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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]
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 ...
One possibility to determine a polygon of points of the intersection curve of two surfaces is the marching method (see section References). It consists of two essential parts: The first part is the curve point algorithm, which determines to a starting point in the vicinity of the two surfaces a point on the intersection curve. The algorithm ...
A Steinmetz curve is the curve of intersection of two right circular cylinders of radii and , whose axes intersect perpendicularly. In case of a = b {\displaystyle a=b} the Steimetz curves are the edges of a Steinmetz solid .
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 ).
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.
In three dimensions, a single equation usually gives a surface, and a curve must be specified as the intersection of two surfaces (see below), or as a system of parametric equations. [18] The equation x 2 + y 2 = r 2 is the equation for any circle centered at the origin (0, 0) with a radius of r.
[3] [4] In 1882, Hertz solved the contact problem of two elastic bodies with curved surfaces. This still-relevant classical solution provides a foundation for modern problems in contact mechanics. For example, in mechanical engineering and tribology, Hertzian contact stress is a description of the stress within mating parts. The Hertzian ...