ifdef(`View3d',,`threeD_init')
divert(-1)
# Shapedefs.m4
# 3D structures with complex surfaces and hidden lines are the domain of more
# sophisticated software packages, but basic shapes can be drawn with pic.
`cylinder3D(xdispl,ydispl,zdispl,diameter,
[colored "color"])'
define(`cylinder3D',`[ Start: (0,0)
xdispl = `$1'; ydispl = `$2'; zdispl = `$3'
define(`M4CL',`xdispl,ydispl,zdispl')dnl
lenc = length3D(M4CL)
diamc = ifelse(`$4',,(lenc/2),`$4') ; radc = diamc/2
cs = dot3D(View3D,M4CL)/lenc
End: Project(M4CL)
az = atan2(ydispl,xdispl)
ae = atan2(zdispl,sqrt(xdispl^2+ydispl^2))
CL: line invis from Start to End; C: CL.c
nls = int(twopi_*radc/lthick)
define(`M4PP',`rot3Dz(az,rot3Dy(-ae,rot3Dx(-i/nls*twopi_,0,0,radc)))')dnl
for i=0 to nls-1 do { if dot3D(View3D,M4PP) > 0 then {
P: Project(M4PP)
ql = sqrta(dot3D(Light3D,M4PP)/radc)
line from P to End+P outlined rgbstring(ql,ql,ql) `$5' } }
Perp: (vperp(CL,radc))
if cs > 0 then { T: End; B: Start } else { T: Start; B: End }
rpoint_(from Start to Perp)
css = sqrta(cs)
Top: rotellipse(diamc,diamc*cs,
thick linethick/3 shaded rgbstring(css,css,css)) with .c at T
W: line thick linethick/3 from T+Perp to B+Perp
Bot: ellipsearc(diamc,diamc*cs,pi_,twopi_,rp_ang,cw,
thick linethick/3) with .C at B
E: line thick linethick/3 from B-Perp to T-Perp
rpoint_(from Start to End)
`$6']')
`cone3D(xdispl,ydispl,zdispl,diameter,
[colored "color"])'
`internal positions:
Start (centre of base),
End (point),
C (axis centre)'
define(`cone3D',`[ Start: (0,0)
xdispl = `$1'; ydispl = `$2'; zdispl = `$3'
define(`M4CL',`xdispl,ydispl,zdispl')dnl
lenc = length3D(M4CL)
diamc = ifelse(`$4',,(lenc/2),`$4') ; radc = diamc/2
End: Project(M4CL)
cs = dot3D(View3D,M4CL)/lenc
az = atan2(ydispl,xdispl)
ae = atan2(zdispl,sqrt(xdispl^2+ydispl^2))
CL: line invis from Start to End; C: CL.c
nls = int(twopi_*radc/lthick)
lt = sqrt(radc^2+lenc^2)
b = 0
for i=0 to nls-1 do { if dot3D(View3D,
rot3Dz(az,rot3Dy(-ae,rot3Dx(-i/nls*twopi_,radc,0,lenc)))) > 0 then {
ql = sqrta(dot3D(Light3D,
rot3Dz(az,rot3Dy(-ae,rot3Dx(-i/nls*twopi_,radc,0,lenc))))/lt)
P: Project(rot3Dz(az,rot3Dy(-ae,rot3Dx(-i/nls*twopi_,0,0,radc))))
line from P to End outlined rgbstring(ql,ql,ql) `$5'
if !b then { WB: P; b = 1 }
} else { if b then { BW: P; b = 0 } } }
if vlength(CL.x,CL.y) != 0 then { Perp: (vperp(CL,radc,R)) } \
else { Perp: (radc,0) }
if cs >= 0 then { T: End; B: Start } else {T: Start; B: End }
rpoint_(from Start to Perp)
pout = (vlength(End.x,End.y) > abs(radc*cs))
if cs < 0 then { css = sqrta(cs)
