diff options
| author | Roger Frank <rfrank@pglaf.org> | 2025-10-15 02:48:13 -0700 |
|---|---|---|
| committer | Roger Frank <rfrank@pglaf.org> | 2025-10-15 02:48:13 -0700 |
| commit | 5c5e4d98db9e19fea18282dcf193c6b29d26cc05 (patch) | |
| tree | cd45c72fdb9d24912cb7691a12b3cae31666b7d1 /29785-t/images | |
Diffstat (limited to '29785-t/images')
52 files changed, 3137 insertions, 0 deletions
diff --git a/29785-t/images/009a.eepic b/29785-t/images/009a.eepic new file mode 100644 index 0000000..b6289a6 --- /dev/null +++ b/29785-t/images/009a.eepic @@ -0,0 +1,27 @@ +%% Generated from 009a.xp on Thu Jun 4 19:35:44 EDT 2009 by +%% ePiX-1.2.6 +%% +%% Cartesian bounding box: [0,2] x [0,1.25] +%% Actual size: 1.875 x 1.1in +%% Figure offset: left by 0in, down by 0in +%% +%% usepackages tikz +%% +\xdefinecolor{rgb_000000}{rgb}{0,0,0}% +\begin{tikzpicture}[cap=round] +\pgfsetlinewidth{0.4pt} +\useasboundingbox (0in,0in) rectangle (1.875in,1.1in); +\pgfsetlinewidth{0.8pt} +\draw (0in,0in)--(1.875in,0in); +\draw (0in,0in)--(0in,1.1in); +\draw (0in,0in)--(1.6238in,0.88in)--(1.6238in,0in); +\pgftext[at={\pgfpoint{-0.055348in}{0in}}] {\makebox(0,0)[r]{\hbox{\color{rgb_000000}$O$}}} +\pgftext[at={\pgfpoint{1.67915in}{0.88in}}] {\makebox(0,0)[l]{\hbox{\color{rgb_000000}$A$}}} +\pgftext[at={\pgfpoint{1.875in}{-0.055348in}}] {\makebox(0,0)[t]{\hbox{\color{rgb_000000}$X$}}} +\pgftext[at={\pgfpoint{-0.055348in}{1.1in}}] {\makebox(0,0)[r]{\hbox{\color{rgb_000000}$Y$}}} +\pgftext[at={\pgfpoint{0.276903in}{0.025992in}}] {\makebox(0,0)[bl]{\hbox{\color{rgb_000000}$\theta$}}} +\pgftext[at={\pgfpoint{0.811899in}{-0.055348in}}] {\makebox(0,0)[t]{\hbox{\color{rgb_000000}$a$}}} +\pgftext[at={\pgfpoint{1.67915in}{0.44in}}] {\makebox(0,0)[l]{\hbox{\color{rgb_000000}$b$}}} +\pgftext[at={\pgfpoint{0.783364in}{0.466785in}}] {\makebox(0,0)[br]{\hbox{\color{rgb_000000}$r$}}} +\pgftext[at={\pgfpoint{0.9375in}{-0.249066in}}] {\makebox(0,0)[t]{\hbox{\color{rgb_000000}\textsc{Fig.~1}}}} +\end{tikzpicture} diff --git a/29785-t/images/010a.eepic b/29785-t/images/010a.eepic new file mode 100644 index 0000000..bacbd60 --- /dev/null +++ b/29785-t/images/010a.eepic @@ -0,0 +1,212 @@ +%% Generated from 010a.xp on Tue Jul 14 11:57:02 EDT 2009 by +%% ePiX-1.2.6 +%% +%% Cartesian bounding box: [-1,1] x [-1,1] +%% Actual size: 2 x 2in +%% Figure offset: left by 0in, down by 0in +%% +%% usepackages tikz +%% +\xdefinecolor{rgb_000000}{rgb}{0,0,0}% +\begin{tikzpicture}[cap=round] +\pgfsetlinewidth{0.4pt} +\useasboundingbox (0in,0in) rectangle (2in,2in); 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+\draw (1.19318in,0.28125in)--(1.22727in,0.2625in); +\draw (1.22727in,0.2625in)--(1.26136in,0.24375in); +\draw (1.32955in,0.20625in)--(1.36364in,0.1875in); +\draw (1.36364in,0.1875in)--(1.39773in,0.16875in); +\draw (1.46591in,0.13125in)--(1.5in,0.1125in); +\draw (0in,0.9375in)--(0.0375in,0.937109in)--(0.075in,0.935937in)-- + (0.1125in,0.933984in)--(0.15in,0.93125in)--(0.1875in,0.927734in)-- + (0.225in,0.923435in)--(0.2625in,0.918354in)--(0.3in,0.912487in)-- + (0.3375in,0.905833in)--(0.375in,0.898389in)-- + (0.4125in,0.890148in)--(0.45in,0.881104in)--(0.4875in,0.871249in)-- + (0.525in,0.86057in)--(0.5625in,0.849053in)--(0.6in,0.836681in)-- + (0.6375in,0.823431in)--(0.675in,0.809277in)-- + (0.7125in,0.794187in)--(0.75in,0.778125in)--(0.7875in,0.761047in)-- + (0.825in,0.742901in)--(0.8625in,0.723631in)--(0.9in,0.703169in)-- + (0.9375in,0.681438in)--(0.975in,0.658354in)-- + (1.0125in,0.633817in)--(1.05in,0.60772in)--(1.0875in,0.57994in)-- + (1.125in,0.550342in)--(1.1625in,0.518774in)--(1.2in,0.485071in)-- + (1.2375in,0.449049in)--(1.275in,0.410508in)-- + (1.3125in,0.369225in)--(1.35in,0.324962in)--(1.3875in,0.277455in)-- + (1.425in,0.226419in)--(1.4625in,0.171546in)--(1.5in,0.1125in); +\pgftext[at={\pgfpoint{-0.027674in}{0.9375in}}] {\makebox(0,0)[r]{\hbox{\color{rgb_000000}$A$}}} +\pgftext[at={\pgfpoint{0in}{0.597326in}}] {\makebox(0,0)[t]{\hbox{\color{rgb_000000}$\alpha$}}} +\pgftext[at={\pgfpoint{1.52767in}{0.1125in}}] {\makebox(0,0)[l]{\hbox{\color{rgb_000000}$B$}}} +\pgftext[at={\pgfpoint{1.5in}{0.652674in}}] {\makebox(0,0)[b]{\hbox{\color{rgb_000000}$\beta$}}} +\pgftext[at={\pgfpoint{1.18622in}{0.652674in}}] {\makebox(0,0)[b]{\hbox{\color{rgb_000000}$T$}}} +\pgftext[at={\pgfpoint{0.538116in}{0.599945in}}] {\makebox(0,0)[tr]{\hbox{\color{rgb_000000}$c$}}} +\pgftext[at={\pgfpoint{0.75in}{-0.166044in}}] {\makebox(0,0)[t]{\hbox{\color{rgb_000000}\textsc{Fig.