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    Collision Detection: Understanding Visual Intersections in Computer Vision
    Collision Detection: Understanding Visual Intersections in Computer Vision
    Collision Detection: Understanding Visual Intersections in Computer Vision
    Ebook137 pages1 hour

    Collision Detection: Understanding Visual Intersections in Computer Vision

    By Fouad Sabry

    ()

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    About this ebook

    What is Collision Detection


    Collision detection is the computational problem of detecting an intersection of two or more spatial objects, commonly computer graphics objects. It has applications in various computing fields, primarily in computer graphics, computer games, computer simulations, robotics and computational physics. Collision detection is a classic problem of computational geometry. Collision detection algorithms can be divided into operating on 2D or 3D spatial objects.


    How you will benefit


    (I) Insights, and validations about the following topics:


    Chapter 1: Collision detection


    Chapter 2: Ray tracing (graphics)


    Chapter 3: Binary space partitioning


    Chapter 4: Centroid


    Chapter 5: Branch and bound


    Chapter 6: Vanishing point


    Chapter 7: Quadtree


    Chapter 8: Bounding volume


    Chapter 9: Cycle detection


    Chapter 10: Arrangement of lines


    (II) Answering the public top questions about collision detection.


    (III) Real world examples for the usage of collision detection in many fields.


    Who this book is for


    Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Collision Detection.

    LanguageEnglish
    PublisherOne Billion Knowledgeable
    Release dateMay 4, 2024
    Collision Detection: Understanding Visual Intersections in Computer Vision

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      Book preview

      Collision Detection - Fouad Sabry

      Chapter 1: Collision detection

      The computer challenge of detecting the intersection of two or more objects is known as collision detection. Collision detection is a classic problem in computational geometry and has applications in a variety of computing domains, most notably computer graphics, computer games, computer simulations, robotics, and computational physics. 2D and 3D collision detection techniques can be distinguished by their respective object dimensions.

      Physical simulation involves conducting tests such as playing pool. Under the umbrella of rigid body motion and elastic collisions, the mechanics of bouncing pool balls is well understood. An first description of the circumstance would include a detailed physical description of the pool table and balls, as well as the starting locations of each ball. Given a force imparted to the cue ball (often the consequence of a player striking the ball with their cue stick), we wish to use a computer program to determine the trajectories, precise motion, and final resting positions of all the balls. A simulation of this game would require multiple modules, one of which would be responsible for computing the exact collisions between the billiard balls. A tiny inaccuracy in any calculation will result in dramatic changes to the final position of the billiard balls, as demonstrated by this example.

      The criteria for video games are comparable, with significant changes. Computer simulation must imitate real-world physics as accurately as feasible, whereas computer games must simulate real-world physics in an acceptable manner, in real time, and with sufficient resilience. As long as the resulting simulation is satisfactory to the game's players, compromises are permitted.

      Different physical simulators respond differently to collisions. Some use the material's softness to compute a force that will resolve the collision in subsequent time steps, as it would in reality. Due to the hardness of some materials, this requires a great deal of processing power. Some simulators estimate the collision time using linear interpolation, roll back the simulation, then calculate the collision using more abstract approaches based on conservation principles.

      Some iterate the linear interpolation (Newton's approach) to compute the collision time with significantly greater precision than the remainder of the simulation. Utilizing temporal coherence, collision detection permits increasingly finer time steps without significantly increasing CPU demand, such as in air traffic control.

      Special states of sliding and resting can occur after an inelastic collision, and the Open Dynamics Engine employs constraints to model these. Constraints prevent inertia and, as a result, instability. Implementing rest via a scene graph prevents drift.

      In other words, physical simulators typically detect collisions either a posteriori (after the collision occurs) or a priori (before the collision occurs) (before the collision occurs). In addition to the distinction between a posteriori and a priori, practically all recent collision detection algorithms are organized hierarchically. Typically, discrete and continuous are used instead of a posteriori and a priori.

      In the a posteriori instance, the physical simulation is progressed a tiny amount, and then it is determined whether or not any objects overlap or are visibly considered to intersect. At each simulation step, the positions and trajectories of all intersecting bodies are fixed to account for the collision. This method is referred to as a posteriori since it generally misses the exact moment of impact and only detects it after the fact.

