% truncated cone diagram

% 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
<labeled> 2
<> 2.3
def dy
<labeled> 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> {labeled_cone}
<> {basic_cone}

put { view((10,4,2)) } {cone}