~26}}}} +\end{tikzpicture} diff --git a/29785-t/images/sources/009a.xp b/29785-t/images/sources/009a.xp new file mode 100644 index 0000000..6a1b4e1 --- /dev/null +++ b/29785-t/images/sources/009a.xp @@ -0,0 +1,37 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double dp(4); + +int main() +{ + picture(P(0,0), P(2,1.25), "1.875 x 1.1in"); + // offset(P(0,0.1)); + begin(); + + P A(polar(2, M_PI/6)), A1(A&E_1), O(0,0), X(xmax(),0), Y(0,ymax()); + + bold(); + line(O, X); + line(O, Y); + + path Tr(O, A); + Tr.pt(A1).draw(); + + label(O, P(-dp,0), "$O$", l); + label(A, P( dp,0), "$A$", r); + label(X, P(0,-dp), "$X$", b); + label(Y, P(-dp,0), "$Y$", l); + + label(O, P(20,2), "$\\theta$", tr); + + label(0.5*A1, P(0,-dp), "$a$", b); + label(0.5*(A+A1), P(dp,0), "$b$", r); + label(0.5*A, P(-2,2), "$r$", tl); + + label(P(0.5*xmax(), ymin()), P(0,-18), "\\textsc{Fig.~1}",b); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/010a.xp b/29785-t/images/sources/010a.xp new file mode 100644 index 0000000..1b11b74 --- /dev/null +++ b/29785-t/images/sources/010a.xp @@ -0,0 +1,52 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +int main() +{ + picture(P(-1,-1), P(1,1), "2 x 2in"); + + begin(); + arrow_inset(0.25); + arrow_ratio(1); + degrees(); + P O(0, 0), z0(1, 0), z1(cis(120)), z2(cis(240)); + + double rad1(0.25), rad2(0.66*rad1), dp(2), dt(5); + + bold(); + circle(); + + line(P(-0.5), z0); + line(O, z1); + line(O, z2); + + arc_arrow(O, rad1, 0, 120-dt); + arc_arrow(O, rad2, 0, 240-dt); + + plain(); + dashed(); + triangle(z0, z1, z2); + + label(z0, dp*z0, "$1$", r); + label(z1, dp*z1, "$\\omega$", tl); + label(z2, dp*z2, "$\\omega^2$", bl); + + label(O, P(0,-dp), "$O$", br); + + label(P(-0.375), P(0,dp), "$\\frac{1}{2}$", t); + label(P(-0.5, 0.25*sqrt(3)), P(-dp,0), "$\\frac{1}{2}\\sqrt{3}$", l); + label(0.5*z1, dp*J(z1), "$1$", bl); + + label(P(0, ymin()), P(0,-6), "\\textsc{Fig.~2}", b); + + font_size("scriptsize"); + label_angle(-30); + label(polar(rad1, 60), -4*z2, "$120°$", c); + + label_angle(60); + label(polar(rad2, 150), P(-4,4), "$240°$", c); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/012a.xp b/29785-t/images/sources/012a.xp new file mode 100644 index 0000000..497845b --- /dev/null +++ b/29785-t/images/sources/012a.xp @@ -0,0 +1,55 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +void myquad(const P& p1, const P& p2, const P& p3, const P& p4) +{ + line(p1, p2); + line(p2, p3); + line(p3, p4); + line(p4, p1); +} + +int main() +{ + picture(P(0,0), P(3,2), "2 x 1.33in"); + + begin(); + + P ptA(1.25, 0.5), ptC(0.6, 1.375), ptS(ptA+ptC), X(xmax()), Y(0,ymax()); + P O(0,0), ptE(ptA&E_1), ptF(ptC&E_1), ptH(ptS&E_1), ptG(ptS.x1(), ptA.x2()); + double dp(2); + + dashed(); + line(ptA, ptE); + line(ptC, ptF); + line(ptS, ptH); + line(ptA, ptG); + + solid(); + bold(); + line(O, X); + line(O, Y); + + myquad(O, ptA, ptS, ptC); + line(O, ptS); + + label(X, P(0,-dp), "$X$", b); + label(Y, P(-dp,0), "$Y$", l); + label(O, P(-dp,0), "$O$", l); + + label(ptE, P(0,-dp), "$E$", b); + label(ptF, P(0,-dp), "$F$", b); + label(ptH, P(0,-dp), "$H$", b); + + label(ptG, P(dp,0), "$G$", r); + label(ptS, P(dp,0), "$S$", r); + + label(ptA, P(-dp, dp), "$A$", tl); + label(ptC, P(-dp, dp), "$C$", tl); + + label(P(0.5*xmax(), ymin()), P(0,-18), "\\textsc{Fig.