From 888555a9bff68c47c95f991e82e736212113f0d3 Mon Sep 17 00:00:00 2001 From: jemmybutton Date: Sat, 7 Jan 2017 22:21:31 +0300 Subject: [PATCH] automatic angle naming --- byrne.mp | 32 +- byrne_context.tex | 1042 +++++++++++++++++++++--------------------- byrne_euclid_man.tex | 17 +- 3 files changed, 556 insertions(+), 535 deletions(-) diff --git a/byrne.mp b/byrne.mp index 2cc6ac5..d690c72 100644 --- a/byrne.mp +++ b/byrne.mp @@ -1,4 +1,4 @@ -% byrne-euclid 0.0.1 +% byrne-euclid 0.0.2 % MetaPost library that implements most of the graphical % features present in Oliver Byrne's version of Euclid's "Elements" % Copyright 2017 Sergey Slyusarev @@ -662,7 +662,7 @@ enddef; % Angles % -vardef byAngleDefine(suffix a, b, c)(expr col, sty)(suffix angleName) = +vardef byAngleDefineWithName(suffix a, b, c)(expr col, sty)(suffix angleName) = path angleArc.angleName; color angleColor.angleName, angleOptionalColor.angleName[]; numeric angleDirection.angleName; @@ -686,19 +686,27 @@ begingroup endgroup enddef; -vardef byAngle(suffix a, b, c)(expr col, sty)(suffix angleName) = +vardef byAngleDefine(suffix a, b, c)(expr col, sty) = + byAngleDefineWithName(a, b, c)(col, sty)(scantokens(str a & str b & str c)); +enddef; + +vardef byAngleWithName(suffix a, b, c)(expr col, sty)(suffix angleName) = begingroup - byAngleDefine(a, b, c, col, sty)(angleName); + byAngleDefineWithName(a, b, c, col, sty)(angleName); byNamedAngle(angleName) endgroup enddef; -vardef byAngleExtended(suffix a, b, c)(expr col, sty)(suffix angleName)(text optionalColors) = +vardef byAngle(suffix a, b, c)(expr col, sty) = + byAngleWithName(a, b, c)(col, sty)(scantokens(str a & str b & str c)) +enddef; + +vardef byAngleExtendedWithName(suffix a, b, c)(expr col, sty)(suffix angleName)(text optionalColors) = begingroup save n; numeric n; n := 0; - byAngleDefine(a, b, c, col, sty)(angleName); + byAngleDefineWithName(a, b, c, col, sty)(angleName); forsuffixes oC=optionalColors: angleOptionalColor.angleName[n] := oC; n := n + 1; @@ -707,6 +715,10 @@ begingroup endgroup enddef; +vardef byAngleExtended(suffix a, b, c)(expr col, sty)(text optionalColors) = + byAngleExtendedWithName(a, b, c)(col, sty)(scantokens(str a & str b & str c))(optionalColors) +enddef; + vardef byNamedAngle(text anglesList) = begingroup save p, q; @@ -892,10 +904,10 @@ pointS := (0, -2u*angleScale); pointW := (-2u*angleScale, 0); pointO := (0, 0); -byAngleDefine (pointN, pointO, pointE)(black, 1)(rightAngleNE); -byAngleDefine (pointE, pointO, pointS)(black, 1)(rightAngleES); -byAngleDefine (pointS, pointO, pointW)(black, 1)(rightAngleSE); -byAngleDefine (pointW, pointO, pointN)(black, 1)(rightAngleWN); +byAngleDefineWithName (pointN, pointO, pointE)(black, 1)(rightAngleNE); +byAngleDefineWithName (pointE, pointO, pointS)(black, 1)(rightAngleES); +byAngleDefineWithName (pointS, pointO, pointW)(black, 1)(rightAngleSE); +byAngleDefineWithName (pointW, pointO, pointN)(black, 1)(rightAngleWN); % % Magnitudes diff --git a/byrne_context.tex b/byrne_context.tex index 4b390e4..c27d313 100644 --- a/byrne_context.tex +++ b/byrne_context.tex @@ -86,9 +86,9 @@ draw byPolygon ((J--M--I--K--cycle), byblue)(JMIK); draw byPolygon ((M--C--I--cycle), byblue)(MCK); draw byPolygon ((B--J--K--H--cycle), byyellow)(BJKH); -draw byAngle (F, C, A, byyellow, 0)(FCA); -draw byAngle (B, C, I, byyellow, 0)(BCI); -draw byAngle (A, C, B, black, 0)(ACB); +draw byAngle(F, C, A, byyellow, 0); +draw byAngle(B, C, I, byyellow, 0); +draw byAngle(A, C, B, black, 0); draw byLine(A, K, black, 1, 0); draw byLineFull(B, F, black, 0, 0)(C, G, 1, 1, 0); draw byLineFull(A, I, black, 0, 0)(C, H, 1, 1, 0); @@ -163,9 +163,9 @@ B := (0, 0); A := B shifted (dir(-145)*3u); C = whatever[A, A shifted (1,0)] = whatever[B, B shifted dir(-145+90)]; - draw byAngle (A, B, C, byyellow, 0)(B); - draw byAngle (B, C, A, byblue, 0)(C); - draw byAngle (C, A, B, byred, 0)(A); + draw byAngleWithName(A, B, C, byyellow, 0)(B); + draw byAngleWithName(B, C, A, byblue, 0)(C); + draw byAngleWithName(C, A, B, byred, 0)(A); byLineDefine(A, B, byblue, 0, 0); byLineDefine(B, C, byred, 0, 0); byLineDefine(C, A, byyellow, 0, 0); @@ -248,9 +248,9 @@ A := dir(0) scaled 3u; B := dir(120) scaled 3u; C := dir(240) scaled 3u; - draw byAngle (A, O, B, byred, 0)(AOB); - draw byAngle (B, O, C, byblue, 0)(BOC); - draw byAngle (C, O, A, byyellow, 0)(COD); + draw byAngle(A, O, B, byred, 0); + draw byAngle(B, O, C, byblue, 0); + draw byAngle(C, O, A, byyellow, 0); } Let three colours \drawCurrentPictureInMargin meet and cover a portion of the paper, where they meet is not blue, nor it is yellow, nor it is red, as it occupies no portion of the plane, for if it did, it would belong to the blue, the red, or the yellow part; yet it exists, and has position without magnitude, so that with a little reflectionm this junction of three colours on a plane, gives a good idea of a mathematical point. @@ -316,16 +316,16 @@ D := 9/5[A,B]; E := 9/5[A,C]; q := image( -draw byAngle(E, B, D, white, 0)(EBD); -draw byAngle(D, C, E, white, 0)(DCE); +draw byAngle(E, B, D, white, 0); +draw byAngle(D, C, E, white, 0); ); -draw byAngle(B, A, C, black, 0)(A); -draw byAngle(A, B, C, byblue, 0)(B); -draw byAngle(B, C, A, byblue, 0)(C); -draw byAngle(C, B, E, byyellow, 0)(CBE); -draw byAngle(D, C, B, byyellow, 0)(DCB); -draw byAngle(B, D, C, byred, 0)(D); -draw byAngle(C, E, B, byred, 0)(E); +draw byAngleWithName(B, A, C, black, 0)(A); +draw byAngleWithName(A, B, C, byblue, 0)(B); +draw byAngleWithName(B, C, A, byblue, 0)(C); +draw byAngle(C, B, E, byyellow, 0); +draw byAngle(D, C, B, byyellow, 0); +draw byAngleWithName(B, D, C, byred, 0)(D); +draw byAngleWithName(C, E, B, byred, 0)(E); byLineDefine(B, D, byyellow, 0, 0); byLineDefine(C, E, byyellow, 0, 0); byLineDefine(B, E, byblue, 0, 0); @@ -334,8 +334,8 @@ byLineDefine(A, C, byred, 0, 0); byLineDefine(B, C, black, 0, 0); draw byNamedLineSeq(0)(BE,noLine,BC,noLine,CD,BD,AB,AC,CE); -byAngleDefine(E, B, D, white, 0)(EBD); -byAngleDefine(D, C, E, white, 0)(DCE); +byAngleDefine(E, B, D, white, 0); +byAngleDefine(D, C, E, white, 0); } \figureInMargin{ \startMPcode{\currentInstance} @@ -451,7 +451,7 @@ A := (0, 0); B := (u, u); C := (3/2u, ypart(A)); - draw byAngle(B, A, C, byyellow, 0)(A); + draw byAngleWithName(B, A, C, byyellow, 0)(A); byLineDefine(A, B, byblue, 0, 0); byLineDefine(A, C, byred, 0, 0); draw byNamedLineSeq(0)(AB,AC); @@ -469,8 +469,8 @@ B := (4/3u, 0); C := (0, u); D := (-4/3u, 0); - draw byAngle(B, A, C, black, 1)(BAC); - draw byAngle(D, A, C, black, 1)(DAC); + draw byAngle(B, A, C, black, 1); + draw byAngle(D, A, C, black, 1); draw byLine(D, B, black, 0, 0); draw byLine(A, C, black, 0, 0); } @@ -486,7 +486,7 @@ A := (0, 0); B := (-u, u); C := (3/2u, ypart(A)); - draw byAngle(B, A, C, byred, 0)(A); + draw byAngleWithName(B, A, C, byred, 0)(A); byLineDefine(A, B, byyellow, 0, 0); byLineDefine(A, C, byblue, 0, 0); draw byNamedLineSeq(0)(AB,AC); @@ -503,7 +503,7 @@ A := (0, 0); B := (u, u); C := (3/2u, ypart(A)); - draw byAngle(B, A, C, byblue, 0)(A); + draw byAngleWithName(B, A, C, byblue, 0)(A); byLineDefine(A, B, byyellow, 0, 0); byLineDefine(A, C, byred, 0, 0); draw byNamedLineSeq(0)(AB,AC); @@ -926,8 +926,8 @@ F := (xpart(E), -1/6s); G = whatever[A, B] = whatever[E, F]; H = whatever[C, D] = whatever[E, F]; - draw byAngle(B, G, E, byred, 0)(G); - draw byAngle(D, H, F, byyellow, 0)(H); + draw byAngleWithName(B, G, E, byred, 0)(G); + draw byAngleWithName(D, H, F, byyellow, 0)(H); draw byLine(A, B, byblue, 0, 0); draw byLine(C, D, byred, 0, 0); draw byLine(E, F, black, 0, 0); @@ -956,7 +956,7 @@ A := (0, s); B := (1/2s, 0); C := B xscaled -1; - draw byAngle(B, A, C, byyellow, 0)(A); + draw byAngleWithName(B, A, C, byyellow, 0)(A); byLineDefine(B, A, byblue, 0, 0); byLineDefine(C, A, byred, 0, 0); draw byNamedLineSeq(0)(BA,CA); @@ -975,12 +975,12 @@ G := D scaled -1; H := B scaled -1; angleScale := 4/3; - draw byAngle(E, C, B, byyellow, 0)(ECB); - draw byAngle(B, C, D, black, 0)(BCD); - draw byAngle(D, C, F, byblue, 0)(DCF); - draw byAngle(F, C, H, byred, 0)(DCF); - draw byAngle(H, C, G, byyellow, 1)(HCG); - draw byAngle(G, C, E, byblue, 1)(GCE); + draw byAngle(E, C, B, byyellow, 0); + draw byAngle(B, C, D, black, 0); + draw byAngle(D, C, F, byblue, 0); + draw byAngle(F, C, H, byred, 0); + draw byAngle(H, C, G, byyellow, 1); + draw byAngle(G, C, E, byblue, 1); draw byLine(B, H, byblue, 0, 0); draw byLine(D, G, byred, 0, 0); draw byLine(E, F, black, 0, 0); @@ -1099,8 +1099,8 @@ B := dir(0)*s; C := dir(50)*s; D := dir(90)*s; - draw byAngle(B, A, C, white, 0)(BAC); - draw byAngle(B, A, D, white, 0)(BAD); + draw byAngle(B, A, C, white, 0); + draw byAngle(B, A, D, white, 0); } \symb{\drawAngle{BAC}} @@ -1304,16 +1304,16 @@ D := A shifted d; E := B shifted d; F := C shifted d; -draw byAngle(B, A, C, byyellow, 0)(A); -draw byAngle(A, B, C, byblue, 0)(B); -draw byAngle(B, C, A, byred, 0)(C); +draw byAngleWithName(B, A, C, byyellow, 0)(A); +draw byAngleWithName(A, B, C, byblue, 