , then we can take three vertices, , find a plane going through all three vertices, and check to see if this is a separating plane. If any such plane is a separating plane, then the triangles are deemed to be disjoint. On the other hand, if none of these planes are separating planes, then the triangles are deemed to intersect. There are twenty such planes.

If the triangles are coplanar, this test is not entirely successful. One can add some extra planes, for instance, planes that are normal to triangle edges, to fix the problem entirely. In other cases, objects that meet at a flat face must necessarily also meet at an angle elsewhere, hence the overall collision detection will be able to find the collision.

Better methods have since been developed. Very fast algorithms are available for finding the closest points on the surface of two convex polyhedral objects. Early work by Ming C. Lin ^{ [3] } used a variation on the simplex algorithm from linear programming. The Gilbert-Johnson-Keerthi distance algorithm has superseded that approach. These algorithms approach constant time when applied repeatedly to pairs of stationary or slow-moving objects, when used with starting points from the previous collision check.

The end result of all this algorithmic work is that collision detection can be done efficiently for thousands of moving objects in real time on typical personal computers and game consoles.

Where most of the objects involved are fixed, as is typical of video games, a priori methods using precomputation can be used to speed up execution.

Pruning is also desirable here, both *n*-body pruning and pairwise pruning, but the algorithms must take time and the types of motions used in the underlying physical system into consideration.

When it comes to the exact pairwise collision detection, this is highly trajectory dependent, and one almost has to use a numerical root-finding algorithm to compute the instant of impact.

As an example, consider two triangles moving in time and . At any point in time, the two triangles can be checked for intersection using the twenty planes previously mentioned. However, we can do better, since these twenty planes can all be tracked in time. If is the plane going through points in then there are twenty planes to track. Each plane needs to be tracked against three vertices, this gives sixty values to track. Using a root finder on these sixty functions produces the exact collision times for the two given triangles and the two given trajectory. We note here that if the trajectories of the vertices are assumed to be linear polynomials in then the final sixty functions are in fact cubic polynomials, and in this exceptional case, it is possible to locate the exact collision time using the formula for the roots of the cubic. Some numerical analysts suggest that using the formula for the roots of the cubic is not as numerically stable as using a root finder for polynomials.^{[ citation needed ]}

Alternative algorithms are grouped under the spatial partitioning umbrella, which includes octrees, binary space partitioning (or BSP trees) and other, similar approaches. If one splits space into a number of simple cells, and if two objects can be shown not to be in the same cell, then they need not be checked for intersection. Since BSP trees can be precomputed, that approach is well suited to handling walls and fixed obstacles in games. These algorithms are generally older than the algorithms described above.

Bounding boxes (or bounding volumes) are most often a 2D rectangle or 3D cuboid, but other shapes are possible. A bounding box in a video game is sometimes called a Hitbox. The bounding diamond, the minimum bounding parallelogram, the convex hull, the bounding circle or bounding ball, and the bounding ellipse have all been tried, but bounding boxes remain the most popular due to their simplicity.^{ [4] } Bounding boxes are typically used in the early (pruning) stage of collision detection, so that only objects with overlapping bounding boxes need be compared in detail.

A triangle mesh object is commonly used in 3D body modeling. Normally the collision function is a triangle to triangle intercept or a bounding shape associated with the mesh. A triangle centroid is a center of mass location such that it would balance on a pencil tip. The simulation need only add a centroid dimension to the physics parameters. Given centroid points in both object and target it is possible to define the line segment connecting these two points.

The position vector of the centroid of a triangle is the average of the position vectors of its vertices. So if its vertices have Cartesian coordinates , and then the centroid is .

Here is the function for a line segment distance between two 3D points.

Here the length/distance of the segment is an adjustable "hit" criteria size of segment. As the objects approach the length decreases to the threshold value. A triangle sphere becomes the effective geometry test. A sphere centered at the centroid can be sized to encompass all the triangle's vertices.