~3}", b); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/012b.xp b/29785-t/images/sources/012b.xp new file mode 100644 index 0000000..b6ecd3d --- /dev/null +++ b/29785-t/images/sources/012b.xp @@ -0,0 +1,47 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +P times(const P& arg1, const P& arg2) +{ + return P(arg1.x1()*arg2.x1() - arg1.x2()*arg2.x1(), + arg1.x1()*arg2.x2() + arg1.x2()*arg2.x1()); +} + +void mytri(const P& p1, const P& p2, const P& p3) +{ + line(p1, p2); + line(p2, p3); + line(p3, p1); +} + +int main() +{ + picture(P(0,0), P(2,1.33), "2 x 1.33in"); + + begin(); + + P ptA(1.25, 0.6), ptC(0.5, 0.5), ptP(times(ptA, ptC)), X(xmax()); + P O(0,0), ptU(1); + double dp(2); + + bold(); + line(O, X); + + mytri(O, ptU, ptA); + mytri(O, ptC, ptP); + + label(X, P(0,-dp), "$X$", b); + label(ptU, P(0,-dp), "$U$", b); + label(O, P(-dp,0), "$O$", l); + + label(ptA, P(dp,0), "$A$", r); + label(ptC, P(dp,0), "$C$", r); + + label(ptP, P(-dp,dp), "$P$", tl); + + label(P(0.5*xmax(), ymin()), P(0,-18), "\\textsc{Fig.~4}", b); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/014a.xp b/29785-t/images/sources/014a.xp new file mode 100644 index 0000000..aa95153 --- /dev/null +++ b/29785-t/images/sources/014a.xp @@ -0,0 +1,32 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +int main() +{ + picture(P(-1.25,-1.25), P(1.25,1.25), "1.5 x 1.5in"); + offset(P(0,0.125)); + + begin(); + degrees(); + double dp(2); + + bold(); + circle(); + P i0(1,0), i1(0,1), i2(-1,0), i3(0,-1); + + quad(i0, i1, i2, i3); + line(i0, i2); + line(i1, i3); + + label(P(0,0), P(-dp,-dp), "$O$", bl); + label(i0, dp*i0, "$1$", r); + label(i1, dp*i1, "$i$", t); + label(i2, dp*i2, "$-1$", l); + label(i3, dp*i3, "$-i$", b); + + label(P(0,ymin()), P(0,-6), "\\textsc{Fig.~5}", b); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/035a.xp b/29785-t/images/sources/035a.xp new file mode 100644 index 0000000..3f6772a --- /dev/null +++ b/29785-t/images/sources/035a.xp @@ -0,0 +1,46 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +int main() +{ + picture(P(-1,-1), P(8,5), "2.4 x 1.6in"); + + begin(); + double ca(6), cb(4); + double dp(2); + P O(0,0), ptB(0,1), ptQ(ca, cb), X(xmax(),0), Y(0,ymax()); + Circle Crc(0.5*(ptB+ptQ), ptQ); + Segment Xax(O, X), Yax(O, Y), MN(Crc*Xax), OC(Crc*Yax); + + P ptC(OC.end1()), ptM(MN.end1()), ptN(MN.end2()), ptT(ptQ&E_1); + + Segment QT(ptQ, ptT), QD(Crc*QT); + P ptD(QD.end1()); + + bold(); + Crc.draw(); + Xax.draw(); + + line(O, ptC); + line(ptQ, ptT); + line(ptQ, ptB); + + label(O, P(-dp,0), "$O$", l); + label(ptC, P(-dp,0), "$C$", l); + label(ptB, P(-dp,-dp), "$B$", l); + label(ptQ, P( dp, dp), "$Q$", r); + + label(ptM, P(-2*dp,dp), "$M$", t); + label(ptN, P( 2*dp,dp), "$N$", t); + + label(ptD, P(dp,-dp), "$D$", r); + + label(ptT, P(0,-dp), "$T$", b); + label(X, P(0,-dp), "$X$", b); + + label(P(0.5*(xmin()+xmax()), ymin()), P(0,-6), "\\textsc{Fig.~6}", b); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/037a.xp b/29785-t/images/sources/037a.xp new file mode 100644 index 0000000..701afe9 --- /dev/null +++ b/29785-t/images/sources/037a.xp @@ -0,0 +1,30 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +int main() +{ + picture(P(0,0), P(3,3), "1.5 x 1.5in"); + + begin(); + degrees(); + bold(); + double ca(1.5), cb(1.25), cp(ca*cb), th(30); + double dp(2); + P O(0,0), p1(1+cb,0), p2(polar(ca+cp, th)), p2b(polar(ca, th)); + + triangle(O, p1, p2); + triangle(O, P(1), p2b); + + label(P(0.5), P(0,-dp), "$1$", b); + label(P(1+0.5*cb), P(0,-dp), "$b$", b); + + label(polar(0.5*ca, th), P(-dp,dp), "$a$", tl); + label_angle(th); + label(polar(ca*(1+0.5*cb), th), 3*P(-dp,dp), "$p=a·b$", c); + + label_angle(0); + label(P(0.5*xmax()), P(0,-18), "\\textsc{Fig.~7}", b); + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/037b.xp b/29785-t/images/sources/037b.xp new file mode 100644 index 0000000..f46ef2a --- /dev/null +++ b/29785-t/images/sources/037b.xp @@ -0,0 +1,30 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +// illogical variables; modified labels from 037a.xp +int main() +{ + picture(P(0,0), P(2.5,3), "1.25 x 1.5in"); + + begin(); + degrees(); + bold(); + double ca(1.9), cb(1.25), cp(ca*cb), th(50); + double dp(2); + P O(0,0), p1(1+cb,0), p2(polar(ca+cp, th)), p2b(polar(ca, th)); + + triangle(O, p1, p2); + triangle(O, P(1), p2b); + + label(P(0.5), P(0,-dp), "$1$", b); + label(P(1+0.5*cb), P(0,-dp), "$q=a/b$", b); + + label(polar(0.5*ca, th), P(-dp,dp), "$b$", tl); + label(polar(ca*(1+0.5*cb), th), P(-dp,dp), "$a$", tl); + + label_angle(0); + label(P(0.5*xmax()), P(0,-18), "\\textsc{Fig.