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.PS
# graysurf.m4
threeD_init
NeedDpicTools
Overall: [
Surface:[
# This just draws the facets back to front
setview(20,30)
dimen = 1.5
xmax = 2*dimen
ymax = 1.5*dimen
zmax = 1*dimen
define(`fn',
`expe(-(`$1')/tt)*cos((`$2')/xmax*1.75*twopi_)*cos((`$1')/ymax*twopi_)')
nx = 24; dx = xmax/nx
ny = 30; dy = ymax/ny
tt = 1.5
fnmax = fn(0,0,0)
Orig: (0,0)
linethick_(1.2)
arrow from Orig to 1.2 <Orig,(Project(xmax,0,0))> ; "$x$" below
arrow from Orig to 1.2 <Orig,(Project(0,ymax,0))> ; "$y$" ljust
arrow from Orig to 1.2 <Orig,(Project(0,0,zmax))> ; "$z$" rjust
linethick_(0)
for i = 0 to nx-1 do {
x = xmax*i/nx
for j = 0 to ny-1 do {
y = ymax*j/ny
fnxy = fn(x,y)
shade((fnmax+fnxy)/fnmax/2,
line from (Project(x,y,fnxy)) to (Project(x,(y+dy),`fn(x,(y+dy))'))\
then to (Project((x+dx),(y+dy),`fn((x+dx),(y+dy))'))\
then to (Project((x+dx),y,`fn((x+dx),y)'))\
then to (Project(x,y,fnxy))
) } }
] #with .w at last [].e+(-0.2,0)
Torus: [
# Calculate all the facet centres but draw
# only a subset of them after sorting
viewazimuth = 20 # Set view angles in degrees
viewelevation = 30
setview(viewazimuth,viewelevation,0)
sfactor = 0.7
tradius = 2*sfactor
sradius = 0.75*sfactor
define(`torus',`rot3Dz((`$1')*dtor_,
sum3D(tradius,0,0,rot3Dy((`$2')*dtor_,sradius,0,0)))')
define(`tvisible',
`dot3D(View3D, rot3Dz((`$1')*dtor_,rot3Dy((`$2')*dtor_,1,0,0)))')
Orig: (0,0)
X: arrow from Orig to (Project(tradius+sradius*4,0,0)); "x" rjust
Y: arrow from Orig to (Project(0,tradius+sradius*2,0)); "y" ljust
dt = 10 # major angle degrees per facet
ds = 10 # minor angle degrees per facet
# create the arrays and sort
n = 0
for t = dt to 360+dt/2 by dt do {
for s=ds/2 to 360.1 by ds do {
if tvisible(t,s) >= 0 then {
n +=1
t[n] = t
s[n] = s
d[n] = dot3D(torus(t,s),view3D1,view3D2,view3D3) # view distance
ix[n] = n
} } }
#prval(n)
dpquicksort(d,1,n,ix)
# draw the facets
thinlines_
for i = 1 to n do {
tc = t[ix[i]]; sc = s[ix[i]]
SE: (Project(torus(tc+dt/2,sc-ds/2)))
SW: (Project(torus(tc-dt/2,sc-ds/2)))
NW: (Project(torus(tc-dt/2,sc+ds/2)))
NE: (Project(torus(tc+dt/2,sc+ds/2)))
f = ((dcosine3D(3,torus(tc,sc))/sradius+1)/2)^2
g = min(f,0.9)
setrgb(g,g,g)
line fill f ifpdf( invis ) \
from SE to SW then to NW then to NE then to SE
# line invis shaded rgbstring(f,f^3,f^3) \
# f from SE to SW then to NW then to NE then to SE
resetrgb
}
thicklines_
arrow from Orig to (Project(0,0,tradius*1.4)); "z" above
dashline(from Orig to (Project(torus(0,0))),,,,G)
arrow to X.end
dashline(from Orig to (Project(torus(90,0))),,,,G)
arrow to Y.end
] with .sw at last [].se+(0.2,0)
Hat: [
# Sort as for the torus but draw edges too
azimuth = 25 # View angles in degrees
elevation = 20
setview(azimuth,elevation)
# the 3D object: `hat(t,y)'
define(`hat',`cosd($1)*($2),sind($1)*($2),(($2)^2-1)^2')
define(`gradient',`(-4*($2)*(($2)^2-1)*cosd(`$1')),
(-4*($2)*(($2)^2-1)*sind(`$1')),1')
define edge {$2=dot3D(View3D,gradient($1,y))}
define(`hatvis',
`(($2 > 0.6) || (dot3D(View3D,gradient($1,$2)) > 0))')
# grid parameters
dang = 09
maxy = 1.25
dy = 0.05
Orig: (0,0)
X: arrow from Orig to (Project(maxy*1.2,0,0)); "x" rjust
Y: arrow from Orig to (Project(0,maxy*1.2,0)); "y" ljust
Xv: (Project(1,0,0))
Yv: (Project(0,1,0))
Zv: (Project(0,0,1))
# create the arrays and sort
n = 0
for t = dang/2 to 360.1 by dang do {
for y=dy/2 to maxy by dy do {
if hatvis(t,y) then {
n +=1
t[n] = t
y[n] = y
d[n] = dot3D(hat(t,y),View3D) #distance toward the front
ix[n] = n
} } }
#prval(n)
dpquicksort(d,1,n,ix)
# draw the facets
ellipse wid maxy*2 ht maxy*2*sind(elevation) \
with .c at (Project(0,0,(maxy^2-1)^2)+(0,linethick bp__/2))
thinlines_
for i = 1 to n do {
tc = t[ix[i]]; yc = y[ix[i]]
SE: (Project(hat(tc+dang/2,yc-dy/2)))
SW: (Project(hat(tc-dang/2,yc-dy/2)))
NW: (Project(hat(tc-dang/2,yc+dy/2)))
NE: (Project(hat(tc+dang/2,yc+dy/2)))
f = abs(yc^2-1)
line invis fill f from SE to SW then to NW then to NE then to SE
}
# Outline where the surface goes invisible
mm = int(maxy/dy)
nr = -1
for i=1 to mm do { y = i/(mm+3)
findroot(edge,(azimuth+2),(azimuth+180-2),1e-8,t)
nr +=1
R[mm+nr]: (Project(hat(t,y)))
R[mm-1-nr]: (-R[mm+nr].x,R[mm+nr].y)
}
fitcurve(R,mm*2-1)
# Z axis
thicklines_
Z: arrow from Zv to (Project(0,0,1.2)); "z" ljust
line dashed from Orig to Zv chop 0 chop dashwid/2
line dashed from Orig to Xv
line dashed from Orig to Yv
# Partial rim
ellipsearc(maxy*2,maxy*2*sind(elevation),-pi_*1.4,pi_/3) \
with .C at (Project(0,0,(maxy^2-1)^2)+(0,linethick bp__/2))
] scaled 1.25 with .s at 1st [].ne+(0,-0.75)
] scaled 0.85
.PE
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