Search results

In analytic [[geometry]], the '''intersection of two [[plane (mathematics)|planes]]''' in [[three-dimensional space]] is The line of intersection between two planes <math>\Pi_1 : \boldsymbol {n}_1 \cdot \boldsymbol r = h_ ...

{{Short description|Curve that is common to two geometric objects}} ...planes in Euclidean 3-space is a [[line (geometry)|line]]. In general, an intersection curve consists of the common points of two ''transversally'' intersecting [ ...

In [[mathematics]], the '''intersection form''' of an [[oriented]] compact [[4-manifold]] is a special [[symmetric ==Definition using intersection== ...

...tic geometry]] for real three-dimensional space, the curve formed from the intersection between a [[sphere]] and a [[cylinder (geometry)|cylinder]] can be a [[circ The intersection is the collection of points satisfying both equations. ...

{{about|a broad mathematical concept|the point where roads meet|Intersection (road)|other uses}} [[File:Venn0001.svg|220px|thumb|The intersection (red) of two disks (white and red with black boundaries).]] ...

...h with cubicity 2.svg|thumb|upright=1.2|A cubicity 2 graph realized as the intersection graph of unit cubes, i.e. squares, in the plane.]] ...]] that considers the smallest dimension needed to represent a graph as an intersection graph of axis-parallel [[Hyperrectangle|rectangles]] in Euclidean space.<re ...

...hthouse3d.com/tutorials/maths/ray-triangle-intersection|title=Ray-Triangle Intersection|date=26 March 2011 |publisher=lighthouse3d|accessdate=2017-09-10}}</ref> ...ane that the triangle is on, which is needed to calculate the ray-triangle intersection, is defined by a point on the plane, such as <math>v_1</math>, and a vector ...

...]. QGA is a super-algebra over <math>\mathcal{G}_{4, 1}</math> [[conformal geometric algebra]] (CGA) and <math>\mathcal{G}_{1, 3}</math> [[spacetime algebra]] ( ...ranslation]], [[rotation]], [[dilation (affine geometry)|dilation]], and [[intersection]]) that apply to them. QGA extends CGA to also include representations of s ...

...ed by the [[Intersection (set theory)|intersection]] of <math>X</math> and geometric shapes such as disks and axis-parallel rectangles. The goal is to select a ...> of points such that every range of <math>\mathcal{R}</math> has nonempty intersection with <math>H</math>, i.e., is ''hit'' by <math>H</math>. ...

...ty or zero-dimensional. The difference between the topological and algebro-geometric context comes from the topological structure of the fiber product (in the c == Use in intersection theory == ...

...Yellow line lies tangent to the cylinder, so has infinitely many points of intersection.]] ...ersection''' is the calculation of any points of [[Intersection (geometry)|intersection]], given an [[analytic geometry]] description of a [[Line (geometry)|line]] ...

:2. The [[Set intersection|intersection]] of any two polyhedra <math>\sigma_1, \sigma_2 \in \mathcal{K}</math> is a Note that the empty set is a face of every polyhedron, and so the intersection of two polyhedra in <math>\mathcal{K}</math> may be empty. ...

...in direction ''u'' is the (''n''&nbsp;–&nbsp;1)-dimensional volume of the intersection of ''K'' with the hyperplane ''u''^&perp;. Equivalently, the radial function of the intersection body ''IK'' is the [[Funk transform]] of the radial function of ''K''. ...

*Appendix 1 of R. MacPherson, Intersection homology and perverse sheaves, 1990 notes ...ic and Geometric Study of Stratified Spaces: Contributions to Analytic and Geometric Aspects (Lecture Notes in Mathematics, 1768); Publisher, Springer; ...

...[scheme-theoretic intersection]] after some perturbation of factors in the intersection. ...=Example 11.4.5.}}</ref> after some perturbation of cycles on ''X'', their intersection has expected dimension. ...

...vg|thumb|upright=1.2|A graph of the vertices of a pentagon, realized as an intersection graph of disks in the plane. This is an example of a graph with sphericity ...[[dimension]] of [[Euclidean space]] required to realize the graph as an [[intersection graph]] of [[Unit sphere|unit spheres]]. The sphericity of a graph is a gen ...

...troid#Flats|flat]]s of finite, or finite and infinite, matroids, and every geometric or matroid lattice comes from a matroid in this way. | year = 2010}}.</ref> A '''geometric lattice''' is a ''finite'' matroid lattice.<ref name="w10-51">{{harvtxt|Wel ...

...tudy of adversarial geometry involves analyzing the vulnerabilities in the geometric representations of data and designing methods to either enhance the robustn ...oit the high-dimensional space in which neural networks operate, revealing geometric vulnerabilities. ...

...ion if and only if every symmetric convex body is an intersection body. An intersection body is a star body whose radial function in a given direction ''u'' is the ...'</sup> norm]] are intersection bodies for ''n''&nbsp;=&nbsp;4 but are not intersection bodies for ''n''&nbsp;≥&nbsp;5, showing that Zhang's result was incorrect. ...

...blem is an example of [[Resection (orientation)|resection]] (as opposed to intersection). == Solutions via Geometric Algebra == ...