~8}", b); + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/037c.xp b/29785-t/images/sources/037c.xp new file mode 100644 index 0000000..fe2eeaa --- /dev/null +++ b/29785-t/images/sources/037c.xp @@ -0,0 +1,28 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +int main() +{ + picture(P(-3,0), P(3,6), "1.5 x 1.5in"); + + begin(); + degrees(); + bold(); + double rad(3), X(-2), ht(sqrt((rad-X)*(rad+X))); + double dp(2); + + arc(P(0,0), rad, 0, 180); + line(P(-rad), P(rad)); + line(P(X,0), P(X,ht)); + + label(P(0.5*(-rad+X)), P(0,-dp), "$1$", b); + label(P(0.5*( rad+X)), P(0,-dp), "$n$", b); + + label(P(X, 0.5*ht), P(dp,0), "$s$", r); + + label(P(0), P(0,-18), "\\textsc{Fig.~9}", b); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/045a.xp b/29785-t/images/sources/045a.xp new file mode 100644 index 0000000..fb37295 --- /dev/null +++ b/29785-t/images/sources/045a.xp @@ -0,0 +1,40 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +int main() +{ + picture(P(-1,-1), P(1,1), "1.75 x 1.75in"); + offset(P(0,-0.5)); + + begin(); + degrees(); + bold(); + double dp(2); + + P O(0,0), A(-1,0), Ap(1,0), B(0,1), Bp(0,-1), M(0.5,0), C(0.5*(1-sqrt(5))); + P R(B-M); + + circle(); + line(A, Ap); + line(B, Bp); + + arc(M, norm(R), Atan2(R.x2(), R.x1()), 180); + line(M, B); + line(B, C); + + label(A, P(-dp,0), "$A$", l); + label(Ap, P( dp,0), "$A'$", r); + + label(B, P(0, dp), "$B$", t); + label(Bp, P(0,-dp), "$B'$", b); + + label(M, P(0,-dp), "$M$", b); + label(C, P(0,-dp), "$C$", b); + label(O, P(-dp,-dp), "$O$", bl); + + label(P(0,ymin()), P(0,-18), "\\textsc{Fig.~10}", b); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/049a.xp b/29785-t/images/sources/049a.xp new file mode 100644 index 0000000..8227301 --- /dev/null +++ b/29785-t/images/sources/049a.xp @@ -0,0 +1,79 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +int main() +{ + picture(P(-1.25,-1), P(2.25,1), "3.0625 x 1.75in"); + // offset(P(0,-0.5)); + + begin(); + degrees(); + bold(); + double dp(2); + + P O(0,0), pD(-1,0), pC(1,0), pB(0,1), pA(0,-1), pS(-1,-1), pE(-0.25,-1); + P pF(pE+P(sqrt(1.0625))), pFp(pE-P(sqrt(1.0625))); // F and F' + P pH(pF+P(norm(pF))), pHp(pFp+P(norm(pFp))); // H and H' + P pT(pH.x1()), pQ(pT+P(0, pHp.x1() - pA.x1())); // T and Q + + P ctr(0.5*(pB+pQ)), dir(pB-pQ); // circ(BQ) parameters + Circle Crc(ctr, pB); + Segment Xax(O, pT), MN(Crc*Xax); + P pM(MN.end1()), pN(MN.end2()); // M and N + + double L(0.5*pM.x1()); + + P pL(L), pP(L, sqrt((1-L)*(1+L))); // L and P + + circle(); + line(pA, pB); + line(pD, pT); + + line(pFp, pH); + line(pH, pQ); + line(pQ, pB); + line(O, pE); + line(O, pF); + line(O, pFp); + line(pD, pS); + line(pL, pP); + + arc(pF, norm(pF), 0, Atan2(-pF.x2(), -pF.x1())); + arc(pFp, norm(pFp), 0, Atan2(-pFp.x2(), -pFp.x1())); + + double th(Atan2(dir.x2(), dir.x1())); + arc(ctr, 0.5*norm(dir), th, th+180); + + label(P(0.5*(xmin()+xmax()), ymin()), P(0,-18), "\\textsc{Fig.~11}", b); + + font_size("footnotesize"); + + label(pA, P(0,-dp), "$A$", b); + label(pB, P(0, dp), "$B$", t); + + label(pC, P( dp,-dp), "$C$", br); + label(pD, P(-dp,0), "$D$", l); + + label(pM, P(-2*dp,dp), "$M$", t); + label(pN, P( 14, -dp), "$N$", b); + + label(pL, P(-dp,-dp), "$L$", b); + label(pP, P( dp, 0), "$P$", r); + + label(O, P(-dp,dp), "$O$", tl); + + label(pFp, P(0,-dp), "$F'$", b); + label(pS, P(0,-dp), "$S$", b); + label(pE, P(-dp,-dp), "$E$", b); + label(pA, P(0,-dp), "$A$", b); + label(pHp, P(0,-dp), "$H'$", b); + label(pF, P(0,-dp), "$F$", b); + label(pH, P(0,-dp), "$H$", b); + + label(pQ, P(dp,0), "$Q$", r); + label(pT, P(dp,0), "$T$", r); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/061a.xp