divert(-1) lib3D.m4 Macros for rotation, projection, and other operations on argument triples representing 3D vectors or colors. * Circuit_macros Version 10.5, copyright (c) 2024 J. D. Aplevich under * * the LaTeX Project Public Licence in file Licence.txt. The files of * * this distribution may be redistributed or modified provided that this * * copyright notice is included and provided that modifications are clearly * * marked to distinguish them from this distribution. There is no warranty * * whatsoever for these files. * define(`lib3D_') ifdef(`libgen_',,`include(libgen.m4)divert(-1)') ============================================================================= `setview(azimuth, elevation, rotation) Set view angles (degrees) for projection onto a plane. The view vector is obtained by looking in along the x axis, then rotating about -x, -y, and z in that order. 3D vectors are projected onto the resulting yz plane using the project() macro. If rotation = 0, the projection matrix P is P =( -sin(az), cos(az), 0 ) (-sin(el)cos(az),-sin(az)sin(el),cos(el))' define(`setview',` `# setview($@)' define(`m4azim',ifelse(`$1',,0,prod_($1,dtor_)))dnl define(`m4elev',ifelse(`$2',,0,prod_($2,dtor_)))dnl define(`m4rot', ifelse(`$3',,0,prod_($3,dtor_)))dnl define(`m4azimr',`ifelse(`$1',,0,`prod_(`$1',dtor_)')')dnl define(`m4elevr',`ifelse(`$2',,0,`prod_(`$2',dtor_)')')dnl define(`m4rotx',`ifelse(`$3',,0,`prod_(`$3',dtor_)')')dnl define(`m4caz', `ifelse(`$1',,1,`$1',0,1,`$1',90,0,`$1',-90, 0,m4cos(m4azim))')dnl define(`m4saz', `ifelse(`$1',,0,`$1',0,0,`$1',90,1,`$1',-90,-1,m4sin(m4azim))')dnl define(`m4cel', `ifelse(`$2',,1,`$2',0,1,`$2',90,0,`$2',-90, 0,m4cos(m4elev))')dnl define(`m4sel', `ifelse(`$2',,0,`$2',0,0,`$2',90,1,`$2',-90,-1,m4sin(m4elev))')dnl define(`m4cro',`ifelse(`$3',,1,`$3',0,1,`$3',90,0,`$3',-90, 0,m4cos(m4rot))')dnl define(`m4sro',`ifelse(`$3',,0,`$3',0,0,`$3',90,1,`$3',-90,-1,m4sin(m4rot))')dnl view3D1=m4caz*m4cel;dnl view3D2=m4saz*m4cel;dnl view3D3=m4sel ifdef(`setlight_',,`light3D1=view3D1; light3D2=view3D2; light3D3=view3D3') dnl Unit vectors projected on the view plane UPx_: project(1,0,0) UPy_: project(0,1,0) UPz_: project(0,0,1) `# setview end' ') define(`m4cos',`ifelse(`$1',0,1,cos(`$1'))') define(`m4sin',`ifelse(`$1',0,0,sin(`$1'))') The resulting view vector #efine(`View3D',`PtoBase3D(1,0,0)') define(`View3D',`view3D1,view3D2,view3D3') `Extract the x-y, x-z, or y-z coordinate pair from a triple' define(`Pr_xy',`$1,$2') define(`Pr_xz',`$1,$3') define(`Pr_yz',`$2,$3') Projection coords back to orig 3D coords define(`PtoBase3D', `rot3Dz(m4azim,rot3Dy(-m4elev,rot3Dx(-m4rot,`$1',`$2',`$3')))') This does the 3D to 2D axonometric projection i.e. project(x,y,z) produces coordinate pair u,v on the 2D plane defined by the view angles and Project(x,y,z) produces position (u,v) ifdpic( `define(`project', `Pr_yz(rot3Dx(m4rot,rot3Dy(m4elev,rot3Dz(-m4azim,`$1',`$2',`$3'))))') define(`Project',`(ifelse(`$1',0, `ifelse(`$2',0,`ifelse(`$3',0,`(0,0)',UPz_*(`$3'))', `UPy_*(`$2')`'ifelse(`$3',0,,+UPz_*(`$3'))')', `UPx_*(`$1')`'ifelse(`$2',0,,+UPy_*(`$2'))`'ifelse(`$3',0,,+UPz_*(`$3'))'))')', `define(`project', `Pr_yz(rot3Dx(m4rot,rot3Dy(m4elev,rot3Dz(-m4azim,`$1',`$2',`$3'))))') define(`Project',`(project($@))')') `Rotation about x axis rot3Dx(angle,x1,x2,x3)' define(`rot3Dx',``$2',diff_(prod_(m4cos(`$1'),`$3'),prod_(m4sin(`$1'),`$4')),dnl