0)(B); +draw byAngleWithName(B, C, A, byred, 0)(C); byLineDefine(A, B, byred, 0, 0); byLineDefine(B, C, black, 0, 0); byLineDefine(C, A, byblue, 0, 0); draw byNamedLineSeq(0)(AB,BC,CA); -draw byAngle(E, D, F, byyellow, 0)(D); -draw byAngle(D, E, F, byblue, 0)(E); -draw byAngle(E, F, D, byred, 0)(F); +draw byAngleWithName(E, D, F, byyellow, 0)(D); +draw byAngleWithName(D, E, F, byblue, 0)(E); +draw byAngleWithName(E, F, D, byred, 0)(F); byLineDefine(D, E, byred, 0, 1); byLineDefine(E, F, black, 0, 1); byLineDefine(F, D, byblue, 0, 1); @@ -1336,13 +1336,13 @@ C := B xscaled -1; D := 9/5[A,B]; E := 9/5[A,C]; -draw byAngle(B, A, C, black, 0)(A); -draw byAngle(A, B, C, byblue, 0)(B); -draw byAngle(B, C, A, byblue, 0)(C); -draw byAngle(C, B, E, byyellow, 0)(CBE); -draw byAngle(D, C, B, byyellow, 0)(DCB); -draw byAngle(B, D, C, byred, 0)(D); -draw byAngle(C, E, B, byred, 0)(E); +draw byAngleWithName(B, A, C, black, 0)(A); +draw byAngleWithName(A, B, C, byblue, 0)(B); +draw byAngleWithName(B, C, A, byblue, 0)(C); +draw byAngle(C, B, E, byyellow, 0); +draw byAngle(D, C, B, byyellow, 0); +draw byAngleWithName(B, D, C, byred, 0)(D); +draw byAngleWithName(C, E, B, byred, 0)(E); byLineDefine(B, D, byyellow, 0, 0); byLineDefine(C, E, byyellow, 0, 0); byLineDefine(B, E, byblue, 0, 0); @@ -1351,8 +1351,8 @@ byLineDefine(A, C, byred, 0, 0); byLineDefine(B, C, black, 0, 0); draw byNamedLineSeq(0)(BE,noLine,BC,noLine,CD,BD,AB,AC,CE); -byAngleDefine(E, B, D, white, 0)(EBD); -byAngleDefine(D, C, E, white, 0)(DCE); +byAngleDefine(E, B, D, white, 0); +byAngleDefine(D, C, E, white, 0); } \drawCurrentPictureInMargin \problemNP{I}{n}{any isosceles triangle \drawLine[bottom]{AB,AC,BC} if the equal sides be produced, the external angles at the base are equal, and the internal angles at the base are also equal.} @@ -1396,8 +1396,8 @@ B := A shifted (7/2u, 0); D := A shifted (7/4u, 3u); C := 2/3[A, D]; -draw byAngle(B, A, C, byyellow, 0)(A); -draw byAngle(A, B, D, black, 0)(B); +draw byAngleWithName(B, A, C, byyellow, 0)(A); +draw byAngleWithName(A, B, D, black, 0)(B); byLineDefine(B, C, byyellow, 0, 0); byLineDefine(A, B, byred, 0, 0); byLineDefine(B, D, byblue, 0, 0); @@ -1436,14 +1436,14 @@ F := E shifted (0, -2u); G := 5/4[A, E]; H := 5/4[A, F]; -draw byAngle(B, C, A, black, 0)(C); -draw byAngle(D, C, B, byred, 0)(DCB); -draw byAngle(A, D, B, byyellow, 0)(D); -draw byAngle(C, D, A, byblue, 0)(CDA); -draw byAngle(B, F, H, black, 0)(BFH); -draw byAngle(B, F, E, byred, 0)(BFE); -draw byAngle(B, E, G, byyellow, 0)(BEG); -draw byAngle(G, E, F, byblue, 0)(GEF); +draw byAngleWithName(B, C, A, black, 0)(C); +draw byAngle(D, C, B, byred, 0); +draw byAngleWithName(A, D, B, byyellow, 0)(D); +draw byAngle(C, D, A, byblue, 0); +draw byAngle(B, F, H, black, 0); +draw byAngle(B, F, E, byred, 0); +draw byAngle(B, E, G, byyellow, 0); +draw byAngle(G, E, F, byblue, 0); draw byLine(C, D, black, 1, 0); draw byLine(E, F, black, 1, 0); draw byLine(A, B, black, 0, 0); @@ -1495,8 +1495,8 @@ D := A shifted d; E := B shifted d; F := C shifted d; -draw byAngle(F, D, E, black, 0)(D); -draw byAngle(C, A, B, black, 0)(A); +draw byAngleWithName(F, D, E, black, 0)(D); +draw byAngleWithName(C, A, B, black, 0)(A); byLineDefine(A, B, byred, 0, 0); byLineDefine(B, C, black, 0, 0); byLineDefine(C, A, byyellow, 0, 0); @@ -1531,8 +1531,8 @@ D := A yscaled -1; E := 5/4[A, B]; F := 5/4[A, C]; -draw byAngle(B, A, D, byblue, 0)(BAD); -draw byAngle(C, A, D, byyellow, 0)(CAD); +draw byAngle(B, A, D, byblue, 0); +draw byAngle(C, A, D, byyellow, 0); byLineDefine(B, C, byyellow, 0, 0); byLineDefine(A, D, black, 0, 0); byLineDefine(D, B, byblue, 0, 0); @@ -1571,8 +1571,8 @@ B := (-7/4u, 0); C := B xscaled -1; D := 1/2[B, C]; -draw byAngle(B, A, D, byblue, 0)(BAD); -draw byAngle(C, A, D, byyellow, 0)(CAD); +draw byAngle(B, A, D, byblue, 0); +draw byAngle(C, A, D, byyellow, 0); draw byLine(A, D, byred, 0, 0); byLineDefine(D, B, black, 0, 0); byLineDefine(C, D, black, 1, 0); @@ -1607,8 +1607,8 @@ D := 1/2[B, C]; E := 3/2[D, B]; F := 3/2[D, C]; -draw byAngle(A, D, B, byred, 0)(ADB); -draw byAngle(C, D, A, byblue, 0)(CDA); +draw byAngle(A, D, B, byred, 0); +draw byAngle(C, D, A, byblue, 0); draw byLine(A, D, byyellow, 0, 0); byLineDefine(A, B, byblue, 0, 0); byLineDefine(C, A, byblue, 0, 0); @@ -1654,8 +1654,8 @@ c := fullcircle scaled 2r shifted A; a1 := xpart(c intersectiontimes (F--1/2[B, C])); a2 := xpart(c intersectiontimes (E--1/2[B, C])); -draw byAngle(A, D, B, byyellow, 0)(ADB); -draw