<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div></div><div><br></div><div><br></div><div>However, when I uncomment the \psset{solidmemory} command</div><div>as well as the \pstSolid[object=fusion... and \composeSolid commands,</div><div>and insert [none] at the beginning of each of the three argument lists,</div><div>I get an error message</div><div><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; ">Error: /undefined in cuthyperboloid</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; ">Operand stack:</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; "> base --nostringval--</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; ">Execution stack:</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; "> %interp_exit .runexec2 --nostringval-- --nostringval-- --nostringval-- 2 %stopped_push --nostringval-- --nostringval-- --nostringval-- false 1 %stopped_push 1862 1 3 %oparray_pop 1861 1 3 %oparray_pop 1845 1 3 %oparray_pop 1739 1 3 %oparray_pop --nostringval-- %errorexec_pop .runexec2 --nostringval-- --nostringval-- --nostringval-- 2 %stopped_push --nostringval--</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; ">Dictionary stack:</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; "> --dict:1150/1684(ro)(G)-- --dict:0/20(G)-- --dict:80/200(L)-- --dict:771/1012(L)-- --dict:175/300(L)-- --dict:38/200(L)-- --dict:122/200(L)--</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; ">Current allocation mode is local</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; ">Last OS error: 2</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; ">Current file position is 432819</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; ">GPL Ghostscript 8.70: Unrecoverable error, exit code 1</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; ">### FAILED to generate /tmp/altpdflatex.47607-1279721078/pst3dtest5.1.pdf ()</div></blockquote></div><div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 10px/normal Monaco; "><font class="Apple-style-span" face="Helvetica"><span class="Apple-style-span" style="font-size: medium;"><font class="Apple-style-span" face="Monaco" size="2"><span class="Apple-style-span" style="font-size: 10px;"><br></span></font></span></font></div></div><div>It appears that something is not getting through, but I can't see what it is, or how.</div><div><br></div><div>On a related but different question, is there a way I could turn the master command into a macro calling the other three,</div><div>whose inputs would be similar to the above, but with the height of each adjusted from a single input value h so that the height</div><div>is a different fraction of h depending on which surface is being defined; along the same lines, so that I input two colors, say color1</div><div>and color2, and the calls to the two hyperboloid macros would enter for theme an incolor value color1!65 for the fillcolor and color1!25 for the incolor </div><div>(for the first surface, and same but with color2 instead of color1 for the second)?</div><div>I guess this question is, how can I get the macro to compute something from input that could then be used as an input to one of the called macros?</div><div>Of course, answering this question is only useful if I can resolve the first problem.</div><div><br></div><div><blockquote type="cite"><div><font class="Apple-style-span" color="#000000">%************************************************************************</font></div><div><font class="Apple-style-span" color="#000000">\newcommand{\cuthyperboloid}[9][draw**]{%</font></div><div><font class="Apple-style-span" color="#000000">%surface (x^{2}+y^{2})/A^{2}-z^{2}/B^{2}=1</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">action=#1: default= draw**, alternative=none</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">A=#2</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">B=#3</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">h=#4 (total height of hyperboloid)</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">a=#5 number of levels (vertical division)</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b=#6 number of meridians (division of circles)</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">#7=fillcolor</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">#8=incolor</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">#9=number of cells removed at each level</font></div><div><font class="Apple-style-span" color="#000000">\psSolid</font></div><div><font class="Apple-style-span" color="#000000">[</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">object=new,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">fillcolor=#7,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">incolor=#8,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">hollow, </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">a=#5, %% nb d’etages </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b=#6, %% diviseur de 360, nb de meridiens </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">h=#4, %% hauteur</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">c=#9</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%one cell automatically taken off;</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/c1 {#9 2 idiv} def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%c1=number of extra cells to take off on right</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/c2 {#9 1 sub 2 idiv} def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%c2=number of extra cells to take off on left </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">sommets=</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/A #2 def</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/B #3 def</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/z0 h neg 2 div def </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%z0:=-h/2</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/a1 a 1 add 2 idiv 2 mul def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%a1=floor{(a+1)/2}*2=a if even, a+1 if odd</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% (make no. facelevels even by subdividing middle one into two</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% (for consistency with \cutcone)</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> a 1 add 2 idiv 2 mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">a</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> -1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> 0 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/k exch def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%k:=counter1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">0 1 b 1 sub </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%stack is a 0 0 1 b-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/i exch def </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%i:=counter2</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/r z0 h a div </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> k mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">add</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">B div </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">dup mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 add</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">sqrt </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">A mul</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">def </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%r:=A*\sqrt{(({hk/a}+z0)^2)/B^{2}+1}</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">360 b idiv </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">cos r mul </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%add to stack r*cos([360/b]i)</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">360 b idiv </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">sin r mul </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%add to stack r*sin([360/b]i)</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">z0 h a div </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">add</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%add to stack (hk/a)+z0</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% stack is 0 0 1 b-1 {r*cos([360/b]i) r*sin([360/b]i) (hk/a)+z0}</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% so: for counter2 starting at 