sum_(prod_(m4sin(`$1'),`$3'),prod_(m4cos(`$1'),`$4'))') `Rotation about y axis rot3Dy(angle,x1,x2,x3)' define(`rot3Dy',`sum_(prod_(m4cos(`$1'),`$2'),prod_(m4sin(`$1'),`$4')),`$3',dnl diff_(prod_(m4cos(`$1'),`$4'),prod_(m4sin(`$1'),`$2'))') `Rotation about z axis rot3Dz(angle,x1,x2,x3)' define(`rot3Dz',`diff_(prod_(m4cos(`$1'),`$2'),prod_(m4sin(`$1'),`$3')),dnl sum_(prod_(m4sin(`$1'),`$2'),prod_(m4cos(`$1'),`$3')),`$4'') `Cross product cross3D(x1,y1,z1,x2,y2,z2)' define(`cross3D',`diff_(prod_(`$2',`$6'),prod_(`$3',`$5')),dnl diff_(prod_(`$3',`$4'),prod_(`$1',`$6')),dnl diff_(prod_(`$1',`$5'),prod_(`$2',`$4'))') `Dot product dot3D(x1,y1,z1,x2,y2,z2)' define(`dot3D',`(sum_( sum_(prod_(`$1',`$4'),prod_(`$2',`$5')),prod_(`$3',`$6')))') Vector addition, subtraction, scalar product define(`sum3D',`sum_(`$1',`$4'),sum_(`$2',`$5'),sum_(`$3',`$6')') define(`diff3D',`diff_(`$1',`$4'),diff_(`$2',`$5'),diff_(`$3',`$6')') define(`sprod3D',`prod_(`$1',`$2'),prod_(`$1',`$3'),prod_(`$1',`$4')') Extract direction cosine `eg v = dcosine3D(1,x,y,z) assigns x to v' define(`dcosine3D',`(ifelse(`$1',1,`$2',`$1',2,`$3',`$4'))') Euclidian length define(`length3D',`sqrt((`$1')^2+(`$2')^2+(`$3')^2)') Unit vector define(`unit3D',`sprod3D(1/length3D(`$1',`$2',`$3'),`$1',`$2',`$3')') Proportion: between3D(x,Vec1,Vec2), i.e. Vec1 * (1-x) + Vec2 * x define(`between3D',`sum3D(sprod3D((1-(`$1')),`$2',`$3',`$4'), sprod3D( `$1',`$5',`$6',`$7'))') `assign3D([u],[v],[w],x,y,z); eg assign3D(u,v,w,cross3D(x1,y1,z1,x2,y2,z2)) assigns u = 4th arg, v = 5th arg, w = 6th arg, for nonblank u, v, or w' define(`assign3D',`assign3($@)') `vassign3D(name,x,y,z); eg vassign3D(u,x,y,z) assigns u[1] = x, u[2] = y, u[3] = z' define(`vassign3D',`for i_vassign3D = 1 to 3 do { exec sprintf("`$1'[i_vassign3D] = $%g",i_vassign3D+3) }') Write out the 3 arguments for debug define(`print3D',`print sprintf("`$1'(%g,%g,%g)",`$2',`$3',`$4')') `setlight (azimuth, elevation, rotation) Set angles (degrees) for 3D highlighting. Defaults are the previous values for setview(). The Light3D vector is defined as for View3D.' define(`setlight',`define(`setlight_') define(`m4hzim',`ifelse(`$1',,m4azimr,`prod_(`$1',dtor_)')')dnl define(`m4hlev',`ifelse(`$2',,m4elevr,`prod_(`$2',dtor_)')')dnl define(`m4hot',`ifelse(`$3',,m4rotx,`prod_(`$3',dtor_)')')dnl define(`m4chz',`ifelse(`$1',0,1,`$1',90,0,`$1',-90, 0,cos(m4hzim))')dnl define(`m4shz',`ifelse(`$1',0,0,`$1',90,1,`$1',-90,-1,sin(m4hzim))')dnl define(`m4chl',`ifelse(`$2',0,1,`$2',90,0,`$2',-90, 0,cos(m4hlev))')dnl define(`m4shl',`ifelse(`$2',0,0,`$2',90,1,`$2',-90,-1,sin(m4hlev))')dnl define(`m4cho',`ifelse(`$3',0,1,`$3',90,0,`$3',-90, 0,cos(m4hot))')dnl define(`m4sho',`ifelse(`$3',0,0,`$3',90,1,`$3',-90,-1,sin(m4hot))')dnl light3D1=m4chz*m4chl light3D2=m4shz*m4chl light3D3=m4shl ') The resulting vector #efine(`Light3D',`PtoBase3D(1,0,0)') define(`Light3D', `ifdef(`setlight_',`light3D1,light3D2,light3D3',`view3D1,view3D2,view3D3')') `Fector(x,y,z,nx,ny,nz) with .Origin at pos Arrow with flat 3D head. The second vector, (i.e. args nx,ny,nz) is the normal to the head flat surface' define(`Fector', `[ Origin: 0,0 define(`M4F_V',``$1',`$2',`$3'')dnl the whole vector V lV = length3D(M4F_V) define(`M4F_T',``$4',`$5',`$6'')dnl normal to the top surface lT = length3D(M4F_T) define(`M4F_Vn',`sprod3D(1/lV,M4F_V)')dnl unit