Video games have to split their very limited computing time between several tasks. Despite this resource limit, and the use of relatively primitive collision detection algorithms, programmers have been able to create believable, if inexact, systems for use in games.^{[ citation needed ]}

For a long time, video games had a very limited number of objects to treat, and so checking all pairs was not a problem. In two-dimensional games, in some cases, the hardware was able to efficiently detect and report overlapping pixels between sprites on the screen.^{ [5] } In other cases, simply tiling the screen and binding each *sprite* into the tiles it overlaps provides sufficient pruning, and for pairwise checks, bounding rectangles or circles called hitboxes are used and deemed sufficiently accurate.

Three-dimensional games have used spatial partitioning methods for -body pruning, and for a long time used one or a few spheres per actual 3D object for pairwise checks. Exact checks are very rare, except in games attempting to simulate reality closely. Even then, exact checks are not necessarily used in all cases.

Because games do not need to mimic actual physics, stability is not as much of an issue. Almost all games use *a posteriori* collision detection, and collisions are often resolved using very simple rules. For instance, if a character becomes embedded in a wall, they might be simply moved back to their last known good location. Some games will calculate the distance the character can move before getting embedded into a wall, and only allow them to move that far.

In many cases for video games, approximating the characters by a point is sufficient for the purpose of collision detection with the environment. In this case, binary space partitioning trees provide a viable, efficient and simple algorithm for checking if a point is embedded in the scenery or not. Such a data structure can also be used to handle "resting position" situation gracefully when a character is running along the ground. Collisions between characters, and collisions with projectiles and hazards, are treated separately.

A robust simulator is one that will react to any input in a reasonable way. For instance, if we imagine a high speed racecar video game, from one simulation step to the next, it is conceivable that the cars would advance a substantial distance along the race track. If there is a shallow obstacle on the track (such as a brick wall), it is not entirely unlikely that the car will completely leap over it, and this is very undesirable. In other instances, the "fixing" that posteriori algorithms require isn't implemented correctly, resulting in bugs that can trap characters in walls or allow them to pass through them and fall into an endless void where there may or may not be a deadly bottomless pit, sometimes referred to as "black hell", "blue hell", or "green hell", depending on the predominant color. These are the hallmarks of a failing collision detection and physical simulation system. * Big Rigs: Over the Road Racing * is an infamous example of a game with a failing or possibly missing collision detection system.

A **hitbox** is an invisible shape commonly used in video games for real-time collision detection; it is a type of bounding box. It is often a rectangle (in 2D games) or cuboid (in 3D) that is attached to and follows a point on a visible object (such as a model or a sprite). Circular or spheroidial shapes are also common, though they are still most often called "boxes". It is common for animated objects to have hitboxes attached to each moving part to ensure accuracy during motion.^{ [6] }^{[ unreliable source? ]}

Hitboxes are used to detect "one-way" collisions such as a character being hit by a punch or a bullet. They are unsuitable for the detection of collisions with feedback (e.g. bumping into a wall) due to the difficulty experienced by both humans and AI in managing a hitbox's ever-changing locations; these sorts of collisions are typically handled with much simpler axis-aligned bounding boxes instead. Players may use the term "hitbox" to refer to these types of interactions regardless.

A **hurtbox** is a related term, used to differentiate "object that deals damage" from "object that receives damage". For example, an attack may only land if the hitbox around an attacker's punch connects with one of the opponent's hurtboxes on their body, while opposing hitboxes colliding may result in the players trading or cancelling blows, and opposing hurtboxes do not interact with each other. The term is not standardized across the industry; some games reverse their definitions of "hitbox" and "hurtbox", while others only use "hitbox" for both sides.

In 3D computer graphics, **ray tracing** is a technique for modeling light transport for use in a wide variety of rendering algorithms for generating digital images.

In computer science, **binary space partitioning** (**BSP**) is a method for space partitioning which recursively subdivides a Euclidean space into two convex sets by using hyperplanes as partitions. This process of subdividing gives rise to a representation of objects within the space in the form of a tree data structure known as a **BSP tree**.

