//4bridge.fe (by Rob Kusner, 2 June 1994, at Geometry Center Solder Workshop) // (minor modifications to script by RK, 25 April 1996, at NIST) /*test for optimal solder bead parameters in symmetric periodic pad arrays*/ /* this file gives an array of solder beads connected by bridges which will evolve to a nice disconnected array of solder beads if the volume fraction and gravity:surface tension fraction are correct; by varying these fractions, as well as the other parameters, optimal configurations can easily be obtained: note, my gravity has negative (pendant) sign*/ square_curvature 0 /*to allow some smoothing - turn on later!*/ /*pad radius*/ PARAMETER RR=.8 /*wedge angle for the array*/ PARAMETER TT=pi/4 /*pi/6: hexagonal; pi/4: square; pi/3: triangle; pi/2: linear*/ /*half interpin distance*/ PARAMETER DD=1 /*volume fraction*/ PARAMETER FF=.1918 /*gravity:surface tension fraction*/ PARAMETER GG=1 constraint 1 /*the pad*/ formula: z=0 constraint 2 /*the pad rim*/ formula: x^2+y^2=RR^2 constraint 3 /*mirror through wall*/ formula: y=0 constraint 4 /*mirror through wall corner*/ formula: x*sin(TT)-y*cos(TT)=0 constraint 5 /*the wall*/ formula: x=DD VIEW_TRANSFORM_GENERATORS 3 //reflect through y-axis 1 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 1 //rotate by 2*TT cos(2*TT) -sin(2*TT) 0 0 sin(2*TT) cos(2*TT) 0 0 0 0 1 0 0 0 0 1 //reflect through wall x=DD -1 0 0 2*DD 0 1 0 0 0 0 1 0 0 0 0 1 vertices 1 0 0 1 constraint 3 constraint 4 2 1 0 1 constraint 3 constraint 5 3 1 .25 .75 constraint 5 4 1 0 .5 constraint 3 constraint 5 5 .75 0 0 constraint 1 constraint 2 constraint 3 6 .6 .6 0 constraint 1 constraint 2 constraint 4 7 .5 .5 .5 constraint 4 8 0 0 0 fixed /*display green board*/ 9 DD 0 0 fixed 10 DD DD 0 fixed 11 0 DD 0 fixed edges 1 1 2 constraint 3 2 2 3 constraint 5 3 3 4 constraint 5 4 4 5 constraint 3 5 5 6 constraint 1 constraint 2 6 6 7 constraint 4 7 7 1 constraint 4 8 8 9 fixed /*display green board*/ 9 9 10 fixed 10 10 11 fixed 11 11 8 fixed faces 1 8 9 10 11 density 0 /*display green board*/ 2 1 2 3 4 5 6 7 bodies 1 2 volume FF*TT density 1 read P 9 P 8 transform_expr "2c2a5b" col:=set facet color brown where id=1 or id=3 or id=4 or id =5 col inf:={printf "volume fraction"; print FF; printf "gravity:surface tension fraction"; print GG;printf "number of bridges"; print pi/TT;printf "1/2 interpin distance"; print DD;printf "pad radius"; print RR} inf doit:={G -2*GG;r;l .2;r;V;u;V;u;g;t .06;w .003;V;u;V;u;V;{g5; l .2;t .06; w .003; t .06;V;u}2;V;u;U;{g5;l .1; t .04; w .002; t .04;u}10;g10;inf}