b/29785-t/images/sources/061a.xp new file mode 100644 index 0000000..dd8dc01 --- /dev/null +++ b/29785-t/images/sources/061a.xp @@ -0,0 +1,59 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double f(double x) +{ + return -3 + x*(x-6); +} + +void label(double x, double f(double), const P& offset, epix_label_posn A) +{ + P loc(x, f(x)); + std::stringstream buf; + buf << "$(" << x << "," << f(x) << ")$"; + + marker(loc, TIMES); + label(loc, offset, buf.str(), A); +} + +int main() +{ + picture(P(-4,-12), P(8,4), "1.8 x 2.4in"); + + begin(); + double dp(4); + P Q(4), pP(4,f(4)); + + bold(); + line(P(-2,0), P(9,0)); + line(P(0,-7), P(0,ymax())); + + line(Q, pP); + + plot(f, -1, 7, 40); + label(-1, f, P(-dp, 0), l); + label( 0, f, P(-dp, 0), l); + label( 1, f, P(-dp, 0), l); + label( 2, f, P(-dp, 0), l); + label( 3, f, P( 0,-dp), b); + label( 4, f, P( dp, 0), r); + label( 5, f, P( dp, 0), r); + label( 6, f, P( dp, 0), r); + label( 7, f, P( dp, 0), r); + + label(P(2), P(0,-dp), "$4$", b); + label(P(4,-5.5), P(-dp,0), "$11$", l); + + label(P(0,0), P(2,2), "$O$", tr); + label(pP, P(-4,2), "$P$", l); + label(Q, P(0,2), "$Q$", t); + + label(P(0,ymax()), P(dp,0), "$Y$", r); + label(P(9,0), P(0,-dp), "$X$", b); + + label(P(2.5, ymin()), P(0,-24), "\\textsc{Fig.~12}", b); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/062a.xp b/29785-t/images/sources/062a.xp new file mode 100644 index 0000000..4c1637d --- /dev/null +++ b/29785-t/images/sources/062a.xp @@ -0,0 +1,39 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double f(double x) +{ + return -2 + x*(11 + x*(-9 + x*(-14 + 8*x))); +} + +void cross(double x, double f(double)) +{ + marker(P(x, f(x)), TIMES); +} + +int main() +{ + picture(P(-1.5,-13), P(3.5,2), "1.15 x 3.45in"); + + begin(); + bold(); + line(P(xmin(),0), P(3,0)); + line(P(0,-3), P(0,ymax())); + set_crop(); + + plot(f, xmin(), xmax(), 240); + + cross(-1, f); + cross( 0, f); + cross( 1, f); + cross( 2, f); + + label(P(0,0), P(-2,2), "$O$", tl); + label(P(-0.5,0), P(0,-2), "$1$", b); + + label(P(0.5*(xmin()+xmax()), ymin()), P(0,-12), "\\textsc{Fig.~13}", b); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/062b.xp b/29785-t/images/sources/062b.xp new file mode 100644 index 0000000..f71f0d9 --- /dev/null +++ b/29785-t/images/sources/062b.xp @@ -0,0 +1,39 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double f(double x) +{ + return -11 + x*x*(4 + x); +} + +double df(double x) +{ + return x*(8 + 3*x); +} + +int main() +{ + picture(P(-5,-15), P(5,5), "1.5 x 3in"); + offset(P(0,0.125)); + + begin(); + bold(); + line(P(xmin(),0), P(xmax(),0)); + line(P(0,ymin()), P(0,ymax())); + set_crop(); + + plot(f, xmin(), xmax(), 120); + + label(P(0,0), P(-2,2), "$O$", tl); + label(P(xmax(),0), P(0,-2), "$X$", b); + label(P(0,ymax()), P(-2,0), "$Y$", l); + + label(P(-8./3, f(-8./3)), P(0,2), "$M'$", t); + label(P(0,f(0)), P(2,-2), "$M$", br); + + label(P(0.5*(xmin()+xmax()), ymin()), P(0,-12), "\\textsc{Fig.~14}", b); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/063a.xp b/29785-t/images/sources/063a.xp new file mode 100644 index 0000000..b9f8057 --- /dev/null +++ b/29785-t/images/sources/063a.xp @@ -0,0 +1,30 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double f(double x) +{ + return x*x*x; +} + +int main() +{ + picture(P(-2,-2), P(2,2), "2.25 x 2.25in"); + + begin(); + bold(); + set_crop(); + line(P(xmin(),0), P(xmax(),0)); + line(P(0,ymin()), P(0,ymax())); + + plot(f, xmin(), xmax(), 120); + + label(P(xmax(),0), P(0,-2), "$X$", b); + label(P(0,ymax()), P(2, 0), "$Y$", r); + label(P(0,0), P(2, -2), "$O$", br); + + label(P(0,ymin()), P(0,-12), "\\textsc{Fig.