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Collision Detection
Collision detection is the computational problem of detecting an intersection of two or more objects in virtual space. More precisely, it deals with the questions of ''if'', ''when'' and ''where'' two or more objects intersect. Collision detection is a classic problem of computational geometry with applications in computer graphics, physical simulation, video games, robotics (including autonomous driving) and computational physics. Collision detection algorithms can be divided into operating on 2D or 3D spatial objects. Overview Collision detection is closely linked to calculating the distance between objects, as two objects (or more) intersect when the distance between them reaches zero or even becomes negative. Negative distance indicates that one object has penetrated another. Performing collision detection requires more context than just the distance between the objects. Accurately identifying the points of contact on both objects' surfaces is also essential for the co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sweep And Prune
In physical simulations, sweep and prune is a broad phase algorithm used during collision detection to limit the number of pairs of solids that need to be checked for collision, i.e. intersection. This is achieved by sorting the starts (lower bound) and ends (upper bound) of the bounding volume of each solid along a number of arbitrary axes. As the solids move, their starts and ends may overlap. When the bounding volumes of two solids overlap in all axes they are flagged to be tested by more precise and time-consuming algorithms. Sweep and prune exploits temporal coherence as it is likely that solids do not move significantly between two simulation steps. Because of that, at each step, the sorted lists of bounding volume starts and ends can be updated with relatively few computational operations. Sorting algorithms which are fast at sorting almost-sorted lists, such as insertion sort, are particularly good for this purpose. According with the type of bounding volume used, it is ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Problem
In theoretical computer science, a computational problem is one that asks for a solution in terms of an algorithm. For example, the problem of factoring :"Given a positive integer ''n'', find a nontrivial prime factor of ''n''." is a computational problem that has a solution, as there are many known integer factorization algorithms. A computational problem can be viewed as a set of ''instances'' or ''cases'' together with a, possibly empty, set of ''solutions'' for every instance/case. The question then is, whether there exists an algorithm that maps instances to solutions. For example, in the factoring problem, the instances are the integers ''n'', and solutions are prime numbers ''p'' that are the nontrivial prime factors of ''n''. An example of a computational problem without a solution is the Halting problem. Computational problems are one of the main objects of study in theoretical computer science. One is often interested not only in mere existence of an algorithm, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Space Partitioning
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), tree data structure known as a BSP tree. Binary space partitioning was developed in the context of 3D computer graphics in 1969. The structure of a BSP tree is useful in rendering (computer graphics), rendering because it can efficiently give spatial information about the objects in a scene, such as objects being ordered from front-to-back with respect to a viewer at a given location. Other applications of BSP include: performing geometrical operations with shapes (constructive solid geometry) in Computer-aided design, CAD, collision detection in robotics and 3D video games, ray tracing (graphics), ray tracing, virtual landscape simulation, and other applications tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimum Bounding Box
In geometry, the minimum bounding box or smallest bounding box (also known as the minimum enclosing box or smallest enclosing box) for a point set in dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie. When other kinds of measure are used, the minimum box is usually called accordingly, e.g., "minimum-perimeter bounding box". The minimum bounding box of a point set is the same as the minimum bounding box of its convex hull, a fact which may be used heuristically to speed up computation. In the two-dimensional case it is called the ''minimum bounding rectangle''. Axis-aligned minimum bounding box The axis-aligned minimum bounding box (or AABB) for a given point set is its minimum bounding box subject to the constraint that the edges of the box are parallel to the (Cartesian) coordinate axes. It is the Cartesian product of ''N'' intervals each of which is defined by the minimal and maximal value o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bounding Volume
In computer graphics and computational geometry, a bounding volume (or bounding region) for a set of objects is a closed region that completely contains the union of the objects in the set. Bounding volumes are used to improve the efficiency of geometrical operations, such as by using simple regions, having simpler ways to test for overlap. A bounding volume for a set of objects is also a bounding volume for the single object consisting of their union, and the other way around. Therefore, it is possible to confine the description to the case of a single object, which is assumed to be non-empty and bounded (finite). Uses Bounding volumes are most often used to accelerate certain kinds of tests. In ray tracing, bounding volumes are used in ray-intersection tests, and in many rendering algorithms, they are used for viewing frustum tests. If the ray or viewing frustum does not intersect the bounding volume, it cannot intersect the object contained within, allowing trivia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spline (mathematics)
