The UV-map

Exhibit: table of content

Mathematics Maths21a, Summer 2005
Multivariable Calculus
Oliver Knill, SciCtr 434,
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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Oliver Knill, Maths21a, Multivariable Calculus, Summer 2005, Department of Mathematics, Faculty of Art and Sciences, Harvard University