.PS # exp.m4 threeD_init NeedDpicTools # Graduated shading is probably best done using the built-in functions # of PSTricks or the somewhat equivalent tikz capabilities. Other # postprocessors do not have the same functionality so the following # demonstrates how it can be done in the pic language with m4 macros. # See the macro `PhadedPolygon' in libgen.m4 # Projected box object: [ g = 1.2 define(`axlen',1.2*g) define(`O3',`0,0,0') define(`X0',`axlen,0,0') define(`Y0',`0,axlen,0') define(`Z0',`0,0,axlen') # diagram viewing angle dazim = 54 delev = 15 setview(dazim,delev) # projection azimuth, elevation pazim = 20*dtor_ pelev = 35*dtor_ arad = 0.6*g # object displacement define(`D3',`0.3*g,0.6*g,0.9*g') # fixed coordinate frame O: Project(O3) X: Project(X0) Y: Project(Y0) Fector(X0,Z0) with .Origin at O ; "$x_0$" at X rjust Fector(Y0,Z0) with .Origin at O ; "$y_0$" at Y ljust below Fector(Z0,Y0) with .Origin at O ; "`$z_0$'" at Project(Z0) above define(`R01',`rot3Dz(pazim,rot3Dy(-pelev,$1,$2,$3))') define(`R10',`rot3Dy(pelev,rot3Dz(-pazim,$1,$2,$3))') thinlines_ ; psset_(linecolor=gray) line from O to Project(rot3Dz(pazim,axlen,0,0)) psset_(linecolor=black) arc -> ccw from Project(arad,0,0) to Project(rot3Dz(pazim,arad,0,0)) rad arad "$\theta$" below up_ arc -> cw from Project(rot3Dz(pazim,arad,0,0)) \ to Project(R01(arad,0,0)) rad arad "$\phi$" rjust at Project(rot3Dz(pazim,rot3Dy(-pelev/2,arad,0,0))) arc -> from Project(0,arad,0) to Project(R01(0,arad,0)) rad arad "$\theta$" above right_ arc -> cw from Project(0,0,arad/2) to Project(R01(0,0,arad/2)) rad arad/2 "$\phi$" ljust at Here+(-1pt__,-3pt__) Fector(R01(X0),R01(Z0)) with .Origin at O ; "$x_1$" above rjust at Project(R01(X0)) Fector(R01(Y0),R01(Z0)) with .Origin at O ; "$y_1$" ljust at Project(R01(Y0)) Fector(R01(Z0),R01(Y0)) with .Origin at O ; "$z_1$" above at Project(R01(Z0)) thicklines_ # box object dimension b = 0.6*g d = 0.4*g h = 0.20*g # box object corners define(`B0',`D3') define(`B1',`sum3D(D3,d,0,0)') PB1: Project(B1) define(`B2',`sum3D(D3,d,b,0)') PB2: Project(B2) define(`B3',`sum3D(D3,0,b,0)') PB3: Project(B3) define(`B4',`sum3D(D3,0,0,h)') PB4: Project(B4) define(`B5',`sum3D(D3,d,0,h)') PB5: Project(B5) define(`B6',`sum3D(D3,d,b,h)') PB6: Project(B6) define(`B7',`sum3D(D3,0,b,h)') PB7: Project(B7) # projected corners P0:Project(R01(0,dcosine3D(2,R10(B0)),dcosine3D(3,R10(B0)))) P1:Project(R01(0,dcosine3D(2,R10(B1)),dcosine3D(3,R10(B1)))) P2:Project(R01(0,dcosine3D(2,R10(B2)),dcosine3D(3,R10(B2)))) P3:Project(R01(0,dcosine3D(2,R10(B3)),dcosine3D(3,R10(B3)))) P4:Project(R01(0,dcosine3D(2,R10(B4)),dcosine3D(3,R10(B4)))) P5:Project(R01(0,dcosine3D(2,R10(B5)),dcosine3D(3,R10(B5)))) P6:Project(R01(0,dcosine3D(2,R10(B6)),dcosine3D(3,R10(B6)))) P7:Project(R01(0,dcosine3D(2,R10(B7)),dcosine3D(3,R10(B7)))) thinlines_ line from PB1 to P1 line from PB2 to P2 line from PB7 to P7 line from PB4 to P4 thicklines_ # draw the object ifdpic(`line invis fill_(1) from PB4 to PB7 to PB6 to PB5 line from PB4 to PB7; line to PB6; line to PB5 ; line to PB4 line invis fill_(0.5) from PB5 to PB6 to PB2 to PB1 line from PB5 to PB6; line to PB2; line to PB1 ; line to PB5 line invis fill_(0.85) from PB6 to PB7 to PB3 to PB2 line from PB6 to PB7; line to PB3; line to PB2 ; line to PB6', `gshade(1,PB4,PB7,PB6,PB5,PB4,PB7) gshade(0.5,PB5,PB6,PB2,PB1,PB5,PB6) gshade(0.85,PB6,PB7,PB3,PB2,PB6,PB7)') line