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2. Surface (mathematics) - Wikipedia

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

   A sphere is the surface of a solid ball, here having radius r. In mathematics, a surface is a mathematical model of the common concept of a surface.It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line.

3. Genus g surface - Wikipedia

   en.wikipedia.org/wiki/Genus_g_surface

   The genus (sometimes called the demigenus or Euler genus) of a connected non-orientable closed surface is a positive integer representing the number of cross-caps attached to a sphere. Alternatively, it can be defined for a closed surface in terms of the Euler characteristic χ, via the relationship χ = 2 − g, where g is the non-orientable ...

4. Differential geometry of surfaces - Wikipedia

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

   A ruled surface is one which can be generated by the motion of a straight line in E 3. [46] Choosing a directrix on the surface, i.e. a smooth unit speed curve c(t) orthogonal to the straight lines, and then choosing u(t) to be unit vectors along the curve in the direction of the lines, the velocity vector v = c t and u satisfy

5. Atlas (topology) - Wikipedia

   en.wikipedia.org/wiki/Atlas_(topology)

   A transition map provides a way of comparing two charts of an atlas. To make this comparison, we consider the composition of one chart with the inverse of the other. This composition is not well-defined unless we restrict both charts to the intersection of their domains of definition. (For example, if we have a chart of Europe and a chart of ...

6. Surface - Wikipedia

   en.wikipedia.org/wiki/Surface

   A sphere is the surface of a solid ball, here having radius r. In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be curved; this is analogous to a curve generalizing a straight line.

7. Bidirectional scattering distribution function - Wikipedia

   en.wikipedia.org/wiki/Bidirectional_scattering...

   BSSRDF (Bidirectional scattering-surface reflectance distribution function or Bidirectional surface scattering RDF) [4] [5] describes the relation between outgoing radiance and the incident flux, including the phenomena like subsurface scattering (SSS). The BSSRDF describes how light is transported between any two rays that hit a surface.