~15}", b); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/063b.xp b/29785-t/images/sources/063b.xp new file mode 100644 index 0000000..c25322c --- /dev/null +++ b/29785-t/images/sources/063b.xp @@ -0,0 +1,48 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double f(double u) +{ + double x(0.5*u-1.25); + return 2 + 1.2*x*x*x; +} + +int main() +{ + picture(P(-0.5,-0.5), P(2.5,2), "2.7 x 2.25in"); + + begin(); + bold(); + double xp(0.375), xq(1.75); + P pP(xp, f(xp)), pQ(xq, f(xq)); + + line(P(xmin(),0), P(xmax(),0)); + line(P(0,ymin()), P(0,ymax())); + + line(pP, pP&E_1); + line(pQ, pQ&E_1); + line(pP, P(pQ.x1(), pP.x2())); + line(pP, pP + 1.2*(pQ - pP)); + + label(P(xmax(),0), P(0,-2), "$X$", b); + label(P(0,ymax()), P(-2,0), "$Y$", l); + label(P(0,0), P(-2, -2), "$O$", bl); + + label(P(0.5*xp), P(0,2), "$x$", t); + label(P(0.5*(xp+xq)), P(0,2), "$h$", t); + label(P(xp, 0.5*f(xp)), P(2,0), "$y$", r); + + label(P(xq, 0.5*(pP.x2() + pQ.x2())), P(2,0), "$Y-y$", r); + + label(pP, P(-2,0), "$P$", l); + label(pQ, P(-2,2), "$Q$", tl); + + set_crop(); + plot(f, 0.25, 2, 60); + + label(P(0.5*(xmin()+xmax()),ymin()), P(0,-12), "\\textsc{Fig.~16}", b); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/069a.xp b/29785-t/images/sources/069a.xp new file mode 100644 index 0000000..b54276f --- /dev/null +++ b/29785-t/images/sources/069a.xp @@ -0,0 +1,53 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +const std::string Ax("-{\\small Axis}"); + +int main() +{ + picture(P(0,0), P(2,2), "1.75 x 1.75in"); + // picture(P(0,0), P(2,2), "2 x 2in"); + + begin(); + degrees(); + bold(); + double x0(1.1), th(30); + P O(0,0), XY(P(x0, ymax())), dir(polar(0.5*x0*Sec(th), th)), Yax(XY-2*dir); + + line(P(xmin(),0), P(xmax(),0)); + line(P(0,ymin()), P(0,ymax())); + + line(O, 4*dir); + line(P(x0), XY); + + dashed(); + line(XY, Yax); + + label(P(0.5*x0,0), P(0,-2), "$X$", b); + label(P(0.5*(xmax()+x0),0), P(0,-2), "$X$"+Ax, b); + + label(0.5*Yax, P(2, 0), "$y$", r); + label(0.5*Yax + 2*dir, P(2, 0), "$y$", r); + label(P(x0, dir.x2()), P(2, 0), "$Y-y$", r); + + label(XY, P(-2, 2), "$(X,Y)$", tr); + label(XY, P(2,-2), "$(x,y)$", br); + + label(P(0,0), P(-2, 0), "$O$", l); + label(P(0,0), P(18, 2), "$\\theta$", tr); + + label(P(0.5*xmax(), ymin()), P(0,-18), "\\textsc{Fig.~17}", b); + + label_angle(th); + label(dir, P(0,2), "$x$", t); + label(dir+Yax, P(0,2), "$x$", t); + label(3*dir, P(0,0), "$x$"+Ax, r); + + label_angle(90); + label(Yax, P(-2,12), "$Y$"+Ax, tl); + label(Yax, P( 2,14), "$y$"+Ax, tr); + + tikz_format(); + end(); +} diff --git a/29785-t/images/sources/071a.xp b/29785-t/images/sources/071a.xp new file mode 100644 index 0000000..3242310 --- /dev/null +++ b/29785-t/images/sources/071a.xp @@ -0,0 +1,46 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +const double ht(0.375); +const double wd(sqrt(1.5)); +const double x0(wd*sqrt(1.0/3)); // critical point + +double g(double x) +{ + return -0.35*x*(wd-x)*(wd+x); +} + +double f(double x) +{ + return g(x) + ht; +} + +int main() +{ + picture(P(-1.5,-1), P(1.5,1), "2.4 x 1.25in"); + + begin(); + bold(); + P O(0,0); + + line(P(xmin(),0), P(xmax(),0)); + line(P(0,ymin()), P(0,ymax())); + + set_crop(); + plot(f, xmin(), xmax(), 60); + marker(P(x0, f(x0)), TIMES); + marker(P(-x0, f(-x0)), TIMES); + + label(O, P(-2,-2), "$O$", bl); + label(P(xmax(),0), P(0,-2), "$X$", b); + label(P(0,ymax()), P(2, 0), "$Y$", r); + + masklabel(P(0,ymin()), P(0,0), "$q\\geqq 2l\\sqrt{l}$", t); + + label(P(0,ymin()), P(0,-6), "\\textsc{Fig.~18}", b); + + tikz_format(); + + end(); +} diff --git a/29785-t/images/sources/071b.xp b/29785-t/images/sources/071b.xp new file mode 100644 index 0000000..20c64f5 --- /dev/null +++ b/29785-t/images/sources/071b.xp @@ -0,0 +1,46 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +const double ht(-0.375); +const double wd(sqrt(1.5)); +const double x0(wd*sqrt(1.0/3)); // critical point + +double g(double x) +{ + return -0.35*x*(wd-x)*(wd+x); +} + +double f(double x) +{ + return g(x) + ht; +} + +int main() +{ + picture(P(-1.5,-1), P(1.5,1), "2.4 x 1.25in"); + + begin(); + bold(); + P O(0,0); + + line(P(xmin(),0), P(xmax(),0)); + line(P(0,ymin()), P(0,ymax())); + + masklabel(P(0,ymin()), P(0,0), "$q\\leqq -2l\\sqrt{l}$", t); + + set_crop(); + plot(f, xmin(), xmax()-0.15, 60); + marker(P(x0, f(x0)), TIMES); + marker(P(-x0, f(-x0)), TIMES); + + label(O, P(-2,-2), "$O$", bl); + label(P(xmax(),0), P(0,-2), "$X$", b); + label(P(0,ymax()), P(2, 0), "$Y$", r); + + label(P(0,ymin()), P(0,-6), "\\textsc{Fig.