vector Vn aln = 0.15*scale ;dnl arrowhead length awd = 0.09*scale ;dnl " width adp = 0.0375*scale ;dnl " depth (thickness) define(`M4F_Vt',`sprod3D((lV-aln),M4F_Vn)')dnl head base vector Start: Origin End: project(M4F_V) rpoint_(from Origin to End) lTdp = adp/2/lT vtx = dcosine3D(1,M4F_Vt); vty = dcosine3D(2,M4F_Vt) # Vt coords vtz = dcosine3D(3,M4F_Vt) dnl half-thickness vector in direction of T tx = prod_(lTdp,`$4'); ty = prod_(lTdp,`$5') tz = prod_(lTdp,`$6') dnl half-width vector right rf = awd/2/lT/lV rx = rf*dcosine3D(1,cross3D(M4F_V,M4F_T)) ry = rf*dcosine3D(2,cross3D(M4F_V,M4F_T)) rz = rf*dcosine3D(3,cross3D(M4F_V,M4F_T)) dnl top and bottom points of V TV: project(sum3D(M4F_V, tx,ty,tz)) BV: project(diff3D(M4F_V, tx,ty,tz)) dnl top, bottom right, left of base TR: project(sum3D(vtx,vty,vtz, sum3D(tx,ty,tz,rx,ry,rz))) BR: project(sum3D(vtx,vty,vtz, diff3D(rx,ry,rz,tx,ty,tz))) BL: project(diff3D(vtx,vty,vtz, sum3D(rx,ry,rz,tx,ty,tz))) TL: project(diff3D(vtx,vty,vtz, diff3D(rx,ry,rz,tx,ty,tz))) lthickness = linethick dnl base if dot3D(M4F_V,View3D) < 0 then { thinlines_ ifgpic(`gshade(0.5,BR,BL,TL,TR,BR,BL)', `line thick 0 fill_(0.5) from BR to BL then to TL then to TR then to BR') line from BR to BL ; line to TL ; line to TR ; line to BR linethick_(lthickness) } dnl shaft linethick_(1.2) psset_(arrows=c-c) line from Origin to project(vtx,vty,vtz) psset_(arrows=-) thinlines_ dnl top or bottom if dot3D(M4F_T,View3D) > 0 then { ifgpic(`gshade(1,TR,TL,TV,TR,TL)', `line thick 0 fill_(1) from TV to TR then to TL then to TV') line from TV to TR ; line to TL ; line to TV } else { ifgpic(`gshade(0,BR,BL,BV,BR,BL)', `line thick 0 fill_(0) from BV to BR then to BL then to BV') line from BV to BR ; line to BL ; line to BV } dnl starboard normal; draw right face define(`M4F_S', `cross3D(diff3D(sprod3D(aln,M4F_Vn),rx,ry,rz),M4F_T)')dnl if dot3D(M4F_S,View3D) > 0 then { ifgpic(`gshade(1,TV,BV,BR,TR,TV,BV)', `line thick 0 fill_(1) from TV to BV then to BR then to TR then to TV') line from TV to BV ; line to BR ; line to TR ; line to TV } dnl port normal; draw left face define(`M4F_P', `cross3D(M4F_T,sum3D(sprod3D(aln,M4F_Vn),rx,ry,rz))')dnl if dot3D(M4F_P,View3D) > 0 then { ifgpic(`gshade(1,TV,BV,BL,TL,TV,BV)', `line thick 0 fill_(1) from TV to BV then to BL then to TL then to TV') line from TV to BV ; line to BL ; line to TL ; line to TV } linethick_(lthickness) `$7'] ') # End Fector `shadedball( rad, highlight rad, highlight degrees, initial shade, final shade ) The highlight is by default at radius rad*3/5 and angle 110 deg (or arg2 deg); if setlight has been invoked then the highlight is as given by its azimuth and elevation arguments' define(`shadedball',`[ C: (0,0); r = ifelse(`$1',,circlerad,`$1') ifdef(`setlight_', `H: (project(sprod3D(r,light3D1,light3D2,light3D3))) hr = distance(C,H)', `hr = ifelse(`$2',,r*3/5,`$2'); ha = ifelse(`$3',,110,`$3') H: (cosd(ha)*hr,sind(ha)*hr)') u0 = ifelse(`$4',,1,`$4'); uf = ifelse(`$5',,0.25,`$5') rm = r+hr; n = int(rm/(linethick bp__)) for i=1 to n-1 do { x = i/n*rm; u = u0+(i/n)^2*(uf-u0) if x <= (r-hr) then { circle rad x thick linethick*1.6 outlined rgbstring(u,u,u) at H } \ else { arc cw thick linethick*ifpgf(2,1.6) outlined rgbstring(u,u,u) \ from Cintersect(H,x,C,r) to Cintersect(H,x,C,r,R) with .c at H } } circle rad r ifpgf(+linethick bp__/2) at C `$6']') divert(0)dnl