**Elliptic geometry** is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point. Because of this, the elliptic geometry described in this article is sometimes referred to as *single elliptic geometry* whereas spherical geometry is sometimes referred to as *double elliptic geometry*.

**Branch and bound** is a method for solving optimization problems by breaking them down into smaller sub-problems and using a bounding function to eliminate sub-problems that cannot contain the optimal solution. It is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores *branches* of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated *bounds* on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm.

In computational complexity theory, the **3SUM** problem asks if a given set of real numbers contains three elements that sum to zero. A generalized version, *k*-SUM, asks the same question on *k* numbers. 3SUM can be easily solved in time, and matching lower bounds are known in some specialized models of computation.

A **vanishing point** is a point on the image plane of a perspective rendering where the two-dimensional perspective projections of mutually parallel lines in three-dimensional space appear to converge. When the set of parallel lines is perpendicular to a picture plane, the construction is known as one-point perspective, and their vanishing point corresponds to the oculus, or "eye point", from which the image should be viewed for correct perspective geometry. Traditional linear drawings use objects with one to three sets of parallels, defining one to three vanishing points.

A **quadtree** is a tree data structure in which each internal node has exactly four children. Quadtrees are the two-dimensional analog of octrees and are most often used to partition a two-dimensional space by recursively subdividing it into four quadrants or regions. The data associated with a leaf cell varies by application, but the leaf cell represents a "unit of interesting spatial information".

In computer graphics and computational geometry, a **bounding volume** for a set of objects is a closed volume that completely contains the union of the objects in the set. Bounding volumes are used to improve the efficiency of geometrical operations by using simple volumes to contain more complex objects. Normally, simpler volumes have simpler ways to test for overlap.

In computer science, **cycle detection** or **cycle finding** is the algorithmic problem of finding a cycle in a sequence of iterated function values.

In geometry, **space partitioning** is the process of dividing a space into two or more disjoint subsets. In other words, space partitioning divides a space into non-overlapping regions. Any point in the space can then be identified to lie in exactly one of the regions.

**Geometry processing**, or mesh processing, is an area of research that uses concepts from applied mathematics, computer science and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation and transmission of complex 3D models. As the name implies, many of the concepts, data structures, and algorithms are directly analogous to signal processing and image processing. For example, where image smoothing might convolve an intensity signal with a blur kernel formed using the Laplace operator, geometric smoothing might be achieved by convolving a surface geometry with a blur kernel formed using the Laplace-Beltrami operator.

A **bounding volume hierarchy** (**BVH**) is a tree structure on a set of geometric objects. All geometric objects, which form the leaf nodes of the tree, are wrapped in bounding volumes. These nodes are then grouped as small sets and enclosed within larger bounding volumes. These, in turn, are also grouped and enclosed within other larger bounding volumes in a recursive fashion, eventually resulting in a tree structure with a single bounding volume at the top of the tree. Bounding volume hierarchies are used to support several operations on sets of geometric objects efficiently, such as in collision detection and ray tracing.

**Soft-body dynamics** is a field of computer graphics that focuses on visually realistic physical simulations of the motion and properties of deformable objects. The applications are mostly in video games and films. Unlike in simulation of rigid bodies, the shape of soft bodies can change, meaning that the relative distance of two points on the object is not fixed. While the relative distances of points are not fixed, the body is expected to retain its shape to some degree. The scope of soft body dynamics is quite broad, including simulation of soft organic materials such as muscle, fat, hair and vegetation, as well as other deformable materials such as clothing and fabric. Generally, these methods only provide visually plausible emulations rather than accurate scientific/engineering simulations, though there is some crossover with scientific methods, particularly in the case of finite element simulations. Several physics engines currently provide software for soft-body simulation.

A **bounding interval hierarchy** (**BIH**) is a partitioning data structure similar to that of bounding volume hierarchies or kd-trees. Bounding interval hierarchies can be used in high performance ray tracing and may be especially useful for dynamic scenes.