byAngle(C, D, A, byblue, 0)(CDA); +draw byAngle(A, D, B, byyellow, 0); +draw byAngle(C, D, A, byblue, 0); draw byLine(A, D, byred, 0, 0); byLineDefine(A, B, byblue, 0, 0); byLineDefine(C, A, byblue, 0, 0); @@ -1704,9 +1704,9 @@ C := B xscaled -1; D := (xpart(A), ypart(B)); E := (2/3xpart(C), 2/3ypart(A)); -draw byAngle(A, D, B, byyellow, 0)(ADB); -draw byAngle(E, D, A, byred, 0)(EDA); -draw byAngle(C, D, E, byblue, 0)(CDE); +draw byAngle(A, D, B, byyellow, 0); +draw byAngle(E, D, A, byred, 0); +draw byAngle(C, D, E, byblue, 0); draw byLine(A, D, black, 0, 0); draw byLine(E, D, byyellow, 0, 0); draw byLine(B, C, byred, 0, 0); @@ -1739,9 +1739,9 @@ C := B xscaled -1; D := (0, 0); E := (xpart(C), -1/2ypart(A)); -draw byAngle(B, D, A, byyellow, 0)(BDA); -draw byAngle(C, D, A, byblue, 0)(CDA); -draw byAngle(E, D, C, byred, 0)(EDC); +draw byAngle(B, D, A, byyellow, 0); +draw byAngle(C, D, A, byblue, 0); +draw byAngle(E, D, C, byred, 0); draw byLine(A, D, byred, 0, 0); draw byLine(E, D, byyellow, 0, 0); draw byLine(B, D, byblue, 0, 0); @@ -1772,10 +1772,10 @@ C := A xscaled -1; D := C scaled -1; E := (A--B) intersectionpoint (C--D); -draw byAngle(B, E, C, byyellow, 0)(BEC); -draw byAngle(C, E, A, byred, 0)(CEA); -draw byAngle(A, E, D, black, 0)(AED); -draw byAngle(D, E, B, byblue, 0)(DEB); +draw byAngle(B, E, C, byyellow, 0); +draw byAngle(C, E, A, byred, 0); +draw byAngle(A, E, D, black, 0); +draw byAngle(D, E, B, byblue, 0); draw byLine(A, B, byred, 0, 0); draw byLine(C, D, black, 0, 0); } @@ -1806,13 +1806,13 @@ E = whatever[A, D] = whatever[B, C]; F := (xpart(D), ypart(A)); G := 4/3[B, C]; -draw byAngle(B, A, C, byblue, 0)(A); -draw byAngle(C, B, A, black, 0)(B); -draw byAngle(A, E, B, byyellow, 0)(AEB); -draw byAngle(D, E, C, byyellow, 0)(DEC); -draw byAngle(E, C, D, black, 0)(ECD); -draw byAngle(A, C, G, byred, 0)(GCA); -draw byAngle(D, C, F, black, 1)(DCF); +draw byAngleWithName(B, A, C, byblue, 0)(A); +draw byAngleWithName(C, B, A, black, 0)(B); +draw byAngle(A, E, B, byyellow, 0); +draw byAngle(D, E, C, byyellow, 0); +draw byAngle(E, C, D, black, 0); +draw byAngle(G, C, A, byred, 0); +draw byAngle(D, C, F, black, 1); byLineDefine(C, F, black, 1, 0); byLineDefine(C, G, black, 0, 0); byLineDefine(B, E, byblue, 0, 0); @@ -1853,10 +1853,10 @@ B := A shifted (3/2u, 5/2u); C := A shifted (9/4u, 0); D := C shifted (u, 0); -draw byAngle(B, A, C, byblue, 0)(A); -draw byAngle(A, B, C, black, 0)(B); -draw byAngle(A, C, B, byred, 0)(ACB); -draw byAngle(D, C, B, byyellow, 0)(BCD); +draw byAngleWithName(B, A, C, byblue, 0)(A); +draw byAngleWithName(A, B, C, black, 0)(B); +draw byAngle(A, C, B, byred, 0); +draw byAngle(B, C, D, byyellow, 0); byLineDefine(A, B, byred, 0, 0); byLineDefine(B, C, byblue, 0, 0); byLineDefine(A, C, black, 0, 0); @@ -1887,10 +1887,10 @@ B := A shifted (5/2u, -1/2u); C := A shifted (3/2u, 2u); D := 2[C, A]; -draw byAngle(C, A, B, byblue, 0)(A); -draw byAngle(A, B, C, black, 0)(ABC); -draw byAngle(D, B, A, byred, 0)(DBA); -draw byAngle(B, D, A, byyellow, 0)(D); +draw byAngleWithName(C, A, B, byblue, 0)(A); +draw byAngle(A, B, C, black, 0); +draw byAngle(D, B, A, byred, 0); +draw byAngleWithName(B, D, A, byyellow, 0)(D); byLineDefine(A, B, byyellow, 0, 0); byLineDefine(A, C, byred, 0, 0); byLineDefine(B, C, byblue, 0, 0); @@ -1922,8 +1922,8 @@ A := (0, 0); B := A shifted (7/2u, 0); C := A shifted (u, 3u); -draw byAngle(C, A, B, byblue, 0)(A); -draw byAngle(A, B, C, byred, 0)(B); +draw byAngleWithName(C, A, B, byblue, 0)(A); +draw byAngleWithName(A, B, C, byred, 0)(B); byLineDefine(A, B, black, 0, 0); byLineDefine(B, C, byblue, 0, 0); byLineDefine(C, A, byred, 0, 0); @@ -1957,9 +1957,9 @@ B := A shifted (7/2u, 0); D := A shifted (4/3u, 3/2u); C := ((fullcircle scaled 2arclength(D--B)) shifted D) intersectionpoint (D--10[A, D]); -draw byAngle(B, C, A, byred, 0)(C); -draw byAngle(C, B, D, byblue, 0)(CBD); -draw byAngle(D, B, A, byyellow, 0)(DBA); +draw byAngleWithName(B, C, A, byred, 0)(C); +draw byAngle(C, B, D, byblue, 0); +draw byAngle(D, B, A, byyellow, 0); byLineDefine(B, D, byred, 0, 0); byLineDefine(A, B, black, 0, 0); byLineDefine(B, C, byyellow, 0, 0); @@ -1997,9 +1997,9 @@ C := A shifted (3u, 4u); D := 1/2[1/2[A, B], C]; E = whatever[A, D] = whatever[B, C]; -draw byAngle(B, D, A, byred, 0)(D); -draw byAngle(B, E, D, byblue, 0)(E); -draw byAngle(B, C, A, byyellow, 0)(C); +draw byAngleWithName(B, D, A, byred, 0)(D); +draw byAngleWithName(B, E, D, byblue, 0)(E); +draw byAngleWithName(B, C, A, byyellow, 