Search results
Results from the WOW.Com Content Network
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 ...
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 ...
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 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]
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 .
Thus, a plane section is the boundary of a cross-section of a solid in a cutting plane. If a surface in a three-dimensional space is defined by a function of two variables, i.e., z = f(x, y), the plane sections by cutting planes that are parallel to a coordinate plane (a plane determined by two coordinate axes) are called level curves or ...
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.