.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 ; "\$x\$" below arrow from Orig to 1.2 ; "\$y\$" ljust arrow from Orig to 1.2 ; "\$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