0</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">incremented by 1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">until b-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">calculate r*cos([360/b]i) r*sin([360/b]i) (hk/a)+z0</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% stack is a -1 0</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% so: for counter1 starting at a</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% decreased by 1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% until 0</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% do the calculation of the three quantities above (for the values in that loop)</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">, </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">faces=</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%one cell automatically taken off;</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/c1 {#9 2 idiv} def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%c1=number of extra cells to take off on right</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/c2 {#9 1 sub 2 idiv} def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%c2=number of extra cells to take off on left </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">0 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 </font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">a 1 add 2 idiv 2 mul 1 sub</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">a 1 sub</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% stack is 0 1 a1-1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{ </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/k exch def </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% k:=counter1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k b mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 add </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% kb+1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">c1 add</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% kb+1+c1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k 1 add</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b mul </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">sub</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> % (k+1)b-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">c2 sub %(k+1)b-1-c2</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% stack is kb+1+c1 1 (k+1)b-1-c2</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{ </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/i exch def %i=counter1?</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">[</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i 1 sub</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% i-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b i add 1 sub </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% b+i-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b i add</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%b+i</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">]</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% for counter2 starting at kb+1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% incremented by 1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% until (k+1)b-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% calculate the array above</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">[</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k b mul </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% kb</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k 1 add </font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b mul </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 sub </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% (k+1)b-1</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k 2 add </font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b mul </font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 sub </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% (k+2)b-1</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k 1 add</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b mul</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% (k+1)b</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">] </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% for counter1 starting at 0</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% incremented by 1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% until a-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% calculate the array (4 elements) above</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">}, </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">action=#1,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">name=cuthyperboloid,</font></div><div><font class="Apple-style-span" color="#000000">]</font></div><div><font class="Apple-style-span" color="#000000">}</font></div><div><font class="Apple-style-span" color="#000000"><br></font></div><div><font class="Apple-style-span" color="#000000">%************************************************************************************</font></div><div><font class="Apple-style-span" color="#000000">\newcommand{\cutcone}[9][draw**]{%</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">cone with vertical cut opened</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">action=#1default is draw**; alternative is none</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">A=#2</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">B=#3</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">h=#4 (total height of hyperboloid)</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">a=#5 number of levels (vertical division)</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b=#6 number of meridians (division of circles)</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">#7=fillcolor</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">#8=incolor</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">#9=number of cells removed at each level</font></div><div><font class="Apple-style-span" color="#000000">\psSolid</font></div><div><font class="Apple-style-span" color="#000000">[</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">object=new,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">fillcolor=#7,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">incolor=#8,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">hollow, </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">a=#5, %% nb d’etages </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b=#6, %% diviseur de 360, nb de meridiens </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">h=#4, %% hauteur</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">c=#9</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%one cell automatically taken off;</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/c1 {#9 2 idiv} def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%c1=number of extra cells to take off on right</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/c2 {#9 1 sub 2 idiv} def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%c2=number of extra cells to take off on left </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">sommets=</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/A #2 def</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/B #3 def</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/z0 h neg 2 div def </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%z0:=-h/2</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/a1 a 1 add 2 idiv 2 mul def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%a1=floor{(a+1)/2}*2=a if even, a+1 if odd</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% (make no. facelevels even by subdividing middle one into two</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> a 1 add 2 idiv 2 mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> a </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> -1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> 0 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/k exch def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%k:=counter1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">0 1 b 1 sub </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%stack is a 0 0 1 