In geometry, an intersection curve is a curve that is common to two geometric objects. In the simplest case, the intersection of two non-parallel planes...

In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case...

constant, then the above argument proves that the intersection curve C is indeed an ellipse. That the intersection of the plane with the cone is symmetric about...

polyhedron with a line Line segment intersection Intersection curve Determination of the intersection of flats – linear geometric objects embedded in a...

conditions under which an implicit curve locally is given by the graph of a function (so in particular it has no self-intersections). If the defining relations...

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical...

any curves with negative self-intersection. In fact, Castelnuovo’s contraction theorem states the converse: every (−1)-curve is the exceptional curve of...

coefficients a and b in K. The curve is required to be non-singular, which means that the curve has no cusps or self-intersections. (This is equivalent to the...

infinity. Find all the intersections of C with this ray. Score up the winding number as follows: for every clockwise intersection (the curve passing through...

{\displaystyle z} respectively yields: The orthogonal projection of the intersection curve onto the x {\displaystyle x} - y {\displaystyle y} -plane is the circle...

mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective...

trajectory of ω ( t ) {\displaystyle \omega (t)} must stay on the intersection curve between two ellipsoids defined by { ∑ i I i ω i 2 = ∑ i I i ω i (...

in algebraic geometry, the intersection number generalizes the intuitive notion of counting the number of times two curves intersect to higher dimensions...

run in a closed economy. The intersection of the "investment–saving" (IS) and "liquidity preference–money supply" (LM) curves illustrates a "general equilibrium"...

A Bézier curve (/ˈbɛz.i.eɪ/ BEH-zee-ay, French pronunciation: [bezje]) is a parametric curve used in computer graphics and related fields. A set of discrete...

A roundabout, a rotary and a traffic circle are types of circular intersection or junction in which road traffic is permitted to flow in one direction...

In mathematical analysis, a space-filling curve is a curve whose range reaches every point in a higher dimensional region, typically the unit square (or...

space, the curve formed from the intersection between a sphere and a cylinder can be a circle, a point, the empty set, or a special type of curve. For the...

mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be...

that point. The curve of intersection of the plane and the surface has zero curvature at that point. An asymptotic curve is a curve such that, at each...

dual curve of a given plane curve C is a curve in the dual projective plane consisting of the set of lines tangent to C. There is a map from a curve to...

and beautiful results in Euclidean geometry. A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of...

mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), or curve of fastest descent, is the one...

compute all parts of the intersection curve. If two surfaces intersect, the result will be a set of isolated points, a set of curves, a set of overlapping...

exactly the points of intersection of the two first polars. By Bézout's theorem these curves have (n−1)2 points of intersection and these are the poles...

An intersection or an at-grade junction is a junction where two or more roads converge, diverge, meet or cross at the same height, as opposed to an interchange...

and shows that intersection with a bitangent plane must produce two conics of the same type as the generator when the intersection curve is real. The torus...

volume 1 of his Principia in 1687, where he claims that two curves have a number of intersection points given by the product of their degrees. However, Newton...

roadway, measured in meters or feet L = curve length (along the x-axis) PVI = point of vertical interception (intersection of initial and final grades) S = headlight...

Dupin's theorem on threefold orthogonal systems of surfaces, the intersection curve of any two confocal quadrics is a line of curvature. Analogously to...