# Rectangle
ifpstricks(
`command "\pscustom[fillstyle=gradient,gradmidpoint=1.0,%"
command sprintf("gradbegin=gray,gradend=white,gradlines=%g]{",rectwid*200)')
line from Project(-rectht/2,-rectwid*1/3,0) \
to Project( rectht/2,-rectwid*1/3,0) \
then to Project( rectht/2, rectwid*2/3,0) \
then to Project(-rectht/2, rectwid*2/3,0) \
then to Project(-rectht/2,-rectwid*1/3,0)
ifpstricks(command "}%")
define(`C3D',`0,0,alpha') # Centre of the sphere
C: Project(C3D)
# Shaded sphere
ifelse(m4postprocessor,pstricks,
`Highlight: Project(sum3D(C3D,rot3Dz(-15*dtor_,rot3Dy(-60*dtor_,alpha,0,0))))
command "\pscustom[fillstyle=gradient,gradmidpoint=0.0,%"
command sprintf("gradbegin=gray,gradend=white,gradlines=%g,%%",alpha*200)
command "GradientCircle=true,GradientScale=1.5,%"
command sprintf("GradientPos={(%g,%g)}]{",Highlight.x,Highlight.y)
circle rad alpha at C
command "}%"',
m4postprocessor,pgf,
`command sprintf(\# A little too dark, maybe
"\dpicdraw[ball color=white](%g,%g) circle (%gin)\dpicstop",\
C.x,C.y,alpha/2.54)',
`circle rad alpha at C fill_(1) ')
S: "$S$" at Project(0,0,0) rjust # The sphere bottom touch point
"$\alpha$" at 0.5<S,C> rjust
define(`N3D',`0,0,2*alpha') # North pole
N: "N" at Project(N3D) ljust above
phi = 65*dtor_
define(`Phat3D',`rot3Dz(phi,alpha*2.7,0,0)')
Phat: "$\hat{P}$" at Project(Phat3D) ljust
`define' linevis { # ratio # Visibility function for lines fom S to Xb
$2 = distance(($1 between S and Xb),C)-alpha }
`define' invisline { # name # Draw dashed invisible part of line in
Xb: $1 # the plane
bisect( linevis, 0, 1, 1e-8, x )
line dashed from S to x between S and Xb chop 0 chop 0.05 }
thinlines_ # axes
invisline(X)
arrow to X chop 0.05 chop 0; "$x,\:\xi$" at Here+(0,3pt__) below
invisline(Y)
arrow to Y chop 0.05 chop 0; "$y,\:\eta$" ljust
line dashed from S to N chop 0 chop 0.05
arrow up alpha*0.5 chop 0.05 chop 0 ; "$z,\:\zeta$" above ljust
invisline(Phat)
line to Phat chop 0.05 chop 0
arc ccw -> rad alpha from Project(alpha/2,0,0) to \
Project(rot3Dz(phi,alpha/2,0,0))
"$\phi$" below at 0.5 between last arc.start and last arc.end
# vector (ratio along (N to Phat))
define(`ray',`sum3D(N3D,sprod3D($1,diff3D(Phat3D,N3D)))')
`define' rayvis { # ratio
$2 = length3D(diff3D(ray($1),C3D))-alpha }
bisect( rayvis, 1e-3, 1, 1e-8, p ) # Find P
P: "$P$" at Project(ray(p)) ljust above
thicklines_
line dashed from N to P chop 0 chop 0.05
line to Phat chop 0.05 chop 0
define(`meridian',`rot3Dz(phi,rot3Dy(-($1),alpha,0,0))')
`define' meridianvis { # angle # Visibility function on the meridian
$2 = dot3D(meridian($1),View3D) }
thinlines_ # Draw the meridian
bisect( meridianvis, 0, pi_, 1e-8, y )
n = 0
for ang = y-pi_ to y by pi_/20 do {
Q[n]: Project(sum3D(C3D,meridian(ang))); n+=1 }
fitcurve(Q,n-1)
n = 0
for ang = y to y+pi_ by pi_/20 do {
Q[n]: Project(sum3D(C3D,meridian(ang))); n+=1 }
fitcurve(Q,n-1,dashed)
define(`equator',`rot3Dz($1,alpha,0,0)')
`define' equatorvis { # angle # Visibility function on the equator
$2 = dot3D(View3D,equator($1)) }
bisect( equatorvis, 0, pi_, 1e-8, y )
n = 0
for ang = y-pi_ to y by pi_/20 do {
Q[n]: Project(sum3D(C3D,equator(ang))); n+=1 }
fitcurve(Q,n-1)
n = 0
for ang = y to y+pi_ by pi_/20 do {
Q[n]: Project(sum3D(C3D,equator(ang))); n+=1 }
fitcurve(Q,n-1,dashed)
line dashed from C to P # beta
line dashed from C to Project(sum3D(C3D,equator(phi)))
arc ccw -> from 0.6 along_(last line) to 0.6 between C and P
"$\beta$" above
