% truncated cone diagram def O (0,0,0) def I [1,0,0] def J [0,1,0] def K [0,0,1] def p0 (1,2) def p1 (1.5,0) def N 8 def seg_rot rotate(360 / N, [J]) def dx 2 <> 2.3 def dy 2 <> 3.3 def dz dx def basic_cone { % draw the cone; this is the easy part! sweep[cull=false] { N, [[seg_rot]] } line(p0)(p1) % draw the axes def ax (dx,0,0) def ay (0,dy,0) def az (0,0,dz) line[arrows=<->,linewidth=.4pt](ax)(O)(ay) line[arrows=->,linewidth=.4pt](O)(az) % repeat dotted as an overlay to hint at the hidden lines line[lay=over,linestyle=dotted,linewidth=.4pt](ax)(O)(ay) line[lay=over,linestyle=dotted,linewidth=.4pt](O)(az) % label special|\footnotesize \uput[d]#1{$x$}\uput[u]#2{$y$}\uput[l]#3{$z$}| (ax)(ay)(az) % height measurement mark takes too much code! def c0 (p0) then scale([J]) def hdim_ref unit((p1) - (O)) then [[seg_rot]]^2 def h00 (c0) + 1.1 * [hdim_ref] def h01 (c0) + 1.9 * [hdim_ref] def h02 (c0) + 1.8 * [hdim_ref] line(h00)(h01) def h10 (O) + 1.6 * [hdim_ref] def h11 (O) + 1.9 * [hdim_ref] def h12 (O) + 1.8 * [hdim_ref] line(h10)(h11) line[arrows=<->](h02)(h12) def hm2 ((h02)-(O)+(h12)-(O)) / 2 + (O) special|\footnotesize\rput*#1{$h$}|(hm2) % radius measurement marks def gap [0,.2,0] % first r1 def up1 [0,3.1,0] def r1 ((p1) then [[seg_rot]]^-2) + [up1] def r1c (r1) then scale([J]) def r1t (r1) + [gap] def r1b ((r1t) then scale([1,0,1])) + [gap] line[arrows=<->](r1c)(r1) line(r1b)(r1t) def r1m ((r1) - (O) + (r1c) - (O)) / 2 + (O) special |\footnotesize\rput*#1{$r_1$}|(r1m) % same drill for r0, but must project down first def up0 [0,2.7,0] def r0 ((p0) then scale([1,0,1]) then [[seg_rot]]^-2) + [up0] def r0c (r0) then scale([J]) def r0t (r0) + [gap] def r0b ((p0) then [[seg_rot]]^-2) + [gap] line[arrows=<->](r0c)(r0) line(r0b)(r0t) def r0m ((r0) - (O) + (r0c) - (O)) / 2 + (O) special |\footnotesize\rput*#1{$r_0$}|(r0m) } def labeled_cone { % the "ghost" of the entire cone sweep[linecolor=lightgray,cull=false] { N-1, [[seg_rot]] } line(p0)(p1) % for the highlighted face, we need explicit points def p00 (p0) then [[seg_rot]]^-1 def p10 (p1) then [[seg_rot]]^-1 def p01 (p0) def p11 (p1) polygon[showpoints=true](p00)(p10)(p11)(p01) special|\footnotesize \uput[u]#1{$P_{00}$}\uput[d]#2{$P_{10}$} \uput[u]#3{$P_{01}$}\uput[d]#4{$P_{11}$}| (p00)(p10)(p01)(p11) def mid ((p00)-(O)+(p10)-(O)+(p11)-(O)+(p01)-(O))/4+(O) special|\rput#1{\pscustom{ \scale{1 1.3} \psarc[arrowlength=.5]{->}{.25}{-60}{240}}}| [lay=over](mid) def mid_left ((p00)-(O)+(p10)-(O))/2+(O) def mid_right ((p11)-(O)+(p01)-(O))/2+(O) special|\footnotesize \uput{2pt}[l]#1{$j$}\uput{2pt}[r]#2{$j\hbox{$+$}1$}| (mid_left)(mid_right) def top_lbl (p01) then [[seg_rot]]^2 def bot_lbl (p11) then [[seg_rot]]^2 special|\footnotesize \uput{2pt}[r]#1{$i\hbox{$=$}0$}\uput{2pt}[r]#2{$i\hbox{$=$}1$}| (top_lbl)(bot_lbl) } def cone {labeled_cone} <> {basic_cone} put { view((10,4,2)) } {cone}