divert(-1) lib3D.m4 Macros for rotation, projection, and other operations on argument triples representing 3D vectors. * Circuit_macros Version 8.0, copyright (c) 2014 J. D. Aplevich under * * the LaTeX Project Public License. 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',`m4azim=prod_($1,dtor_) m4elev=prod_($2,dtor_) m4rot=ifelse(`$3',,0,`$3',0,0,`prod_(`$3',dtor_)') m4caz=cos(m4azim) m4saz=sin(m4azim) m4cel=cos(m4elev) m4sel=sin(m4elev) m4cro=ifelse(`$3',,1,`$3',0,1,`$3',90,0,`$3',-90,0,cos(m4rot)) m4sro=ifelse(`$3',,0,`$3',0,0,`$3',90,1,`$3',-90,-1,sin(m4rot))') `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')))') The resulting view vector define(`View3D',`PtoBase3D(1,0,0)') This does the 3D to 2D projection i.e. project(x,y,z) produces coordinate pair u,v on the 2D plane defined by the view angles. define(`project', `Pr_yz(rot3Dx(m4rot,rot3Dy(m4elev,rot3Dz(-m4azim,`$1',`$2',`$3'))))') `Rotation about x axis rot3Dx(angle,x1,x2,x3)' define(`rot3Dx',``$2',diff_(prod_(cos(`$1'),`$3'),prod_(sin(`$1'),`$4')),dnl sum_(prod_(sin(`$1'),`$3'),prod_(cos(`$1'),`$4'))') `Rotation about y axis rot3Dy(angle,x1,x2,x3)' define(`rot3Dy',`sum_(prod_(cos(`$1'),`$2'),prod_(sin(`$1'),`$4')),`$3',dnl diff_(prod_(cos(`$1'),`$4'),prod_(sin(`$1'),`$2'))') `Rotation about z axis rot3Dz(angle,x1,x2,x3)' define(`rot3Dz',`diff_(prod_(cos(`$1'),`$2'),prod_(sin(`$1'),`$3')),dnl sum_(prod_(sin(`$1'),`$2'),prod_(cos(`$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 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')') Write out the 3 arguments for debug define(`print3D',`print sprintf("`$1'(%g,%g,%g)",`$2',`$3',`$4')') `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_ ifpstricks( `\pscustom[linewidth=0pt,fillstyle=solid,fillcolor=gray]{ line from BR to BL then to TL then to TR then to BR \relax}', `gshade(0.5,BR,BL,TL,TR,BR,BL)') 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 { ifpstricks( `\pscustom[linewidth=0pt,fillstyle=solid,fillcolor=white]{ line from TV to TR then to TL then to TV \relax}', `gshade(1,TR,TL,TV,TR,TL)') line from TV to TR ; line to TL ; line to TV } else { ifpstricks( `\pscustom[linewidth=0pt,fillstyle=solid,fillcolor=black]{ line from BV to BR then to BL then to BV \relax}', `gshade(0,BR,BL,BV,BR,BL)') 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 { ifpstricks( `\pscustom[linewidth=0pt,fillstyle=solid,fillcolor=white]{ line from TV to BV then to BR then to TR then to TV \relax}', `gshade(1,TV,BV,BR,TR,TV,BV)') 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 { ifpstricks( `\pscustom[linewidth=0pt,fillstyle=solid,fillcolor=white]{ line from TV to BV then to BL then to TL then to TV \relax}', `gshade(1,TV,BV,BL,TL,TV,BV)') line from TV to BV ; line to BL ; line to TL ; line to TV } linethick_(lthickness) `$7'] ') # End Fector divert(0)dnl