START Calculate umbilics 100 for r, and r2 using w plane Calculate a rigid body 3 transformation Yes No Translate r I and for each pair Y Match the directions of ines of curvature Choose one that END Figure 21.4: A diagram for matching using umbilics 11START Calculate umbilics Correspondence pair search using w plane Estimate a scaling factor Calculate a rigid body transformation Exist? match the normal vectors Transformation for each pair Match the directions of lines of curvature Choose one that minimizes the distance squared objective function END mk = (w1k , w2k) mk < 3 Translate r 1 and and scale r 1 No Yes Yes No 100 102 104 106 108 110 112 1 and r2 for r Figure 21.4: A diagram for matching using umbilics. 11