~19}", b); + + tikz_format(); + + end(); +} diff --git a/29785-t/images/sources/071c.xp b/29785-t/images/sources/071c.xp new file mode 100644 index 0000000..6d49d9a --- /dev/null +++ b/29785-t/images/sources/071c.xp @@ -0,0 +1,46 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +const double ht(0.125); +const double wd(sqrt(1.5)); +const double x0(wd*sqrt(1.0/3)); // critical point + +double g(double x) +{ + return -0.35*x*(wd-x)*(wd+x); +} + +double f(double x) +{ + return g(x) + ht; +} + +int main() +{ + picture(P(-1.5,-1), P(1.5,1), "2.4 x 1.25in"); + + begin(); + bold(); + P O(0,0); + + line(P(xmin(),0), P(xmax(),0)); + line(P(0,ymin()), P(0,ymax())); + + set_crop(); + plot(f, xmin(), xmax()-0.15, 60); + marker(P(x0, f(x0)), TIMES); + marker(P(-x0, f(-x0)), TIMES); + + label(O, P(-2,-2), "$O$", bl); + label(P(xmax(),0), P(0,-2), "$X$", b); + label(P(0,ymax()), P(2, 0), "$Y$", r); + + masklabel(P(0,ymin()), P(0,0), "$-2l\\sqrt{l}<q<2l\\sqrt{l}$", t); + + label(P(0,ymin()), P(0,-6), "\\textsc{Fig.~20}", b); + + tikz_format(); + + end(); +} diff --git a/29785-t/images/sources/073a.xp b/29785-t/images/sources/073a.xp new file mode 100644 index 0000000..4620640 --- /dev/null +++ b/29785-t/images/sources/073a.xp @@ -0,0 +1,43 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +int main() +{ + picture(P(0,-M_PI), P(M_PI,M_PI), "1.25 x 2.5in"); + offset(P(0,-0.5)); + + begin(); + bold(); + double xa(M_PI_4), xb(2.25); + P O(0,0); + + line(P(xmin(),0), P(xmax(),0)); + dashed(); + line(P(M_PI_2,ymin()), P(M_PI_2,ymax())); + solid(); + + line(P(xa,0), P(xa, Tan(xa))); + line(P(xb,0), P(xb, Tan(xb))); + + set_crop(); + plot(Tan, xmin(), M_PI_2-0.001, 30); + plot(Tan, M_PI_2+0.001, xmax(), 30); + + marker(P(xa, Tan(xa)), TIMES); + marker(P(xb, Tan(xb)), TIMES); + + label(O, P(0,-2), "$O$", b); + label(P(M_PI,0), P(0, 2), "$\\pi$", t); + + label(P(xa,0), P(0,-2), "$a$", b); + label(P(xb,0), P(0, 2), "$b$", t); + + label(P(M_PI_2), P(-2,-2), "$\\frac{\\pi}{2}$", bl); + + label(P(M_PI_2, ymin()), P(0,-18), "\\textsc{Fig.~21}", b); + + tikz_format(); + + end(); +} diff --git a/29785-t/images/sources/097a.xp b/29785-t/images/sources/097a.xp new file mode 100644 index 0000000..b920d1b --- /dev/null +++ b/29785-t/images/sources/097a.xp @@ -0,0 +1,68 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double f(double x) +{ + double u(x-7), v(u*u); + return 0.125*v*(0.001*v*v + 1) - 1; +} + +Deriv fp(f); + +double df(double x) +{ + return fp.eval(x); +} + +double iter(double x) +{ + return x - f(x)/df(x); +} + +int main() +{ + picture(P(0,-1), P(8,4), "2.5 x 1.5625in"); + + begin(); + bold(); + + double xQ(2), T(iter(xQ)), T1(iter(T)); + + P O(0,0); + + line(O, P(xmax(),0)); + line(O, P(0,3)); + + line(P(xQ,0), P(xQ, f(xQ))); + line(P(T,0), P(xQ, f(xQ))); + + plot(f, xQ, xmax(), 60); + + line_style("- - "); + line(P(T,0), P(T, f(T))); + line(P(T1,0), P(T, f(T))); + + label(O, P(0,-2), "$O$", b); + label(P(xQ), P(0,-2), "$Q$", b); + label(P(T), P(0,-2), "$T$", b); + label(P(T1), P(0,-2), "$T_1$", b); + + label(P(7,f(7)), P(0,-2), "$P_1$", b); + + label(P(0.5*xQ), P(0, 2), "$a$", t); + label(P(0.5*(xQ+T)), P(0, 2), "$h$", t); + label(P(newton(f, T1)), P(2, 2), "$S$", t); + label(P(xmax()), P(0, 2), "$X$", t); + + label(P(0,3), P(2,0), "$Y$", r); + + label(P(xQ,f(xQ)), P(2,0), "$P$", r); + label(P(xmax(),f(xmax())), P(2,0), "$P_2$", r); + + label(P(0.5*xmax(), ymin()), P(0,-18), "\\textsc{Fig.