.PS
# Geometry.m4
# Some constructions from https://tex.stackexchange.com/
gen_init
maxpswid = 9
Scaled: [
Fig1: [
# FourbarSVG.m4
# https://tex.stackexchange.com/questions/563831/how-to-draw-four-bar-linkage-with-center-of-mass
ls = 1/25.4 # local scale
a = 18*ls
b = 73*ls
c = 47*ls
d = 72*ls
A0: Here
B0: A0+(d,0)
circlerad = 1*ls
define(`pivot',`[
C: circle
line down_ 4*ls from C+(2*ls,0)
arc from last line.start to C+(-2*ls,0) with .c at C
line down_ 4*ls
B: line thick 1.6 right 7*ls with .c at (C,Here)
thinlines_
sep = 0.9*ls
nhash = B.len/sep
for i=0 to nhash do { line down sep left sep from B.end-(i/nhash*B.len,0) }
thicklines_
]')
pivot with .C at A0; "$A_0$" at A0-(5,0)*ls
circle dashed rad a at A0
pivot with .C at B0; "$B_0$" at B0-(5,0)*ls
"$d = A_0B_0$" at 0.5
B1: Cintersect(A0,a+b,B0,c)
B2: Cintersect(A0,b-a,B0,c)
arc dashed from B1 to B2 with .c at B0
A0B1: line thick 1.6 from A0 to B1 chop 2*ls chop 0
line thick 1.6 from B0 to B1 chop 2*ls chop 0 "c" ljust
circle fill_(1) at B1; "$B_1$" wid 3*ls at B1+(5,0)*ls
A1: circle fill_(1) at LCintersect(A0B1,A0,a,R)
"$A_1$" at A1+(5,0)*ls
A2: b/(b-a) between B2 and A0; "$a$" at 0.4 above rjust
"$b$" at 0.4 above rjust
A2B2: line thick 1.6 from A2 to B2
line thick 1.6 from B0 to B2 chop 2*ls chop 0
circle fill_(1) at B2; "$B_2$" at B2+(5,0)*ls
circle fill_(1) at A2; "$A_2$" at A2+(5,0)*ls
thinlines_
line from B0+(3*ls,0) right 4*ls
ArcAngle(Here,B0,B1,5*ls) ->; "$\psi_0$" at last arc.ne above ljust
ArcAngle(B1,B0,B2,8*ls) ->; "$\psi$" at last arc.n+(-3*ls,0) above
ArcAngle(A1,A0,B2,b*0.45) ->; "$\theta$" at last arc.start+(0,4*ls)
line from A0+(3*ls,0) right 8*ls
ArcAngle(Here,A0,B1,9*ls) ->; "$\theta_0$" \
at last arc.start+(2,2)*ls
]
Fig2: [
# FourbarSVG.m4
# https://tex.stackexchange.com/questions/609452/help-drawing-a-more-sophisticated-right-triangle-with-tikz-or-something-else
textkht = 12/72
unit = 0.6
C: Here; { "$C$" at C rjust below }
B: C+(4*unit,0); { "$B$" at B ljust below }
A: C+(0,3*unit); { "$A$" at A rjust above }
H: PerpTo(C,A,B); { "$H$" at H ljust above }
line from C to H then to B then to C shaded rgbstring(0.5,0.8,0.9)
line from C to H then to A then to C shaded rgbstring(0.8,0.9,0.7)
ArcAngle(C,A,B,unit*0.4)
ArcAngle(C,A,B,unit*0.5)
ArcAngle(A,B,C,unit*0.5,,"$\theta$" rjust)
ArcAngle(B,C,H,unit*0.5); {"$\theta$" at C+(unit*0.3,unit*0.17) }
ArcAngle(B,C,A,unit*0.6)
RightAngle(B,C,A,unit*0.17)
RightAngle(C,H,A,unit*0.17)
] with .nw at Fig1.sw+(0.2,0)
Fig3: [ ls = 3/4 # local scale
# https://tex.stackexchange.com/questions/593272/drawing-complex-geometry
P: dot(at Here); "$P$" at P.s below
N: dot(at P+(3.5*ls,1.5*ls)); "$N$" at N.se ljust below
O: dot(at (N,P)); "$O$" at O.s below
R: dot(at 1/3 between O and P);"$R$" at R.s below
M: dot(at (R,N)); "$M$" at M.se ljust below
Q: dot(at (M.x,M.y+distance(M,N)/distance(N,O)*distance(P,O)));"$Q$" at Q.e ljust
line from P to Q then to N then to O
B: line to P chop -0.3
line from M to N
Pu: line from R to Q chop 0 chop -0.3
H: line from P to N chop 0 chop -0.3
X: dot(at Intersect_(Pu,H)); "$X$" at X.se ljust below
thinlines_
RightAngle(Q,M,N)
RightAngle(Q,N,H.end)
RightAngle(N,O,B.start)
ArcAngle(N,P,Q,0.4); "$\beta$" at last arc.ne above ljust
ArcAngle(O,P,N,0.5); "$\alpha$" at last arc.start+(5bp__,8bp__)
ArcAngle(R,Q,N,0.5); "$\alpha$" at last arc.start+(8bp__,-5bp__)
] with .sw at Fig2.e+(-0.2,-0.7)
ifelse(1,1,`
Fig4: [ ls = 2/3 # local scale
A: Here; "$A$" at A above
B: A+(-1*ls,-3.5*ls); "$B$" at B below rjust
C: B+(4.6*ls,0); "$C$" at C below ljust
AB: line from A to B
BC: line from B to C
CA: line from C to A
perpto(A,BC,L); "$L$" at L below
AL: line from A to L; RightAngle(A,L,C)
angleLAC = atan2(C.x-L.x,A.y-L.y)
S: move from A to (sin(angleLAC/2),-cos(angleLAC/2))
AW: line from A to Intersect_(S,BC)
W: Here; "$W$" at W below rjust
perpto(C,AB,N); "$N$" at N above rjust
CN: line from C to N; RightAngle(C,N,B)
perpto(B,CA,M); "$M$" at M above
CM: line from B to M; RightAngle(B,M,C)
H: Intersect_(CN,AL); "$H$" at H +(4bp__,10bp__)
thinlines_
Equidist3(B,L,N,CC1,c1rad); C1: circle rad c1rad at CC1
Equidist3(B,W,N,CC2,c2rad); C2: circle rad c2rad at CC2
Equidist3(B,C,N,CC3,c3rad); C3: circle rad c3rad at CC3
Equidist3(W,C,M,CC4,c4rad); C4: circle rad c4rad at CC4
thicklines_
Z: LCintersect(AW,CC2,C2.rad); "$Z$" at Z+(-5bp__,-5bp__)
HZ: move from H to Z
Y: LCintersect(HZ,CC4,C4.rad,R); "$Y$" at Y above
X: LCintersect(HZ,CC2,C2.rad); "$X$" at X above rjust
foreach_(`P',`dot(at P)',X,Y,Z)
line dashed from X to Y chop -linewid/2
RightAngle(A,Z,Y)
] with .sw at (Fig3.e,Fig2.s)
')
] scaled 0.8
.PE