if pout then { line thick linethick/3 from BW to End then to WB }
Bot: rotellipse(diamc,diamc*cs,thick linethick/3 \
ifelse(`$5',,`shaded rgbstring(css,css,css)',`$5')) with .c at T } \
else { if pout then {
line thick linethick/3 from BW to End then to WB
a = acos((WB.x*Perp.x+WB.y*Perp.y)/radc^2)
Bot: ellipsearc(diamc,diamc*cs,a,pi_-a,rp_ang,cw, thick linethick/3) \
with .C at B } \
else {
Bot: rotellipse(diamc,diamc*cs,thick linethick/3) with .c at B } }
rpoint_(from Start to End)
`$6']')
`Arrow3D(xdispl,ydispl,zdispl,
diam,arrowwid,arrowht)'
define(`Arrow3D',`[ diam_Ar = ifelse(`$4',,linewid/10,`$4')
wid_Ar = ifelse(`$5',,diam_Ar*2,`$5')
ht_Ar = ifelse(`$6',,wid_Ar*2,`$6')
x_Ar = ifelse(`$1',,1,`$1')
y_Ar = ifelse(`$2',,1,`$2')
z_Ar = ifelse(`$3',,1,`$3')
define(`M4Arrow3D',`x_Ar,y_Ar,z_Ar')dnl
len_Ar = length3D(M4Arrow3D)
len_Shaft = len_Ar - ht_Ar
cs_Ar = dot3D(View3D,M4Arrow3D)
if cs_Ar >= 0 then {
Shaft: cylinder3D(sprod3D(len_Shaft/len_Ar,M4Arrow3D),diam_Ar)
Head: cone3D(sprod3D(ht_Ar/len_Ar,M4Arrow3D),wid_Ar) \
with .Start at Shaft.End } \
else {
Head: cone3D(sprod3D(ht_Ar/len_Ar,M4Arrow3D),wid_Ar)
Shaft: cylinder3D(sprod3D(len_Shaft/len_Ar,M4Arrow3D),diam_Ar) \
with .End at Head.Start }
Start: Shaft.Start; End: Head.End
`$7']')
`prism3D(xdispl,ydispl,zdispl,endwid,endht,
(rad)rotation)
args1-3 are the 3D coords of .End wrt .Start
arg6 is rotation about x axis
Defined points .Start, .End, .C'
define(`prism3D',`[ Start: (0,0)
xdispl = ifelse(`$1',,linewid,`$1')
ydispl = ifelse(`$2',,linewid,`$2')
zdispl = ifelse(`$3',,linewid,`$3')
widp = ifelse(`$4',,(linewid/5),`$4')
htp = ifelse(`$5',,(linewid/10),`$5')
rotp = ifelse(`$6',,0,`$6')
End: Project(xdispl,ydispl,zdispl); C: 0.5 between Start and End
lenp = length3D(xdispl,ydispl,zdispl)
az = atan2(ydispl,xdispl); ae = atan2(zdispl,sqrt(xdispl^2+ydispl^2))
wp2 = widp/2; hp2 = htp/2
# 3D coords of corners (B=back, F=front)
f2xyz3D(nwB,rot3Dz(az,rot3Dy(-ae,rot3Dx(rotp, 0,-wp2, hp2))))
f2xyz3D(swB,rot3Dz(az,rot3Dy(-ae,rot3Dx(rotp, 0,-wp2,-hp2))))
f2xyz3D(seB,rot3Dz(az,rot3Dy(-ae,rot3Dx(rotp, 0, wp2,-hp2))))
f2xyz3D(neB,rot3Dz(az,rot3Dy(-ae,rot3Dx(rotp, 0, wp2, hp2))))
f2xyz3D(nwF,rot3Dz(az,rot3Dy(-ae,rot3Dx(rotp,lenp,-wp2, hp2))))
f2xyz3D(swF,rot3Dz(az,rot3Dy(-ae,rot3Dx(rotp,lenp,-wp2,-hp2))))
f2xyz3D(seF,rot3Dz(az,rot3Dy(-ae,rot3Dx(rotp,lenp, wp2,-hp2))))
f2xyz3D(neF,rot3Dz(az,rot3Dy(-ae,rot3Dx(rotp,lenp, wp2, hp2))))
# facets
M4Facet3D(neF,nwF,swF,seF)
M4Facet3D(neB,seB,swB,nwB)
M4Facet3D(neF,seF,seB,neB)
