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2. Ruled surface - Wikipedia

   en.wikipedia.org/wiki/Ruled_surface

   Ruled surface generated by two Bézier curves as directrices (red, green) A surface in 3-dimensional Euclidean space is called a ruled surface if it is the union of a differentiable one-parameter family of lines. Formally, a ruled surface is a surface in is described by a parametric representation of the form

3. Conoid - Wikipedia

   en.wikipedia.org/wiki/Conoid

   In geometry a conoid (from Greek κωνος 'cone' and -ειδης 'similar') is a ruled surface, whose rulings (lines) fulfill the additional conditions: (1) All rulings are parallel to a plane, the directrix plane. (2) All rulings intersect a fixed line, the axis. The conoid is a right conoid if its axis is perpendicular to its directrix ...

4. Differential geometry of surfaces - Wikipedia

   en.wikipedia.org/wiki/Differential_geometry_of...

   Simple examples. A simple example of a regular surface is given by the 2-sphere {(x, y, z) | x 2 + y 2 + z 2 = 1}; this surface can be covered by six Monge patches (two of each of the three types given above), taking h(u, v) = ± (1 − u 2 − v 2) 1/2. It can also be covered by two local parametrizations, using stereographic projection.

5. Developable surface - Wikipedia

   en.wikipedia.org/wiki/Developable_surface

   The cylinder is an example of a developable surface. In mathematics, a developable surface (or torse: archaic) is a smooth surface with zero Gaussian curvature. That is, it is a surface that can be flattened onto a plane without distortion (i.e. it can be bent without stretching or compression).

6. Surface (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Surface_(mathematics)

   The surface of a polyhedron is a topological surface, which is neither a differentiable surface nor an algebraic surface. A hyperbolic paraboloid (the graph of the function z = xy) is a differentiable surface and an algebraic surface. It is also a ruled surface, and, for this reason, is often used in architecture.

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8. Translation surface (differential geometry) - Wikipedia

   en.wikipedia.org/wiki/Translation_surface...

   Helicoid as translation surface with identical generatrices , Helicoid as translation surface: any parametric curve is a shifted copy of the purple helix. A helicoid is a special case of a generalized helicoid and a ruled surface. It is an example of a minimal surface and can be represented as a translation surface.

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