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  2. Line-cylinder intersection - Wikipedia

    en.wikipedia.org/wiki/Line-cylinder_intersection

    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.

  3. Cylinder - Wikipedia

    en.wikipedia.org/wiki/Cylinder

    A right circular hollow cylinder (or cylindrical shell) is a three-dimensional region bounded by two right circular cylinders having the same axis and two parallel annular bases perpendicular to the cylinders' common axis, as in the diagram. Let the height be h, internal radius r, and external radius R.

  4. Capsule (geometry) - Wikipedia

    en.wikipedia.org/wiki/Capsule_(geometry)

    A two-dimensional orthographic projection at the left with a three-dimensional one at the right depicting a capsule. A capsule (from Latin capsula, "small box or chest"), or stadium of revolution, is a basic three-dimensional geometric shape consisting of a cylinder with hemispherical ends. [1] Another name for this shape is spherocylinder. [2 ...

  5. Parabolic cylindrical coordinates - Wikipedia

    en.wikipedia.org/wiki/Parabolic_cylindrical...

    In mathematics, parabolic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional parabolic coordinate system in the perpendicular -direction. Hence, the coordinate surfaces are confocal parabolic cylinders.

  6. Packing problems - Wikipedia

    en.wikipedia.org/wiki/Packing_problems

    A container, usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers may be given depending on the problem. A set of objects, some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that ...

  7. Duocylinder - Wikipedia

    en.wikipedia.org/wiki/Duocylinder

    The duocylinder is bounded by two mutually perpendicular 3-manifolds with torus-like surfaces, respectively described by the formulae: + =, + and + =, + The duocylinder is so called because these two bounding 3-manifolds may be thought of as 3-dimensional cylinders 'bent around' in 4-dimensional space such that they form closed loops in the xy - and zw-planes.

  8. Point groups in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Point_groups_in_three...

    In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices.

  9. Clifford torus - Wikipedia

    en.wikipedia.org/wiki/Clifford_torus

    b each has a radius of ⁠ 1 / √ 2 ⁠, their Clifford torus product will fit perfectly within the unit 3-sphere S 3, which is a 3-dimensional submanifold of R 4. When mathematically convenient, the Clifford torus can be viewed as residing inside the complex coordinate space C 2 , since C 2 is topologically equivalent to R 4 .

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