M4Facet3D(neF,neB,nwB,nwF)
M4Facet3D(seF,swF,swB,seB)
M4Facet3D(nwF,nwB,swB,swF)
`$7']')
`M4Facet3D( a,b,c,d )'
define(`M4Facet3D',`
define(`PFacet',`cross3D(diff3D(`$2'x,`$2'y,`$2'z,`$1'x,`$1'y,`$1'z),
diff3D(`$3'x,`$3'y,`$3'z,`$2'x,`$2'y,`$2'z))')
if dot3D(View3D,PFacet) > 0 then {
fFacet = sqrta(dot3D(Light3D,PFacet)/length3D(PFacet))
P1: Project(`$1'x,`$1'y,`$1'z)
P2: Project(`$2'x,`$2'y,`$2'z)
P3: Project(`$3'x,`$3'y,`$3'z)
P4: Project(`$4'x,`$4'y,`$4'z)
line fill_(fFacet) invis from P1 to P2 then to P3 then to P4 then to P1
line from P1 to P2; round
line to P3; round
line to P4; round
line to P1; round } ')
`M4Pgram3D( c,dne,dnw )'
define(`M4Pgram3D',`
f2xyz3D(ne,sum3D(`$1'x,`$1'y,`$1'z,`$3'x,`$3'y,`$3'z))
f2xyz3D(nw,sum3D(`$1'x,`$1'y,`$1'z,`$2'x,`$2'y,`$2'z))
f2xyz3D(sw,diff3D(`$1'x,`$1'y,`$1'z,`$2'x,`$2'y,`$2'z))
f2xyz3D(se,diff3D(`$1'x,`$1'y,`$1'z,`$3'x,`$3'y,`$3'z))
define(`PPgrapm',`cross3D(
diff3D(nwx,nwy,nwz,nex,ney,nez),
diff3D(swx,swy,swz,nwx,nwy,nwz))')
if dot3D(View3D,PPgram) > 0 then {
fPgram = sqrta(dot3D(Light3D,PPgram)/length3D(PPgram))
P1: Project(`$1'x,`$1'y,`$1'z)
P2: Project(`$2'x,`$2'y,`$2'z)
P3: Project(`$3'x,`$3'y,`$3'z)
P4: Project(`$4'x,`$4'y,`$4'z)
line fill_(fPgram) invis from P1 to P2 then to P3 then to P4 then to P1
line from P1 to P2; round
line to P3; round
line to P4; round
line to P1; round } ')
`prism3D(
xdispl,ydispl,zdispl,endwid,endht,(rad)rotation,
index,dataname,r,g,b)
Defined points .Start, .End, .C
args1-3 are the input 3D coords of .End wrt .Start
args4-5 define the end dimensions
arg6 is rotation about x axis
arg7 is the current depth of the data vector
arg8 is the name (e.g. X) of the vector of
stored face distance, color, and projected coords:
eg X0[n]=[d,r]; X1[n]=[g,b]
X2[n]=proj(C); X3[n]=proj(NE); X4[n]=proj(NW)'
define(`prism3D',`[ Start: (0,0)
xdispl = ifelse(`$1',,linewid,`$1')
ydispl = ifelse(`$2',,linewid,`$2')
zdispl = ifelse(`$3',,linewid,`$3')
widp = ifelse(`$4',,(linewid/5),`$4')
htp = ifelse(`$5',,(linewid/10),`$5')
rotp = ifelse(`$6',,0,`$6')
End: Project(xdispl,ydispl,zdispl); C: 0.5 between Start and End
lenp = length3D(xdispl,ydispl,zdispl)
az = atan2(ydispl,xdispl); ae = atan2(zdispl,sqrt(xdispl^2+ydispl^2))
wp2 = widp/2; hp2 = htp/2
# 3D coords of corners (B=back, F=front)
f2xyz3D(nwB,rot3Dz(az,rot3Dy(-ae,rot3Dx(rotp, 0,-wp2, hp2))))
f2xyz3D(swB,rot3Dz(az,rot3Dy(-ae,rot3Dx(rotp, 0,-wp2,-hp2))))
f2xyz3D(seB,rot3Dz(az,rot3Dy(-ae,rot3Dx(rotp, 0, wp2,-hp2))))
f2xyz3D(neB,rot3Dz(az,rot3Dy(-ae,rot3Dx(rotp, 0, wp2, hp2))))