0)(C); byLineDefine(B, D, byyellow, 0, 0); byLineDefine(A, D, black, 0, 0); byLineDefine(D, E, black, 1, 0); @@ -2126,8 +2126,8 @@ G := B shifted d; H := C shifted d; J := D shifted d; -draw byAngle(B, A, C, byred, 0)(A); -draw byAngle(G, F, H, byblue, 0)(F); +draw byAngleWithName(B, A, C, byred, 0)(A); +draw byAngleWithName(G, F, H, byblue, 0)(F); byLineDefine(B, D, black, 1, 1); byLineDefine(C, E, byblue, 1, 1); byLineDefine(A, B, black, 0, 1); @@ -2171,13 +2171,13 @@ E := A shifted d; F := B shifted d; G := C shifted d; -draw byAngle(B, A, C, black, 2)(BAC); -draw byAngle(C, A, D, black, 3)(CAD); -draw byAngle(F, E, G, black, 2)(FEG); -draw byAngle(B, D, A, byblue, 0)(BDA); -draw byAngle(C, D, B, byred, 0)(CDB); -draw byAngle(D, C, A, byyellow, 0)(DCA); -draw byAngle(A, C, B, black, 0)(ACB); +draw byAngle(B, A, C, black, 2); +draw byAngle(C, A, D, black, 3); +draw byAngle(F, E, G, black, 2); +draw byAngle(B, D, A, byblue, 0); +draw byAngle(C, D, B, byred, 0); +draw byAngle(D, C, A, byyellow, 0); +draw byAngle(A, C, B, black, 0); byLineDefine(A, B, byblue, 0, 0); byLineDefine(B, C, black, 1, 0); draw byLine(C, A, byred, 0, 0); @@ -2234,8 +2234,8 @@ D := A shifted d; E := ((B shifted -A) rotated -10) shifted d; F := C shifted d; -draw byAngle(B, A, C, byyellow, 0)(A); -draw byAngle(E, D, F, black, 0)(D); +draw byAngleWithName(B, A, C, byyellow, 0)(A); +draw byAngleWithName(E, D, F, black, 0)(D); byLineDefine(A, B, byblue, 0, 0); byLineDefine(B, C, black, 0, 0); byLineDefine(C, A, byred, 0, 0); @@ -2277,17 +2277,17 @@ E := B shifted d; F := C shifted d; G := 3/4[D, F]; -draw byAngle(B, A, C, byyellow, 0)(A); -draw byAngle(C, B, A, byred, 0)(B); -draw byAngle(A, C, B, black, 1)(C); +draw byAngleWithName(B, A, C, byyellow, 0)(A); +draw byAngleWithName(C, B, A, byred, 0)(B); +draw byAngleWithName(A, C, B, black, 1)(C); byLineDefine(A, B, byblue, 0, 0); byLineDefine(B, C, black, 0, 0); byLineDefine(C, A, byred, 0, 0); draw byNamedLineSeq(0)(AB,BC,CA); -draw byAngle(E, D, F, byyellow, 0)(D); -draw byAngle(G, E, D, black, 0)(GED); -draw byAngle(F, E, G, byblue, 0)(FEG); -draw byAngle(D, F, E, black, 1)(F); +draw byAngleWithName(E, D, F, byyellow, 0)(D); +draw byAngle(G, E, D, black, 0); +draw byAngle(F, E, G, byblue, 0); +draw byAngleWithName(D, F, E, black, 1)(F); draw byLine(E, G, byyellow, 0, 1); byLineDefine(D, E, byblue, 0, 1); byLineDefine(E, F, black, 0, 1); @@ -2329,15 +2329,15 @@ L := I shifted d; M := J shifted d; N := 3/4[K, L]; -draw byAngle(I, H, J, byyellow, 0)(H); -draw byAngle(J, I, H, byred, 0)(I); +draw byAngleWithName(I, H, J, byyellow, 0)(H); +draw byAngleWithName(J, I, H, byred, 0)(I); byLineDefine(H, I, byblue, 0, 0); byLineDefine(I, J, black, 0, 0); byLineDefine(J, H, byred, 0, 0); draw byNamedLineSeq(0)(HI,IJ,JH); -draw byAngle(L, K, M, byyellow, 0)(K); -draw byAngle(M, N, K, black, 0)(N); -draw byAngle(M, L, K, byred, 0)(L); +draw byAngleWithName(L, K, M, byyellow, 0)(K); +draw byAngleWithName(M, N, K, black, 0)(N); +draw byAngleWithName(M, L, K, byred, 0)(L); draw byLine(M, N, byyellow, 0, 1); byLineDefine(K, N, byblue, 0, 1); byLineDefine(N, L, byblue, 1, 1); @@ -2377,10 +2377,10 @@ G := 3/2[F, E]; H := 3/2[E, F]; I := 1/2[A, C] shifted (-2u, 0); -draw byAngle(A, E, F, byyellow, 0)(AEF); -draw byAngle(F, E, B, byred, 0)(FEB); -draw byAngle(C, F, E, byblue, 0)(CFE); -draw byAngle(E, F, D, byyellow, 0)(EFD); +draw byAngle(A, E, F, byyellow, 0); +draw byAngle(F, E, B, byred, 0); +draw byAngle(C, F, E, byblue, 0); +draw byAngle(E, F, D, byyellow, 0); byLineDefine(I, A, byblue, 0, 0); byLineDefine(A, B, byblue, 0, 0); byLineDefine(I, C, byred, 0, 0); @@ -2410,12 +2410,12 @@ F := 11/20[C, D]; G := 7/4[F, E]; H := 4/3[E, F]; -draw byAngle(G, E, A, black, 0)(GEA); -draw byAngle(B, E, G, byyellow, 0)(BEG); -draw byAngle(A, E, F, byred, 0)(AEF); -draw byAngle(F, E, B, byblue, 0)(FEB); -draw byAngle(C, F, E, byblue, 0)(CFE); -draw byAngle(E, F, D, byred, 0)(EFD); +draw byAngle(G, E, A, black, 0); +draw byAngle(B, E, G, byyellow, 0); +draw byAngle(A, E, F, byred, 0); +draw byAngle(F, E, B, byblue, 0); +draw byAngle(C, F, E, byblue, 0); +draw byAngle(E, F, D, byred, 0); draw byLine(A, B, byred, 0, 0); draw byLine(C, D, byyellow, 0, 0); draw byLine(G, H, black, 0, 0); @@ -2454,11 +2454,11 @@ d2 := (3/2u, 1/2u); I := E shifted -d2; J := E shifted d2; -draw byAngle(I, E, A, byblue, 0)(IEA); -draw byAngle(F, E, I, byyellow, 0)(FEI); -draw byAngle(B, E, F, black, 0)(BEF); -draw byAngle(G, E, B, byred, 