The **smallest-circle problem** is a mathematical problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane. The corresponding problem in *n*-dimensional space, the smallest bounding sphere problem, is to compute the smallest *n*-sphere that contains all of a given set of points. The smallest-circle problem was initially proposed by the English mathematician James Joseph Sylvester in 1857.

The **Gilbert–Johnson–Keerthi distance algorithm** is a method of determining the minimum distance between two convex sets, first published by Elmer G. Gilbert, Daniel W. Johnson, and S. Sathiya Keerthi in 1988. Unlike many other distance algorithms, it does not require that the geometry data be stored in any specific format, but instead relies solely on a support function to iteratively generate closer simplices to the correct answer using the *configuration space obstacle* (CSO) of two convex shapes, more commonly known as the Minkowski difference.

The **Möller–Trumbore ray-triangle intersection algorithm**, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle. Among other uses, it can be used in computer graphics to implement ray tracing computations involving triangle meshes.

A **geometric separator** is a line that partitions a collection of geometric shapes into two subsets, such that proportion of shapes in each subset is bounded, and the number of shapes that do not belong to any subset is small.

In computational geometry, a **maximum disjoint set** (**MDS**) is a largest set of non-overlapping geometric shapes selected from a given set of candidate shapes.

**Numerical certification** is the process of verifying the correctness of a candidate solution to a system of equations. In (numerical) computational mathematics, such as numerical algebraic geometry, candidate solutions are computed algorithmically, but there is the possibility that errors have corrupted the candidates. For instance, in addition to the inexactness of input data and candidate solutions, numerical errors or errors in the discretization of the problem may result in corrupted candidate solutions. The goal of numerical certification is to provide a certificate which proves which of these candidates are, indeed, approximate solutions.

- ↑ Teschner, M.; Kimmerle, S.; Heidelberger, B.; Zachmann, G.; Raghupathi, L.; Fuhrmann, A.; Cani, M.-P.; Faure, F.; Magnenat-Thalmann, N.; Strasser, W.; Volino, P. (2005). "Collision Detection for Deformable Objects".
*Computer Graphics Forum*.**24**: 61–81. doi:10.1111/j.1467-8659.2005.00829.x. S2CID 1359430. - ↑ Jaume, J; Galli, R; Mas, R; Mascaro-Oliver, M (1995) (1995). "Real-time Collision Checking for 3D Object Positioning in Sparse Environments".
*Image Processing for Broadcast and Video Production*. Workshops in Computing. Image Processing for Broadcast and Video Production; Springer-Verlag. pp. 216–225. doi:10.1007/978-1-4471-3035-2_18. ISBN 978-3-540-19947-2.`{{cite book}}`

: CS1 maint: multiple names: authors list (link) - ↑ Lin, Ming C (1993). "Efficient Collision Detection for Animation and Robotics (thesis)" (PDF). University of California, Berkeley. Archived from the original (PDF) on 2014-07-28.
- ↑ Caldwell, Douglas R. (2005-08-29). "Unlocking the Mysteries of the Bounding Box". US Army Engineer Research & Development Center, Topographic Engineering Center, Research Division, Information Generation and Management Branch. Archived from the original on 2012-07-28. Retrieved 2014-05-13.
- ↑ "Components of the Amiga: The MC68000 and the Amiga Custom Chips" (Reference manual) (2.1 ed.). Chapter 1. Archived from the original on 2018-07-17. Retrieved 2018-07-17.
Additionally, you can use system hardware to detect collisions between objects and have your program react to such collisions.

- ↑ "Hitbox".
*Valve Developer Community*. Valve . Retrieved 18 September 2011.

- University of North Carolina at Chapel Hill collision detection research web site
- Prof. Steven Cameron (Oxford University) web site on collision detection
- How to Avoid a Collision by George Beck, Wolfram Demonstrations Project.
- Bounding boxes and their usage
- Separating Axis Theorem
- Unity 3d Collison
- Godot Physics Collison

This page is based on this Wikipedia article

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.