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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 Euclidean 3-space is a line . In general, an intersection curve consists of the common points of two transversally intersecting surfaces , meaning that at any common point the surface ...
The surface-to-surface intersection (SSI) problem is a basic workflow in computer-aided geometric design: Given two intersecting surfaces in R 3, 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 surfaces, or any combination of these cases. [1]
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 in Euclidean geometry is the line–line intersection between two distinct lines, which either is one point (sometimes called a vertex) or does not exist (if the lines are parallel). Other types ...
The generation of a bicylinder Calculating the volume of a bicylinder. A bicylinder generated by two cylinders with radius r has the volume =, and the surface area [1] [6] =.. The upper half of a bicylinder is the square case of a domical vault, a dome-shaped solid based on any convex polygon whose cross-sections are similar copies of the polygon, and analogous formulas calculating the volume ...
The term “cylinder” can refer to a three-dimensional solid or, as in this article, only the curved external surface of the solid. This is why a line piercing a cylinder's volume is considered to have two points of intersection: the surface point where it enters and the one where it leaves.
A simple example with at least one pencil of curved surfaces: 1) all right circular cylinders with the z-axis as axis, 2) all planes, which contain the z-axis, 3) all horizontal planes (see diagram). A curvature line is a curve on a surface, which has at any point the direction of a principal curvature (maximal or minimal curvature). The set of ...
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 in Euclidean geometry is the line–line intersection between two distinct lines, which either is one point (sometimes called a vertex) or does not exist (if the lines are parallel). Other types ...
The envelope of the normals of the tractrix (that is, the evolute of the tractrix) is the catenary (or chain curve) given by y = a cosh x / a . The surface of revolution created by revolving a tractrix about its asymptote is a pseudosphere. The tractrix is a transcendental curve; it cannot be defined by a polynomial equation.