0)(GEB); -draw byAngle(E, F, D, black, 0)(EFD); +draw byAngle(I, E, A, byblue, 0); +draw byAngle(F, E, I, byyellow, 0); +draw byAngle(B, E, F, black, 0); +draw byAngle(G, E, B, byred, 0); +draw byAngle(E, F, D, black, 0); draw byLine(I, E, black, 0, 0); draw byLine(E, J, black, 1, 0); draw byLine(A, B, byyellow, 0, 0); @@ -2492,9 +2492,9 @@ I := (G--H) intersectionpoint (C--D); J := 3/2[H, G]; K := 5/4[G, H]; -draw byAngle(B, G, J, byyellow, 0)(G); -draw byAngle(D, I, J, byblue, 0)(I); -draw byAngle(F, H, J, byred, 0)(H); +draw byAngleWithName(B, G, J, byyellow, 0)(G); +draw byAngleWithName(D, I, J, byblue, 0)(I); +draw byAngleWithName(F, H, J, byred, 0)(H); draw byLine(A, B, byred, 0, 0); draw byLine(C, D, byyellow, 0, 0); draw byLine(E, F, byblue, 0, 0); @@ -2526,8 +2526,8 @@ D := B shifted d; E := 4/5[A, B]; F := 1/5[C, D]; -draw byAngle(F, E, A, byyellow, 0)(E); -draw byAngle(E, F, D, byred, 0)(F); +draw byAngleWithName(F, E, A, byyellow, 0)(E); +draw byAngleWithName(E, F, D, byred, 0)(F); draw byLine(E, F, black, 0, 0); draw byLine(A, E, byred, 0, 0); draw byLine(E, B, byred, 1, 0); @@ -2556,11 +2556,11 @@ C := A shifted (7/4u, -3u); D := 4/3[B, A]; E := A shifted (unitvector(C-B) scaled 3/2u); -draw byAngle (D, A, E, byred, 0)(DAE); -draw byAngle (E, A, C, black, 0)(EAC); -draw byAngle (C, A, B, byblue, 0)(CAB); -draw byAngle (A, B, C, byyellow, 0)(B); -draw byAngle (B, C, A, black, 0)(C); +draw byAngle(D, A, E, byred, 0); +draw byAngle(E, A, C, black, 0); +draw byAngle(C, A, B, byblue, 0); +draw byAngleWithName(A, B, C, byyellow, 0)(B); +draw byAngleWithName(B, C, A, black, 0)(C); draw byLine(A, E, byblue, 0, 0); byLineDefine(A, D, black, 1, 0); byLineDefine(A, B, black, 0, 0); @@ -2600,10 +2600,10 @@ B := A shifted d1; C := A shifted d2; D := C shifted d1; -draw byAngle (B, A, D, byyellow, 0)(BAD); -draw byAngle (D, A, C, byred, 0)(DAC); -draw byAngle (C, D, A, black, 0)(CDA); -draw byAngle (A, D, B, byblue, 0)(ADB); +draw byAngle(B, A, D, byyellow, 0); +draw byAngle(D, A, C, byred, 0); +draw byAngle(C, D, A, black, 0); +draw byAngle(A, D, B, byblue, 0); draw byLine(A, D, black, 0, 0); byLineDefine(A, B, byred, 0, 0); byLineDefine(C, D, byred, 1, 0); @@ -2638,12 +2638,12 @@ B := A shifted d1; C := A shifted d2; D := C shifted d1; -draw byAngle (B, A, D, byblue, 0)(BAD); -draw byAngle (D, A, C, byred, 0)(DAC); -draw byAngle (C, D, A, byyellow, 0)(CDA); -draw byAngle (A, D, B, byred, 0)(ADB); -draw byAngle (A, C, D, black, 0)(C); -draw byAngle (D, B, A, black, 0)(B); +draw byAngle(B, A, D, byblue, 0); +draw byAngle(D, A, C, byred, 0); +draw byAngle(C, D, A, byyellow, 0); +draw byAngle(A, D, B, byred, 0); +draw byAngleWithName(A, C, D, black, 0)(C); +draw byAngleWithName(D, B, A, black, 0)(B); draw byLine(A, D, black, 0, 0); byLineDefine(A, B, byred, 0, 0); byLineDefine(C, D, byred, 1, 0); @@ -2684,10 +2684,10 @@ draw byPolygon ((E--F--D--G--cycle), byyellow)(EFDG); draw byPolygon ((B--E--G--cycle), byyellow)(BEG); draw byPolygon ((C--D--G--cycle), byblue)(CDG); -draw byAngle (B, A, C, byred, 0)(A); -draw byAngle (E, B, D, byblue, 0)(B); -draw byAngle (A, E, C, black, 0)(E); -draw byAngle (A, F, D, white, 0)(F); +draw byAngleWithName(B, A, C, byred, 0)(A); +draw byAngleWithName(E, B, D, byblue, 0)(B); +draw byAngleWithName(A, E, C, black, 0)(E); +draw byAngleWithName(A, F, D, white, 0)(F); byLineDefine(A, C, byblue, 0, 0); byLineDefine(B, D, byred, 0, 0); byLineDefine(C, D, black, 0, 0); @@ -3080,8 +3080,8 @@ draw byPolygon ((D--E--F--cycle), byyellow)(GFE); draw byPolygon ((C--F--E--cycle), byblue)(CFE); draw byPolygon ((E--C--G--cycle), black)(DCG); -draw byAngle(B, E, D, byblue, 0)(E); -draw byAngle(B, E, D, byyellow, 0)(EE) shifted (xpart(G)-xpart(E), -ypart(D)-u); +draw byAngleWithName(B, E, D, byblue, 0)(E); +draw byAngleWithName(B, E, D, byyellow, 0)(EE) shifted (xpart(G)-xpart(E), -ypart(D)-u); draw byLine(A, D, byred, 1, 0); draw byLine(B, E, byred, 0, 0); draw byLine(C, E, byyellow, 0, 0); @@ -3194,10 +3194,10 @@ draw byPolygon ((J--K--L--cycle), byred)(JKL); draw byPolygon ((A--H--E--F--cycle), byyellow)(AHEF); draw byPolygon ((E--G--D--I--cycle), byblue)(EGDI); -draw byAngle (A, F, E, byblue, 0)(F); -draw byAngle (F, E, I, byred, 0)(E); -draw byAngle (E, I, D, black, 0)(I); -draw byAngle (A, F, E, byyellow, 0)(FF) shifted d1 shifted (0, ypart(D)-ypart(F)); +draw byAngleWithName(A, F, E, byblue, 0)(F); +draw byAngleWithName(F, E, I, byred, 0)(E); +draw byAngleWithName(E, I, D, black, 0)(I); +draw