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A parametrization of a surface is also called an uv-map.
In this example, we have the map r(u,v) = (cos(u) sin(v), sin(u) sin(v), cos(v))
defined on the rectangle R= [0,2Pi] x [0,pi]. The image is a sphere.
In class, we have painted the following picture on the rectangle. The uv-map
maped it onto the sphere. This is called a texture.
Here is the povray code, which produced the surface:
// simple UV class demonstration in povray
// maths21a, o. knill, Summer 2005, harvard
camera { location <0,1,-3> right x up y look_at <0,0,0> }
background { rgb <1,1,1> }
light_source { <0,10,0> color rgb <1,1,1> }
#declare A = sphere {0, 1
pigment {image_map {png "texture.png" map_type 1 interpolate 4}}
finish {phong 0.5 ambient 0.5 diffuse 1.0}
}
#object { A rotate y*(360*clock) }
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