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.PS
# Planes.m4
threeD_init
NeedDpicTools
# These 3D diagrams are like many others: define the surface facets,
# use normal vectors to determine visibility, sort and plot the visible
# facets from back to front.
# Store a point as x_[i], y_[i], z_[i]
define(`mktriple',`
x_[$1] = $2
y_[$1] = $3
z_[$1] = $4')
# Recover point coordinates
define(`triple',`x_[$1], y_[$1], z_[$1]')
define(`facetnormal',`cross3D(
diff3D(triple($1*3+1),triple($1*3)),
diff3D(triple($1*3+2),triple($1*3+1)))')
define(`facetcenter',`sprod3D(0.5,sum3D(triple($1*3),triple($1*3+2)))')
# Create npositive, arrays dcosine[1..npositive]
# and index ix[1..npositive] of sorted facets
# Uses macros facetnormal(i) and facetcenter(i)
define(`processfacets',`
npositive = 0
for i=1 to `$1' do {
mktriple(0,facetnormal(i))
dx = dot3D(triple(0),View3D)
if dx > 0 then {
dcosine[i] = dx/length3D(triple(0)) # direction cosine normal wrt View3D
npositive +=1
dist[npositive] = dot3D(facetcenter(i),View3D) # distance
ix[npositive] = i
}
}
dpquicksort(dist,1,npositive,ix) ')
ifelse(1,1,`
Threeplanes: [
# Size parameters
a = 3/2
b = 0.4
d = 1
# Define intersecting lines in the plane
A0: -a,-b
A1: a,-b
B0: Rot_(A0,120)
B1: Rot_(A1,120)
C0: Rot_(A0,240)
C1: Rot_(A1,240)
# Intersections
define(`lintersect',`intersect_(`$1'0,`$1'1,`$2'0,`$2'1)')
AB: lintersect(A,B)
BC: lintersect(B,C)
CA: lintersect(C,A)
# Facets are rectangles here; store 3 corners
define(`mkfacet',`
mktriple((`$1')*3, 0,`$2'.x,`$2'.y)
mktriple((`$1')*3+1, 0,`$3'.x,`$3'.y)
mktriple((`$1')*3+2,-d,`$3'.x,`$3'.y)
')
# Define the facets
mkfacet(m4inx,A0,CA) mkfacet(m4inx,CA,A0)
mkfacet(m4inx,CA,AB) mkfacet(m4inx,AB,CA)
mkfacet(m4inx,AB,A1) mkfacet(m4inx,A1,AB)
mkfacet(m4inx,B0,AB) mkfacet(m4inx,AB,B0)
mkfacet(m4inx,AB,BC) mkfacet(m4inx,BC,AB)
mkfacet(m4inx,BC,B1) mkfacet(m4inx,B1,BC)
mkfacet(m4inx,C0,BC) mkfacet(m4inx,BC,C0)
mkfacet(m4inx,BC,CA) mkfacet(m4inx,CA,BC)
mkfacet(m4inx,CA,C1) mkfacet(m4inx,C1,CA)
nfacets = m4x
# Wierd color
define(`colr',`ifelse(`$1',,"white",
`rgbstring(`$1',ifelse(`$2',,`$1',`$2'),ifelse(`$3',,`$1',`$3'))')')
# Recover the 4th corner and draw
define(`drawfacet',`
NW_facet: project(triple(($1)*3))
NE_facet: project(triple(($1)*3+1))
SE_facet: project(triple(($1)*3+2))
SW_facet: project(x_[($1)*3+2],y_[($1)*3],z_[($1)*3])
N_facet: 0.5 between NW_facet and NE_facet
line from N_facet to NE_facet then to SE_facet then to SW_facet \
then to NW_facet then to N_facet shaded colr(`$2',`$3',`$4')
# fill_(ifelse(`$2',,1,`(1-`$2')'))
')
# View angles azimuth, elevation, rotation (degrees)
setview( 10, 40 )
# Draw facets, shading with view cosines
processfacets(nfacets)
for i=1 to npositive do { drawfacet(ix[i],max(0,1-2*dcosine[ix[i]]),
dcosine[ix[i]],
dcosine[ix[i]])
# for i=1 to npositive do { drawfacet(ix[i],dcosine[ix[i]])
}
] # Threeplanes
')
# Bowl
# vertx_(facet_no,vertex_no)
define vertx_ { ($1-1)*nvertices + $2 }
# Normal vector to a facet
define(`facetnormal',`cross3D(
diff3D(triple(vertx_($1,2)),triple(vertx_($1,1))),
diff3D(triple(vertx_($1,4)),triple(vertx_($1,1))))')
# Facet center
define(`facetcenter',`sprod3D(1/4,sum3D(
sum3D(triple(vertx_(`$1',1)),triple(vertx_(`$1',2))),
sum3D(triple(vertx_(`$1',3)),triple(vertx_(`$1',4)))))')
define(`drawplane',`
NW_plane: project(triple(vertx_($1,1)))
SW_plane: project(triple(vertx_($1,2)))
SE_plane: project(triple(vertx_($1,3)))
NE_plane: project(triple(vertx_($1,4)))
N_plane: 0.5 between NW_plane and NE_plane
shd = (`$2')^(1/4)
line from N_plane to NE_plane then to SE_plane then to SW_plane \
then to NW_plane then to N_plane \
fill_(ifelse(`$2',,1,shd)) outlined rgbstring(shd,shd,shd)
# line from NW_plane to NE_plane
line from SW_plane to SE_plane
')
ifelse(1,1,`
nvertices = 4 # vertices per facet
Bowl: [
elevation = 30
setview( 0, 30 )
nplanes = 40
bigradius = 2
smallradius = 1
cupht = 1.5
thin = smallradius/10
# Define the facet corners
for i=1 to nplanes do {
mktriple(vertx_(i,1),rot3Dz((i-1)/nplanes*twopi_,bigradius,0,0))
mktriple(vertx_(i,2),rot3Dz((i-1)/nplanes*twopi_,smallradius,0,-cupht))
mktriple(vertx_(i,3),rot3Dz((i )/nplanes*twopi_,smallradius,0,-cupht))
mktriple(vertx_(i,4),rot3Dz((i )/nplanes*twopi_,bigradius,0,0))
mktriple(vertx_(nplanes+i,1),triple(vertx_(i,4)))
mktriple(vertx_(nplanes+i,2),triple(vertx_(i,3)))
mktriple(vertx_(nplanes+i,3),triple(vertx_(i,2)))
mktriple(vertx_(nplanes+i,4),triple(vertx_(i,1)))
}
# for i=1 to nplanes do {
# mktriple(vertx_(i,1),rot3Dz((i-1)/nplanes*twopi_,bigradius,0,0))
# mktriple(vertx_(i,2),rot3Dz((i-1)/nplanes*twopi_,smallradius,0,-cupht))
# mktriple(vertx_(i,3),rot3Dz((i-1)/nplanes*twopi_,smallradius-thin,0,-cupht))
# mktriple(vertx_(i,4),rot3Dz((i-1)/nplanes*twopi_,bigradius-thin,0,0))
# }
# Find the visible facets and sort
processfacets(nplanes*2)
for i=1 to npositive do { drawplane(ix[i],dcosine[ix[i]]) }
ellipse wid 2*bigradius ht 2*bigradius*sin(elevation*dtor_) at project(0,0,0)
] #with .sw at Threeplanes.se
')
.PE
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