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-rw-r--r--graphics/circuit_macros/lib3D.m4125
1 files changed, 75 insertions, 50 deletions
diff --git a/graphics/circuit_macros/lib3D.m4 b/graphics/circuit_macros/lib3D.m4
index 12f5170274..38ccc99d23 100644
--- a/graphics/circuit_macros/lib3D.m4
+++ b/graphics/circuit_macros/lib3D.m4
@@ -1,9 +1,9 @@
divert(-1)
lib3D.m4 Macros for rotation, projection, and other
operations on argument triples representing
- 3D vectors.
+ 3D vectors or colors.
-* Circuit_macros Version 9.5, copyright (c) 2021 J. D. Aplevich under *
+* Circuit_macros Version 9.6, copyright (c) 2021 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 *
@@ -26,21 +26,36 @@ ifdef(`libgen_',,`include(libgen.m4)divert(-1)')
P =( -sin(az), cos(az), 0 )
(-sin(el)cos(az),-sin(az)sin(el),cos(el))'
define(`setview',`
-# setview
- m4azim=ifelse(`$1',,0,`$1',0,0,`prod_(`$1',dtor_)')
- m4elev=ifelse(`$2',,0,`$2',0,0,`prod_(`$2',dtor_)')
- m4rot =ifelse(`$3',,0,`$3',0,0,`prod_(`$3',dtor_)')
- m4caz=ifelse(`$1',,1,`$1',0,1,`$1',90,0,`$1',-90, 0,cos(m4azim))
- m4saz=ifelse(`$1',,0,`$1',0,0,`$1',90,1,`$1',-90,-1,sin(m4azim))
- m4cel=ifelse(`$2',,1,`$2',0,1,`$2',90,0,`$2',-90, 0,cos(m4elev))
- m4sel=ifelse(`$2',,0,`$2',0,0,`$2',90,1,`$2',-90,-1,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,`$3',-90,-1,sin(m4rot))
- view3D1=m4caz*m4cel
- view3D2=m4saz*m4cel
- view3D3=m4sel dnl
- ifdef(`setlight_',,`; light3D1=view3D1; light3D2=view3D2; light3D3=view3D3')
+`# setview($@)'
+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')
@@ -51,36 +66,45 @@ define(`Pr_xy',`$1,$2')
define(`Pr_xz',`$1,$3')
define(`Pr_yz',`$2,$3')
- Projection coords back to orig 3D coords
+ 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.
-define(`project',
-`Pr_yz(rot3Dx(m4rot,rot3Dy(m4elev,rot3Dz(-m4azim,`$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_(cos(`$1'),`$3'),prod_(sin(`$1'),`$4')),dnl
- sum_(prod_(sin(`$1'),`$3'),prod_(cos(`$1'),`$4'))')
+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_(cos(`$1'),`$2'),prod_(sin(`$1'),`$4')),`$3',dnl
- diff_(prod_(cos(`$1'),`$4'),prod_(sin(`$1'),`$2'))')
+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_(cos(`$1'),`$2'),prod_(sin(`$1'),`$3')),dnl
- sum_(prod_(sin(`$1'),`$2'),prod_(cos(`$1'),`$3')),`$4'')
+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'))')
+ 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')))')
+ 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')')
@@ -92,40 +116,41 @@ define(`dcosine3D',`(ifelse(`$1',1,`$2',`$1',2,`$3',`$4'))')
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'))')
- `Assign the direction cosines to variables
- assign3D([u],[v],[w],x,y,z); eg
+ `assign3D([u],[v],[w],x,y,z); eg
assign3D(u,v,w,cross3D(x1,y1,z1,x2,y2,z2))
- assigns the 4th arg to u, the 5th to v,
- and the 6th to w as u, v,or w are nonblank'
-define(`assign3D',
-`ifelse(`$1',,,`$1' = `$4')
- ifelse(`$2',,,`$2' = `$5')
- ifelse(`$3',,,`$3' = `$6')')
+ assigns u = 4th arg, v = 5th arg, w = 6th arg,
+ for nonblank u, v, or w'
+define(`assign3D',`assign3($@)')
+
`vassign3D(name,x,y,z); eg
vassign3D(u,x,y,z)
- assigns u[1] to x, u[2] to y, u[3] to 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')')
- `setlightlight (azimuth, elevation, rotation)
+ `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_')
- m4hzim=ifelse(`$1',,m4azim,`$1',0,0,`prod_(`$1',dtor_)')
- m4hlev=ifelse(`$2',,m4elev,`$2',0,0,`prod_(`$2',dtor_)')
- m4hot =ifelse(`$3',,m4rot,`$3',0,0,`prod_(`$3',dtor_)')
- m4chz=ifelse(`$1',0,1,`$1',90,0,`$1',-90, 0,cos(m4hzim))
- m4shz=ifelse(`$1',0,0,`$1',90,1,`$1',-90,-1,sin(m4hzim))
- m4chl=ifelse(`$2',0,1,`$2',90,0,`$2',-90, 0,cos(m4hlev))
- m4shl=ifelse(`$2',0,0,`$2',90,1,`$2',-90,-1,sin(m4hlev))
- m4cho=ifelse(`$3',0,1,`$3',90,0,`$3',-90, 0,cos(m4hot))
- m4sho=ifelse(`$3',0,0,`$3',90,1,`$3',-90,-1,sin(m4hot))
+ 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