      In a priori approaches, there is a collision detection algorithm that can predict the trajectories of physical bodies with great accuracy. The instants of collision are precisely computed, and the physical bodies never truly collide. This is termed a priori because the collision detection method calculates the collision instants prior to updating the configuration of the physical bodies.

      The primary advantages of a posteriori approaches are as follows. A simple list of physical bodies is provided to the algorithm, and the program produces a list of bodies that intersect. The collision detection technique does not require knowledge of friction, elastic or inelastic collisions, or deformable bodies. Moreover, the a posteriori algorithms are one dimension simpler than their a priori counterparts. The time variable is omitted from the a posteriori problem, which necessitates an a priori algorithm.

      On the other hand, a posteriori algorithms present issues during the fixing step, where physically incorrect intersections must be repaired. Furthermore, if the discrete step is too large, the collision may not be recognized, resulting in an object passing through another if it is sufficiently quick or small.

      The advantages of a priori algorithms are enhanced precision and consistency. Separating the physical simulation from the collision detection method is difficult (though not impossible). In all but the simplest circumstances, however, the issue of predicting when two bodies would collide (given beginning data) does not have a closed form solution—a numerical root finder is typically required.

      As an example, a vase resting on a table is in resting contact, or collision, but neither jumping off nor interpenetrating. Resting contact always demands specific treatment: If two items collide (a posteriori) or slide (a priori) and their relative velocity is less than a threshold, friction becomes stiction and both objects are positioned on the same branch of the scene graph.

      The conventional methods for detecting collisions between several objects are extremely sluggish. Obviously, comparing every object to every other object will work, but it is wasteful when the number of objects is significant. Checking complex-geometry objects against one another in the conventional manner, by comparing each face to every other face, is a time-consuming process. Thus, substantial study has been conducted to expedite the solution to the issue.

      In many applications, the configuration of physical bodies varies little from one time step to the next. Many of the objects may be immobile. Algorithms have been created such that computations performed in a previous time step can be utilized in the current time step, resulting in a faster calculation.

      At the coarse level of collision detection, the goal is to identify pairs of objects that could potentially collide. These couples will require additional investigation. Using axis-aligned bounding boxes for all n bodies in the picture, Ming C. Lin of the University of California, Berkeley [1] created an early method with high performance for this purpose.

      Each box is denoted by the product of three intervals (i.e., 1, 2, and 3), a box would be

      I_{1}\times I_{2}\times I_{3}=[a_{1},b_{1}]\times [a_{2},b_{2}]\times [a_{3},b_{3}]

      ).

      sweep and prune is a typical technique for collision detection of bounding boxes.

      Observe that there are two such boxes, I_{1}\times I_{2}\times I_{3} and J_{1}\times J_{2}\times J_{3} intersect if, as well as if, I_{1} intersects J_{1} , I_{2} intersects J_{2} and I_{3} intersects J_3 .

      It is anticipated that, from one time step to the following, if I_{k} and J_{k} intersect, Then it is quite likely that they will continue to overlap at the subsequent time step.

      Likewise, if they did not intersect during the previous time step, then they will not do so now, then they will likely continue to not do so.

      Thus, we simplify the issue to one of tracking, from image to image, which intersecting intervals exist.

      We have three lists of intervals (one for each axis) and all lists are the same length (since each list has length n , the quantity of boundary boxes. In every list, Each interval may intersect with every other interval in the list.

      Thus for every list, we will have an n\times n matrix M=(m_{{ij}}) of zeroes and ones: m_{ij} is 1 if intervals i and j intersect, 0 if the two lines do not intersect.

      In our estimation, the matrix M associated to a list of intervals will remain essentially unchanged from one time step to the next.

      To utilize this, Actually, the list of intervals is kept as a list of labeled endpoints.

      Each item in the list contains the endpoint coordinates of an interval, in addition to a distinct integer identifying that interval.

      Then, The list is ordered by coordinates, and update the matrix M as we go.

      If the configuration of the bounding boxes does not change much from one time step to the next, it is not difficult to think that this method will run quite rapidly.

      In the case of deformable bodies, such as cloth simulation, it may not be practical to employ a more specialized pairwise pruning

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