byAngleWithName(A, F, E, byyellow, 0)(FF) shifted d1 shifted (0, ypart(D)-ypart(F)); draw byLine(B, E, byred, 0, 0); draw byLine(E, C, black, 0, 1); byLineDefine(A, F, byred, 1, 0); @@ -3273,10 +3273,10 @@ draw byPolygon ((F--G--I--H--cycle), byblue)(FGIH); draw byPolygon ((G--J--K--I--cycle), byyellow)(GJKI); draw byPolygon ((J--L--M--K--cycle), byred)(JLMK); -draw byAngle (G, I, H, byyellow, 0)(I); -draw byAngle (J, K, I, black, 0)(K); -draw byAngle (L, M, K, byblue, 0)(M); -draw byAngle (L, M, K, byred, 0)(O) shifted (u, 0); +draw byAngleWithName(G, I, H, byyellow, 0)(I); +draw byAngleWithName(J, K, I, black, 0)(K); +draw byAngleWithName(L, M, K, byblue, 0)(M); +draw byAngleWithName(L, M, K, byred, 0)(O) shifted (u, 0); draw byLine(G, I, byred, 0, 0); draw byLine(J, K, byblue, 0, 0); } @@ -3313,10 +3313,10 @@ B := A shifted (d, 0); C := A shifted (0, -d); D := A shifted (d, -d); -draw byAngle (B, A, C, black, 0)(A); -draw byAngle (D, B, A, byblue, 0)(B); -draw byAngle (C, D, B, byred, 0)(D); -draw byAngle (A, C, D, byyellow, 0)(C); +draw byAngleWithName(B, A, C, black, 0)(A); +draw byAngleWithName(D, B, A, byblue, 0)(B); +draw byAngleWithName(C, D, B, byred, 0)(D); +draw byAngleWithName(A, C, D, byyellow, 0)(C); byLineDefine(A, B, byred, 0, 0); byLineDefine(B, D, byyellow, 0, 0); byLineDefine(D, C, black, 0, 0); @@ -3378,9 +3378,9 @@ draw byPolygon ((J--M--I--K--cycle), byblue)(JMIK); draw byPolygon ((M--C--I--cycle), byblue)(MCK); draw byPolygon ((B--J--K--H--cycle), byyellow)(BJKH); -draw byAngle (F, C, A, byyellow, 0)(FCA); -draw byAngle (B, C, I, byyellow, 0)(BCI); -draw byAngle (A, C, B, black, 0)(ACB); +draw byAngle(F, C, A, byyellow, 0); +draw byAngle(B, C, I, byyellow, 0); +draw byAngle(A, C, B, black, 0); draw byLine(A, K, black, 1, 0); draw byLineFull(B, F, black, 0, 0)(C, G, 1, 1, 0); draw byLineFull(A, I, black, 0, 0)(C, H, 1, 1, 0); @@ -3450,8 +3450,8 @@ B := A shifted (0, 3u); C := A shifted (d, 0); D := A shifted (-d, 0); -draw byAngle (B, A, C, byred, 0)(BAC); -draw byAngle (D, A, B, byyellow, 0)(DAB); +draw byAngle(B, A, C, byred, 0); +draw byAngle(D, A, B, byyellow, 0); draw byLine(A, B, byblue, 0, 0); byLineDefine(A, C, black, 0, 0); byLineDefine(A, D, black, 1, 0); @@ -3722,10 +3722,10 @@ draw byPolygon(G--K--E--F--cycle, byyellow)(GKEF); draw byPolygon(D--H--G--cycle, byblue)(DHG); draw byPolygon(G--B--C--cycle, byred)(GBC); -draw byAngle (F, D, G, byyellow, 0)(FDG); -draw byAngle (F, G, D, byred, 0)(FGD); -draw byAngle (K, G, B, black, 0)(KGB); -draw byAngle (G, B, K, byblue, 0)(GBK); +draw byAngle(F, D, G, byyellow, 0); +draw byAngle(F, G, D, byred, 0); +draw byAngle(K, G, B, black, 0); +draw byAngle(G, B, K, byblue, 0); draw byLine(H, G, byred, 1, 0); draw byLine(G, K, byred, 0, 0); draw byLine(C, G, byblue, 1, 0); @@ -4064,12 +4064,12 @@ F = whatever[E, B] = (xpart(D), whatever); G = whatever[E, C] = (whatever, ypart(F)); H := 1/2[E, F]; -draw byAngle (E, A, B, byyellow, 0)(A); -draw byAngle (A, B, E, byblue, 0)(B); -draw byAngle (A, E, C, byyellow, 0)(AEC); -draw byAngle (C, E, B, byred, 0)(CEB); -draw byAngle (E, F, G, byred, 0)(EFG); -draw byAngle (D, F, B, black, 0)(DFB); +draw byAngleWithName(E, A, B, byyellow, 0)(A); +draw byAngleWithName(A, B, E, byblue, 0)(B); +draw byAngle(A, E, C, byyellow, 0); +draw byAngle(C, E, B, byred, 0); +draw byAngle(E, F, G, byred, 0); +draw byAngle(D, F, B, black, 0); draw byLine(A, F, black, 0, 0); draw byLine(F, D, byred, 1, 0); draw byLine(G, F, byyellow, 0, 2); @@ -4127,13 +4127,13 @@ E := (w/2, w/2); F := (xpart(D), ypart(E)); G = whatever[E, B] = whatever[F, D]; -draw byAngle(E, A, C, black, 0)(A); -draw byAngle(C, E, A, byyellow, 0)(CEA); -draw byAngle(B, E, C, byyellow, 0)(BEC); -draw byAngle(F, E, B, byblue, 0)(FEB); -draw byAngle(C, B, E, byred, 0)(CBE); -draw byAngle(D, B, G, byred, 0)(DBG); -draw byAngle(B, G, D, byblue, 0)(G); +draw byAngleWithName(E, A, C, black, 0)(A); +draw byAngle(C, E, A, byyellow, 0); +draw byAngle(B, E, C, byyellow, 0); +draw byAngle(F, E, B, byblue, 0); +draw byAngle(C, B, E, byred, 0); +draw byAngle(D, B, G, byred, 0); +draw byAngleWithName(B, G, D, byblue, 0)(G); draw byLine(C, E, byred, 0, 2); draw byLine(A, C, byred, 0, 0); draw byLine(C, B, byyellow, 0, 0); @@ -4500,8 +4500,8 @@ B := dir(30) scaled r; C := point b of fullcircle scaled 2r; D := point e of fullcircle scaled 2r; - draw byAngle (C, A, D, byblue, 0) (A); - draw byAngle (C, B, D, byyellow, 0) (B); + draw byAngleWithName(C, A, D, byblue, 0)(A); + draw