from PB4 to PB5 to PB1 to PB2 to PB3 to PB7 to PB4 line from PB5 to PB6 to PB7 line from PB6 to PB2 arrow from O to PB1 chop linethick pt__; "$X$" rjust line from P4 to P5 to P1 to P2 to P3 to P7 to P4 line from P5 to P6 to P7 line from P6 to P2 line dashed from P4 to P0 to P3 line dashed from P0 to P1 ] # Globe: [ # Set small text size iflatex(`textoffset = 1bp__; ifpsfrag(`textht = 9.5bp__', `latexcommand({\small)') ') azimuth = 15 # View angles in degrees elevation = 35 setview(azimuth,elevation) rectwid = 3.5 # Basic dimensions rectht = 2.4 alpha = rectht/3 # # Rectangle NW: Project(-rectht/2,-rectwid*0.25,0) SW: Project( rectht/2,-rectwid*0.25,0) SE: Project( rectht/2, rectwid*0.75,0) NE: Project(-rectht/2, rectwid*0.75,0) ShadedPolygon(NW:NE:SE:SW,,-90, 0,0.25,0.25,0.25, 1,1,1,1) with .Start at NW define(`C3D',`0,0,alpha') # Centre of the sphere C: Project(C3D) # # Shaded sphere using PSTricks or tikz: # # this is black magic but PSTricks # # seems to give more control # ifpstricks( # `Highlight: \ # Project(sum3D(C3D,rot3Dz(-15*dtor_,rot3Dy(-60*dtor_,alpha,0,0)))) # command "\pscustom[fillstyle=gradient,gradmidpoint=0.0,%" # command sprintf("gradbegin=gray,gradend=white,gradlines=%g,%%",alpha*200) # command "GradientCircle=true,GradientScale=1.5,%" # command sprintf("GradientPos={(%g,%g)}]{",Highlight.x,Highlight.y) # circle rad alpha at C # command "}%"', # # `ifpgf( # A little too dark with tikz-pgf, maybe: # `command sprintf(\ # "\dpicdraw[ball color=white](%g,%g) circle (%gin)\dpicstop",\ # C.x,C.y,alpha/2.54)', # # `circle rad alpha at C fill_(1) ')') # Shaded sphere with pic shading: shadedball(alpha) at C S: 0,0 # The sphere bottom touch point "$S$" at S+(0,-2pt__) rjust "$\alpha$" at 0.5 ljust define(`N3D',`0,0,2*alpha') # North pole N: Project(N3D) "$N$" at N+(0,3pt__) ljust phi = 65*dtor_ define(`Phat3D',`rot3Dz(phi,alpha*3,0,0)') Phat: "$\hat{P}$" at Project(Phat3D) ljust X: Project(rectht/2*0.8,0,0) Y: Project(0,rectwid/2*0.8,0) `define' linevis { # ratio # Visibility function for lines fom S to Tmp Tlv: $1 between S and Tmp $2 = distance(Tlv,C)-alpha } `define' invisline { # name # Draw dashed invisible part of line in Tmp: $1 # the plane findroot(linevis, 0, 1, 1e-8, x) line dashed from S to x between S and Tmp chop 0 chop 0.05 } thinlines_ # axes invisline(X) arrow to X chop 0.05 chop 0; "$x$" below invisline(Y) arrow to Y chop 0.05 chop 0; "$y$" ljust line dashed from S to N chop 0 chop 0.05 arrow up alpha*0.5 chop 0.05 chop 0 ; "$z$" above invisline(Phat) line to Phat chop 0.05 chop 0 arc ccw -> rad alpha from Project(alpha/2,0,0) to \ Project(rot3Dz(phi,alpha/2,0,0)) "$\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($1),C3D))-alpha } findroot(rayvis, 1e-3, 1, 1e-8, p) # Find P P: "$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 findroot(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($1)) } findroot(equatorvis, 0, pi_, 1e-8, y) n = 0 for ang = y-pi_ to y by pi_/20 do { Q[n]: Project(sum3D(C3D,equator(ang))); n+=1 } fitcurve(Q,n-1) n = 0 for ang = y to y+pi_ by pi_/20 do { Q[n]: Project(sum3D(C3D,equator(ang))); n+=1 } fitcurve(Q,n-1,dashed) line dashed from C to P # beta line dashed from C to Project(sum3D(C3D,equator(phi))) arc ccw -> from 0.6 along_(last line) to 0.6 between C and P "$\beta$" ljust at last arc.e+(0,2pt__) iflatex(ifpsfrag(,`latexcommand(})')) ] with .w at last [].e+(0.5,0) .PE