b-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/i exch def </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%i:=counter2</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/z z0 h a1 div k mul add def %z=(hk/a1)+z0</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/r z abs A mul B div def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%r=Az/B</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">360 b idiv </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">cos r mul </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%add to stack r*cos([360/b]i)</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">360 b idiv </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">sin r mul </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%add to stack r*sin([360/b]i)</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">z</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% stack is 0 0 1 b-1 {r*cos([360/b]i) r*sin([360/b]i) (hk/a)+z0}</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% so: for counter2 starting at 0</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">incremented by 1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">until b-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">calculate r*cos([360/b]i) r*sin([360/b]i) (hk/a)+z0</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% stack is a1 -1 0</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% so: for counter1 starting at a1=floor{(a+1)/2}*2</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% decreased by 1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% until 0</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% do the calculation of the three quantities above (for the values in that loop)</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">, </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">faces=</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%one cell automatically taken off;</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/c1 {#9 2 idiv} def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%c1=number of extra cells to take off on right</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/c2 {#9 1 sub 2 idiv} def</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%c2=number of extra cells to take off on left </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">0 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">a 1 add 2 idiv 1 sub</font></div><div><font class="Apple-style-span" color="#000000">%</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% stack is 0 1{(a2=floor{(a+1)/2}) -1} </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{ </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/k exch def </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% k:=counter1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k b mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 add </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% kb+1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">c1 add</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% kb+1+c1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k 1 add</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b mul </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">sub</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> % (k+1)b-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">c2 sub %(k+1)b-1-c</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% stack is kb+1+c 1 (k+1)b-1-c</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{ </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/i exch def %i=counter2</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">[</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i 1 sub</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% i-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b i add 1 sub </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% b+i-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b i add</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%b+i</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">]</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% for counter1 starting at 0</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% incremented by 1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% until a2</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% calculate the array (4 elements) above</font></div><div><font class="Apple-style-span" color="#000000">%</font></div><div><font class="Apple-style-span" color="#000000">%%</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/k a 1 add 2 idiv 1 sub def</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%row above tip of upper cone</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k b mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 add </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% kb+1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">c1 add</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% kb+1+c1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k 1 add</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b mul </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">sub</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> % (k+1)b-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">c2 sub %(k+1)b-1-c</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% stack is kb+1+c 1 (k+1)b-1-c</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{ </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/i exch def %i=counter2</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">[</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i 1 sub</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% i-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b i add 1 sub </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% b+i-1</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b i add</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%b+i</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%eliminate extra zero vertex</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">]</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for </font></div><div><font class="Apple-style-span" color="#000000">%</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/k a 1 add 2 idiv def</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% row below tip of lower cone</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k b mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 add </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% kb+1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">c1 add</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% kb+1+c1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k 1 add</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b mul </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">sub</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> % (k+1)b-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">c2 sub %(k+1)b-1-c</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% stack is kb+1+c 1 (k+1)b-1-c</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{ </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/i exch def %i=counter2</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">[</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i 1 sub</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% i-1</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%eliminate extra zero vertex</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b i add 1 sub </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% b+i-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b i add</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%b+i</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">]</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for </font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for</font></div><div><font class="Apple-style-span" color="#000000">%</font></div><div><font class="Apple-style-span" color="#000000">%</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">a 1 add 2 idiv 1 add</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">a 1 add 2 idiv 2 mul 1 sub</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% stack is {(a2=floor{(a+1)/2})+1} 1{(a1=floor{(a+1)/2}*2)-1} </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{ </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/k exch def </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% k:=counter1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k b mul </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 add </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% kb+1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">c1 add</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% kb+1+c1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">k 1 add</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b mul </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">1 </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">sub</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000"> % (k+1)b-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">c2 sub %(k+1)b-1-c</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% stack is kb+1+c 1 (k+1)b-1-c</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{ </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">/i exch def %i=counter2</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">[</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">i 1 sub</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% i-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b i add 1 sub </font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% b+i-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b i add</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">%b+i</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">]</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">} for</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% for counter1 starting at a2</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% incremented by 1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% until a1-1</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">% calculate the array (4 elements) above</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">}, </font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">action=#1,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">name=cutcone,</font></div><div><font class="Apple-style-span" color="#000000">]</font></div><div><font class="Apple-style-span" color="#000000">}</font></div><div><font class="Apple-style-span" color="#000000">%************************************************************************************************</font></div><div><font class="Apple-style-span" color="#000000">\newcommand{\hyperboloidtwosheet}[8][draw**]{%</font></div><div><font class="Apple-style-span" color="#000000">%surface (x^{2}+y^{2})/A^{2}-z^{2}/B^{2}=-1</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">action=#1: default= draw**, alternative=none</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">A=#2</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">B=#3</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">h=#4 (total height of hyperboloid)</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">a=#5 number of levels (vertical division)</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">b=#6 number of meridians (division of circles)</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">#7=fillcolor</font></div><div><font class="Apple-style-span" color="#000000">%</font><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">#8=incolor</font></div><div><font class="Apple-style-span" color="#000000">%</font></div><div><font class="Apple-style-span" color="#000000">%%</font></div><div><font class="Apple-style-span" color="#000000"><br></font></div><div><font class="Apple-style-span" color="#000000">\defFunction{hypup}(u,v)</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{u v cos mul}</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{u v sin mul}</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{u #2 div dup mul 1 add sqrt #3 mul}</font></div><div><font class="Apple-style-span" color="#000000">\psSolid[</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">object=surfaceparametree,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">base=0 #4 #3 div dup mul 1 sub #2 mul 0 360,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">fillcolor=#7,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">incolor=#8,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">function=hypup,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">ngrid=#5 #6,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">action=none,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">name=inner1,</font></div><div><font class="Apple-style-span" color="#000000">]</font></div><div><font class="Apple-style-span" color="#000000">\defFunction{hypdown}(u,v)</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{u v cos mul}</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{u v sin mul}</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">{u #2 div dup mul 1 add sqrt #3 mul neg}</font></div><div><font class="Apple-style-span" color="#000000">\psSolid[</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">object=surfaceparametree,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">base=0 #4 #3 div dup mul 1 sub #2 mul 0 360,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">fillcolor=#7,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">incolor=#8,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">function=hypdown,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">ngrid=#5 #6,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">action=none,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">name=inner2,</font></div><div><font class="Apple-style-span" color="#000000">]</font></div><div><font class="Apple-style-span" color="#000000">\psSolid[</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">object=fusion,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">action=#1,</font></div><div><span class="Apple-tab-span" style="white-space:pre"><font class="Apple-style-span" color="#000000"> </font></span><font class="Apple-style-span" color="#000000">base=inner1 inner2, </font></div><div><font class="Apple-style-span" color="#000000">]</font></div><div><font class="Apple-style-span" color="#000000">%</font></div><div><font class="Apple-style-span" color="#000000">\composeSolid</font></div><div><font class="Apple-style-span" color="#000000">}</font></div><div><font class="Apple-style-span" color="#000000">%************************************************************************************************</font></div></blockquote></div><div><div><br></div></div><div><br></div><div><br><div><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-size: 12px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Zbigniew Nitecki</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-size: 12px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Department of Mathematics</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-size: 12px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Tufts University</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-size: 12px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Medford, MA 02155</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; font-size: 12px; "><br></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-size: 12px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">telephones:</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-size: 12px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Office<span class="Apple-converted-space"><span class="Apple-converted-tab"> <span class="Apple-converted-space"> </span></span></span>(617)627-3843</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-size: 12px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Dept.<span class="Apple-converted-space"><span class="Apple-converted-tab"> <span class="Apple-converted-space"> </span></span></span>(617)627-3234</font></p><p style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font-size: 12px; "><font face="Helvetica" size="3" style="font: normal normal normal 12px/normal Helvetica; ">Dept. fax<span class="Apple-converted-space"><span class="Apple-converted-tab"> <span class="Apple-converted-space"> </span></span></span>(617)627-3966</font></p><span class="Apple-style-span" style="font-size: 12px; "><a href="http://www.tufts.edu/~znitecki/">http://www.tufts.edu/~znitecki/</a></span>
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