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  Fig. 3.25a-c: Diagrams to define first fundamental form for a surface. a) Parameter plane with arbitrary curve u = u(t), v = v(t). b) Fine-scale view of curve. c) Three dimensional view of surface and mapped curve, c[u(t), v(t)], with differential tangent vector, dc, that approximates the arc of the curve. Reprinted from (Pollard et al., 2004) with permission from The Geological Society of London.  
         
 
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