This script shows a few elementary manipulations of an 'Owl' circle packing. You can just click through the script and watch, or you can apply the various manipulations I have attached to icons. For instance, with 'b', the 'boundary' circles of the packing will be displayed in red; press 'u' while the cursor is on a boundary circle and its radius will go up; and so forth. Open the Script if you want more information. The 'Owl' packing is a simple circle packing (just 80 circles) which is convenient for illustrations --- in particular, the 'eyes', colored blue, provide a reference the observe can follow in various manipulations. Here will will work first in euclidean geometry, then hyperbolic geometry (in the unit disc), and finally in spherical geometry.

act 0;cleanse;cleanse -p1;cleanse -p2;infile_read Owl.p;color -c 20 21 22;color -c 180 b;set_disp_text -w -c -cf 21 22;disp -w -c -cf 21 22; In each geometry, the icons 'b', 'k', and 'f' will display, respectively, the boundary circles (in red), the 'complex' K of edges that specify the tangencies that must be maintained, and 'carrier' (triangulation) of faces formed by triples of circles. disp -cf b; disp -f; disp -ff; In euclidean and hyperbolic geometry, you can place the cursor on a boundary circle and press 'u' (up) or 'd' (down) to adjust its radius. A computation --- discussed in the Chapter --- adjusts the packing to incorporate this new boundary data. You might try, for example, to find the boundary circle(s) whose adjustments have the greatest impact on the overall packing. set_vlist z #XY;adjust_rad 1.25 vlist;repack;layout;disp -wr; set_vlist z #XY;adjust_rad .75 vlist;repack;layout;disp -wr;

The next command moves the owl to hyperbolic geometry. The command 'i' increments all boundary radii at once. It is interesting to compare the effect this has in the hyperbolic setting as compared to the euclidean setting. act 1;infile_read Owl.p;geom_to_h;color -c 20 21 22;color -c 180 b;set_disp_text -w -c -cf 21 22;disp -w -c -cf 21 22; [b];[k]; adjust_rad 1.25 b;repack;layout;disp -wr;

Finally, we move the owl to the sphere. You can rotate the sphere with the mouse to see other views. copy 2;act 2;geom_to_s;set_disp_text -w -c -cf 21 22 b;disp -w -c -cf 21 22 b; A final note: Invoking the 'Advanced' menu item, you see that we have a separate copy of the owl for each of the three geometries. You can choose (by double clicking) which of the packings to bring into the main window, where the display options we discussed can be applied. [b];[k];

NODECOUNT: 80 GEOMETRY: euclidean ALPHA/BETA/GAMMA: 8 80 26 PACKNAME: Empty FLOWERS: 1 5 74 73 6 4 2 58 2 8 1 4 7 5 3 56 57 58 1 3 7 56 2 5 8 14 20 37 56 4 4 1 6 7 2 1 5 4 2 7 8 3 2 6 7 73 71 11 9 7 4 1 73 7 8 4 6 9 12 10 8 5 2 4 8 10 18 17 16 15 14 3 5 7 10 13 18 9 4 6 11 12 7 6 10 4 7 12 13 8 7 11 5 43 12 9 6 71 72 12 8 43 42 41 13 10 7 9 11 43 13 7 40 19 18 8 10 12 41 40 14 5 22 20 3 8 15 22 15 4 22 14 8 16 22 16 6 23 22 15 8 17 21 23 17 4 21 16 8 18 21 18 5 21 17 8 13 19 21 19 4 40 21 18 13 40 20 4 3 14 22 37 3 21 15 40 39 38 34 33 32 28 26 25 24 23 16 17 18 19 40 22 15 20 14 15 16 23 24 25 26 27 29 30 31 35 36 37 20 23 4 24 22 16 21 24 24 4 25 22 23 21 25 25 4 26 22 24 21 26 26 5 28 27 22 25 21 28 27 3 29 22 26 28 28 3 27 26 21 32 29 2 30 22 27 30 2 31 22 29 31 2 35 22 30 32 2 28 21 33 33 2 32 21 34 34 2 33 21 38 35 2 36 22 31 36 2 37 22 35 37 4 56 3 20 22 36 38 2 34 21 39 39 2 38 21 40 40 4 39 21 19 13 41 41 4 40 13 12 42 44 42 7 47 46 45 44 41 12 43 47 43 3 47 42 12 11 44 2 41 42 45 45 4 44 42 46 48 50 46 5 49 48 45 42 47 49 47 4 53 49 46 42 43 48 6 52 51 50 45 46 49 52 49 5 53 52 48 46 47 53 50 2 45 48 51 51 3 50 48 52 54 52 6 55 54 51 48 49 53 55 53 3 55 52 49 47 54 2 51 52 55 55 2 54 52 53 56 4 59 57 2 3 37 57 7 58 2 56 59 60 61 62 58 58 3 1 2 57 62 59 2 60 57 56 60 4 64 63 61 57 59 61 5 62 57 60 63 66 62 62 4 58 57 61 66 67 63 6 68 66 61 60 64 65 68 64 2 65 63 60 65 3 70 68 63 64 66 5 68 67 62 61 63 68 67 3 62 66 68 69 68 6 70 69 67 66 63 65 70 69 2 67 68 70 70 2 69 68 65 71 6 76 75 72 11 6 73 76 72 2 11 71 75 73 6 77 76 71 6 1 74 77 74 2 77 73 1 75 3 72 71 76 78 76 7 80 79 78 75 71 73 77 80 77 3 80 76 73 74 78 2 75 76 79 79 2 78 76 80 80 2 79 76 77 RADII: 8.877231134e-02 9.876914391e-02 6.340311383e-02 3.640443023e-02 3.473920616e-02 7.770501683e-02 8.809900175e-02 9.265457151e-02 3.640443025e-02 3.473920618e-02 8.877231132e-02 9.876914407e-02 6.340311385e-02 3.453242824e-02 2.580934240e-02 4.693192201e-02 2.580934240e-02 3.453242824e-02 2.382033777e-02 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