In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees. In the computer science subfields of computer-aided design and computer graphics, the term ''spline'' more frequently refers to a piecewise polynomial ( parametric) curve. Splines are popular curves in these subfields because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design. The term spline comes from the flexible spline devices used by shipbuilders and draftsmen to draw smooth shapes. Introduction The term "spline" is used to refer to a wide class of functions that are used in applications requiring data interpolation and/or smoothing. The data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oriented Bounding Box
In geometry, the minimum bounding box or smallest bounding box (also known as the minimum enclosing box or smallest enclosing box) for a point set in dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie. When other kinds of measure are used, the minimum box is usually called accordingly, e.g., "minimum-perimeter bounding box". The minimum bounding box of a point set is the same as the minimum bounding box of its convex hull, a fact which may be used heuristically to speed up computation. In the two-dimensional case it is called the ''minimum bounding rectangle''. Axis-aligned minimum bounding box The axis-aligned minimum bounding box (or AABB) for a given point set is its minimum bounding box subject to the constraint that the edges of the box are parallel to the (Cartesian) coordinate axes. It is the Cartesian product of ''N'' intervals each of which is defined by the minimal and maximal value o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Tree
In computer science, a binary tree is a tree data structure in which each node has at most two children, referred to as the ''left child'' and the ''right child''. That is, it is a ''k''-ary tree with . A recursive definition using set theory is that a binary tree is a triple , where ''L'' and ''R'' are binary trees or the empty set and ''S'' is a singleton (a single–element set) containing the root. From a graph theory perspective, binary trees as defined here are arborescences. A binary tree may thus be also called a bifurcating arborescence, a term which appears in some early programming books before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of ''binary tree'' to emphasize the fact that the tree is rooted, but as defined above, a binary tree is always rooted. In ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Precomputation
In algorithms, precomputation is the act of performing an initial computation before Run time (program lifecycle phase), run time to generate a lookup table that can be used by an algorithm to avoid repeated computation each time it is executed. Precomputation is often used in algorithms that depend on the results of expensive computations that don't depend on the input of the algorithm. A trivial example of precomputation is the use of hardcoded mathematical constants, such as Pi, π and E (mathematical constant), e, rather than computing their approximations to the necessary precision at run time. In databases, the term materialization is used to refer to storing the results of a precomputation, such as in a materialized view. Overview Precomputing a set of intermediate results at the beginning of an algorithm's execution can often increase algorithmic efficiency substantially. This becomes advantageous when one or more inputs is constrained to a small enough range that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bounding Volume Hierarchy
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 (graphics), ray tracing. Although wrapping objects in bounding volumes and performing collision tests on them before testing the object geometry itself simplifies the tests and can result in significant performance improvements, the same number of pairwise tests between bounding volumes are still being performed. By arranging the bounding volumes into a bounding volu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
If And Only If
In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements. The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, ''P if and only if Q'' means that ''P'' is true whenever ''Q'' is true, and the only case in which ''P'' is true is if ''Q'' is also true, whereas in the case of ''P if Q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axis-aligned Bounding Box
In geometry, the minimum bounding box or smallest bounding box (also known as the minimum enclosing box or smallest enclosing box) for a point set in dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie. When other kinds of measure are used, the minimum box is usually called accordingly, e.g., "minimum-perimeter bounding box". The minimum bounding box of a point set is the same as the minimum bounding box of its convex hull, a fact which may be used heuristically to speed up computation. In the two-dimensional case it is called the ''minimum bounding rectangle''. Axis-aligned minimum bounding box The axis-aligned minimum bounding box (or AABB) for a given point set is its minimum bounding box subject to the constraint that the edges of the box are parallel to the (Cartesian) coordinate axes. It is the Cartesian product of ''N'' intervals each of which is defined by the minimal and maximal value o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
