diff options
Diffstat (limited to 'graphics/circuit_macros/examples/svg/LyapSVG.m4')
-rw-r--r-- | graphics/circuit_macros/examples/svg/LyapSVG.m4 | 159 |
1 files changed, 0 insertions, 159 deletions
diff --git a/graphics/circuit_macros/examples/svg/LyapSVG.m4 b/graphics/circuit_macros/examples/svg/LyapSVG.m4 deleted file mode 100644 index 6ed269a428..0000000000 --- a/graphics/circuit_macros/examples/svg/LyapSVG.m4 +++ /dev/null @@ -1,159 +0,0 @@ -.PS -# Lyap.m4 -threeD_init -scale = 1/1.2 - -viewaz = 30 -viewel = 18 -setview(viewaz,viewel) - -Origin: project(0,0,0) -# Components of view vector W -w1 = view3D1 -w2 = view3D2 -w3 = view3D3 -# Shape factor of the ellipse on the xy plane -q = Cos(40) - -# cost function -h = 0.5 -c = 1 -# The projected ellipse is (x/q)^2 + y^2 = c. -# The cost is v = c+h -define(`vs',``$2'*q*cos(`$1'),`$2'*sin(`$1')') -define(`vp',`vs(`$1',`$2'),0') -define(`vx',`sum3D(vp(`$1',`$2'),0,0,h+(`$2')^2)') - -# The gradient of v is (2x/q, 2y, -1) and the line -# separating front and back is W^T * grad(v) = 0 -# This line intersects the projected ellipse at -# x1,y1 and x2,y2 - ap = w2^2*q^2/w1^2+1 - bp = -w2*w3*q^2/w1^2 - cp = w3^2*q^2/4/w1^2-c - m = sqrt(bp^2-4*ap*cp) - y1 = (-bp+m)/ap/2 ; x1 = (w3-2*y1*w2)*q/2/w1 - y2 = (-bp-m)/ap/2 ; x2 = (w3-2*y2*w2)*q/2/w1 - t1 = atan2(y1,x1) - t2 = atan2(y2,x2) - theta1 = min(t1,t2) - theta2 = max(t1,t2) - -# tangent curve - nT = 11 - for i = 0 to nT do { - y = y1 + (y2-y1)/nT*i - theta = atan2(y,(w3-2*y*w2)*q/2/w1) - r = y/sin(theta) - T[i]: project(vx(theta,r)) - } - -# front and back parts of the top curve - n = 12 - for i = 0 to n do { - theta = theta1 + (theta2-theta1)/n*i - F[i]: project(vx(theta,c)) - Fp[i]: project(vp(theta,c)) - } - for i = 0 to n do { - theta = theta2 + (theta1+twopi_-theta2)/n*i - B[i]: project(vx(theta,c)) - Bp[i]: project(vp(theta,c)) - } - -# trajectory -rotations = 1.55 -nx = 7 -thetas = 75*dtor_ -thetaf = thetas - rotations*twopi_ -rx = c*0.9 -beta = exp(log(.5)/20) - -define(`defX',` rx = `$5' ; np = np-1 - ts = `$1' ; tf = `$2' - for i = 0 to `$3' do { - tha = ts + (tf-ts)*i/(`$3') - for thx = tha to -twopi_ by twopi_ do {} - `$4'[i]: project(vx(thx,rx)) - Xp[np]: project(vp(thx,rx)) - np = np+1 - rx = beta*rx - }') - -np = 1 -defX(thetas,theta1,nx,X1,rx) -defX(theta1,theta2-twopi_,nx,X2,rx/beta) -defX(theta2-twopi_,theta1-twopi_,nx,X3,rx/beta) -defX(theta1-twopi_,thetaf,5,X4,rx/beta) - -# First draw the inside back -# B is the back curve -# T is the outline -ifpstricks(` -\psset{gradbegin=lightgray,gradend=darkgray,gradlines=1000} -\pscustom[fillstyle=gradient,gradmidpoint=0.7]{ - fitcurve(B,n) - for i = 0 to nT do {TT[i]: T[nT-i] } - fitcurve(TT,nT) -\relax} ', -` fitcurve(B,n) - for i = 0 to nT do {TT[i]: T[nT-i] } - fitcurve(TT,nT) ') - -# Centre axis -thinlines_ -line from Origin to project(0,0,h) -# F[0] is the leftmost point of the front curve -line from F[0] to Fp[0] -# F[n] is the rightmost point of the front curve -line from F[n] to Fp[n] -thicklines_ - -# Now draw the outside front -ifpstricks(` -\newgray{gray1}{0.9}% -\newgray{gray2}{0.4}% -\psset{gradbegin=gray1,gradend=gray2,gradlines=1000} -\pscustom[linewidth=0pt,fillstyle=gradient,gradmidpoint=0.99]{ - fitcurve(F,n) - fitcurve(T,nT) -\relax} ', -` shade(1,fitcurve(F,n) - fitcurve(T,nT)) ') -# T is the limit curve of visibility - fitcurve(T,nT) -# F is the top front - fitcurve(F,n) -# Front and back projections of the top on xy - fitcurve(Fp,n) - fitcurve(Bp,n) - -# The trajectory in pieces, to allow dashed parts - fitcurve(X1,nx) - fitcurve(X2,nx,dotted 0.025) - fitcurve(X3,nx) - fitcurve(X4,3,dotted 0.015) - arca(from X4[4] to X4[2],ccw,0.3,<-) - -# Projected trajectory - np = np-2 - fitcurve(Xp,np-1) - arca(from Xp[np] to Xp[np-2],ccw,0.18,<-) - "svg_it(X(t))" at Xp[np]-(2bp__,0) ljust - -# Axes and vertical lines -thinlines_ - line from X1[0] to Xp[0] -arrow from Origin to project(1.5,0,0) -"svg_it(x)`'svg_sub(1)" rjust below -arrow from Origin to project(0,1.5,0) -"svg_it(x)`'svg_sub(2)" wid 10bp__ ljust -line dashed from project(0,0,h) to F[n/2] chop 0 chop arrowht/4 -arrow from F[n/2] to project(0,0,2) -"svg_it(v(X))" ljust - -"svg_it(0)" at Origin+(0,1 pt__) below -"svg_Omega" at project(0,0.9*c,0) above -"svg_it(v(X) = c)" at (project(vp(100*dtor_,c)))+(2bp__,0) above ljust - -.PE |