~22}", b); + + tikz_format(); + + end(); +} diff --git a/29785-t/images/sources/097b.xp b/29785-t/images/sources/097b.xp new file mode 100644 index 0000000..92eedff --- /dev/null +++ b/29785-t/images/sources/097b.xp @@ -0,0 +1,55 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double alpha(-1.25), beta(1.3); + +double g(double x) +{ + return 0.05*pow(fabs(x-alpha), 1.5)*pow(fabs(x-beta),1.25); +} + +double f(double x) +{ + return tanh(x) - 0.05 - g(x); +} + +Deriv fp(f); + +double df(double x) +{ + return fp.eval(x); +} + +double iter(double x) +{ + return x - f(x)/df(x); +} + +int main() +{ + picture(P(-2,-1), P(2,1), "2.5 x 1.25in"); + + begin(); + bold(); + + set_crop(); + line(P(xmin()), P(xmax())); + + line(P(alpha,f(alpha)), P(alpha)); + line(P(alpha,f(alpha)), P(iter(alpha))); + + line(P(beta, f(beta)), P(beta)); + line(P(beta, f(beta)), P(iter(beta))); + + plot(f, alpha, beta, 60); + + label(P(alpha), P(-2,-2), "$\\alpha$", bl); + label(P(beta), P(2, 2), "$\\beta$", tr); + + label(P(0, ymin()), P(0,-18), "\\textsc{Fig.~23}", b); + + tikz_format(); + + end(); +} diff --git a/29785-t/images/sources/098a.xp b/29785-t/images/sources/098a.xp new file mode 100644 index 0000000..c2bb0e5 --- /dev/null +++ b/29785-t/images/sources/098a.xp @@ -0,0 +1,58 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double f(double x) +{ + return -1 + x*(0.5 + 0.125*x + 0.005*pow(x, 6)); +} + +Deriv fp(f); + +double df(double x) +{ + return fp.eval(x); +} + +double iter(double x) +{ + return x - f(x)/df(x); +} + +int main() +{ + picture(P(0,-1), P(2,1), "1.5 x 1.25in"); + + begin(); + bold(); + + double alpha(xmin()), beta(xmax()), T(iter(beta)); + + P xA(alpha), xB(beta), pA(P(alpha, f(alpha))), pB(beta, f(beta)); + + line(xA, xB); + + line(xA, pA); + line(xB, pB); + line(P(T), pB); + + plot(f, alpha, beta, 40); + + dashed(); + line(pA, pB); + + label(xA, P(0,2), "$\\alpha$", t); + label(pA, P(-2,0), "$A$", l); + + label(xB, P(0,-2), "$\\beta$", b); + label(pB, P(2, 0), "$B$", r); + + label(P(T), P(0,-2), "$T$", b); + label(Segment(pA, pB)*Segment(xA, xB), P(-2,2), "$c$", tl); + + label(P(0.5*xmax(), ymin()), P(0,-12), "\\textsc{Fig.~24}", b); + + tikz_format(); + + end(); +} diff --git a/29785-t/images/sources/098b.xp b/29785-t/images/sources/098b.xp new file mode 100644 index 0000000..6f5a37c --- /dev/null +++ b/29785-t/images/sources/098b.xp @@ -0,0 +1,52 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double f(double x) +{ + return 0.5*(1 - 0.5*pow(2-x, 2) - 0.01*pow(2-x, 6)); +} + +Deriv fp(f); + +double df(double x) +{ + return fp.eval(x); +} + +double iter(double x) +{ + return x - f(x)/df(x); +} + +int main() +{ + picture(P(0,-1), P(2,1), "1.5 x 1.25in"); + + begin(); + bold(); + + double alpha(xmin()), beta(xmax()), T(iter(alpha)); + + P xA(alpha), xB(beta), pA(P(alpha, f(alpha))), pB(beta, f(beta)); + + line(xA, xB); + + line(xA, pA); + line(xB, pB); + line(P(T), pA); + + plot(f, alpha, beta, 40); + + label(xA, P(0,2), "$\\alpha$", t); + + label(xB, P(0,-2), "$\\beta$", b); + + label(P(T), P(0, 2), "$T$", t); + + label(P(0.5*xmax(), ymin()), P(0,-12), "\\textsc{Fig.~25}", b); + + tikz_format(); + + end(); +} diff --git a/29785-t/images/sources/098c.xp b/29785-t/images/sources/098c.xp new file mode 100644 index 0000000..fd39835 --- /dev/null +++ b/29785-t/images/sources/098c.xp @@ -0,0 +1,60 @@ +/* -*-ePiX-*- */ +#include "epix.h" +using namespace ePiX; + +double f(double x) +{ + return 0.5*(1 - 0.5*pow(x, 2) - 0.01*pow(x, 6)); +} + +Deriv fp(f); + +double df(double x) +{ + return fp.eval(x); +} + +double iter(double x) +{ + return x - f(x)/df(x); +} + +int main() +{ + picture(P(0,-1), P(2,1), "1.5 x 1.25in"); + + begin(); + bold(); + + double alpha(xmin()), beta(xmax()), T(iter(beta)); + + P xA(alpha), xB(beta), pA(P(alpha, f(alpha))), pB(beta, f(beta)); + + line(xA, xB); + + line(xA, pA); + line(xB, pB); + line(P(T), pB); + + dashed(); + line(pA, pB); + + solid(); + plot(f, alpha, beta, 40); + + label(pA, P(-2,0), "$A$", l); + label(xA, P(0,-2), "$\\alpha$", b); + + label(pB, P(2, 0), "$B$", r); + label(xB, P(0, 2), "$\\beta$", t); + + label(P(T), P(0, 2), "$T$", t); + + label(Segment(pA, pB)*Segment(xA, xB), P(-2,-2), "$c$", bl); + + label(P(0.5*xmax(), ymin()), P(0,-12), "\\textsc{Fig.~26}", b); + + tikz_format(); + + end(); +} |