byAngleWithName(C, B, D, byyellow, 0)(B); draw byArc(O, r, b, e, black, 0, 0, 0, 0)(O); draw byLine(C, A, black, 0, 0); draw byLine(C, B, black, 0, 0); @@ -4523,9 +4523,9 @@ A := dir(80) scaled r; B := point b of fullcircle scaled 2r; C := point e of fullcircle scaled 2r; - draw byAngle (C, A, B, byblue, 0) (A); + draw byAngleWithName(C, A, B, byblue, 0)(A); draw byArc(O, r, b, e, black, 1, 0, 0, 0)(Op); - draw byArc (O, r, e, b + 8, black, 0, 0, 0, 0)(Om); + draw byArc(O, r, e, b + 8, black, 0, 0, 0, 0)(Om); draw byLine(C, A, black, 0, 0); draw byLine(B, A, black, 0, 0); }\drawCurrentPictureInMargin @@ -4604,9 +4604,9 @@ forsuffixes i=A, B, D, C, E, F, G: i := ((i shifted -F) rotated -angle(G-D)) shifted F; endfor; -draw byAngle(A, D, F, byblue, 0)(ADF); -draw byAngle(F, D, G, byyellow, 0)(FDG); -draw byAngle(G, D, B, black, 0)(GDB); +draw byAngle(A, D, F, byblue, 0); +draw byAngle(F, D, G, byyellow, 0); +draw byAngle(G, D, B, black, 0); draw byLine(D, G)(byblue, 1, 0); draw byLine(A, D)(byred, 0, 0); draw byLine(D, B)(byred, 1, 0); @@ -4639,9 +4639,9 @@ B := (dir(-70) scaled r) shifted D; E := 3/5[A, B]; F := (dir(angle(E-D)) scaled r) shifted D; -draw byAngle(D, A, B, byblue, 0)(A); -draw byAngle(A, E, D, byyellow, 0)(E); -draw byAngle(A, B, D, black, 0)(B); +draw byAngleWithName(D, A, B, byblue, 0)(A); +draw byAngleWithName(A, E, D, byyellow, 0)(E); +draw byAngleWithName(A, B, D, black, 0)(B); draw byLine(D, E, black, 0, 0); draw byLine(E, F, black, 1, 0); draw byLine(A, B, byred, 0, 0); @@ -4686,10 +4686,10 @@ C := (dir(90) scaled r) shifted E; D := (dir(-90) scaled r) shifted E; F = whatever[A, B] = whatever[C, D]; -draw byAngle(E, A, F, byblue, 0)(A); -draw byAngle(A, F, E, black, 0)(AFE); -draw byAngle(E, F, B, byyellow, 0)(EFB); -draw byAngle(F, B, E, byred, 0)(B); +draw byAngleWithName(E, A, F, byblue, 0)(A); +draw byAngle(A, F, E, black, 0); +draw byAngle(E, F, B, byyellow, 0); +draw byAngleWithName(F, B, E, byred, 0)(B); draw byLine(C, E, black, 1, 0); draw byLine(E, F, black, 0, 0); draw byLine(F, D, black, 1, 0); @@ -4737,8 +4737,8 @@ C := (dir(-50)*r) shifted F; D := (dir(-10)*r) shifted F; E = whatever[A, C] = whatever[B, D]; -draw byAngle(F, E, D, byblue, 0)(FED); -draw byAngle(D, E, C, byyellow, 0)(DEC); +draw byAngle(F, E, D, byblue, 0); +draw byAngle(D, E, C, byyellow, 0); draw byLine(E, F, black, 1, 0); draw byLine(B, D, byred, 0, 0); draw byLine(A, C, black, 0, 0); @@ -4863,8 +4863,8 @@ H := E shifted (dir(-170)*r); K := E shifted (dir(175)*r); M = whatever[E, H] = whatever[F, K]; -draw byAngle(B, E, C, black, 0)(BEC); -draw byAngle(C, E, F, byyellow, 0)(CEF); +draw byAngle(B, E, C, black, 0); +draw byAngle(C, E, F, byyellow, 0); draw byLine(F, B, byred, 0, 0); draw byLine(E, C, byblue, 1, 0); draw byLine(F, C, byblue, 0, 0); @@ -4903,8 +4903,8 @@ H := E shifted (dir(-170)*r); K := E shifted (dir(175)*r); M = whatever[E, H] = whatever[F, K]; -draw byAngle(G, F, E, byyellow, 0)(GFE); -draw byAngle(K, F, E, byred, 0)(KFE); +draw byAngle(G, F, E, byyellow, 0); +draw byAngle(K, F, E, byred, 0); draw byLine(F, G, byred, 0, 0); draw byLine(E, G, byred, 1, 0); draw byLine(E, M, byyellow, 0, 0); @@ -4951,8 +4951,8 @@ A := (dir(-90)*r) shifted M; E := (dir(-140)*r) shifted M; F := (dir(-170)*r) shifted M; -draw byAngle(D, M, F, byyellow, 0)(DMF); -draw byAngle(F, M, E, black, 0)(FME); +draw byAngle(D, M, F, byyellow, 0); +draw byAngle(F, M, E, black, 0); draw byLine(D, E, byred, 0, 0); draw byLine(M, A, black, 1, 0); draw byLine(M, E, byred, 1, 0); @@ -5030,8 +5030,8 @@ H := (dir(90 + 45)*r) shifted M; N := (dir(90 - 45)*r) shifted M; O = whatever[D, N] = whatever[M, B]; -draw byAngle(H, D, M, byyellow, 0)(HDM); -draw byAngle(M, D, N, byblue, 0)(MDN); +draw byAngle(H, D, M, byyellow, 0); +draw byAngle(M, D, N, byblue, 0); draw byLine(B, O, byred, 0, 0); draw byLine(O, N, byyellow, 0, 0); draw byLine(D, M, black, 0, 0); @@ -5386,8 +5386,8 @@ D := (dir(90+130)*r) shifted E; F = whatever[A, B] = whatever[E, E shifted ((A-B) rotated 90)]; G = whatever[C, D] = whatever[E, E shifted ((C-D) rotated 90)]; -draw byAngle(E, F, A, byyellow, 0)(F); -draw byAngle(E, G, C, black, 1)(G); +draw byAngleWithName(E, F, A, byyellow, 0)(F); +draw byAngleWithName(E, G, C, black, 1)(G); draw byLine(E, A, black, 0, 0); draw byLine(E, C, byblue, 0, 0); byLineDefine(E, F, black, 1, 0); @@ -5453,9 +5453,9 @@ G := (dir(90+30)*r) shifted E; M := (dir(90-60)*r) shifted E; N := (dir(90+60)*r) shifted E; -draw byAngle(N, E, G, byred, 0)(NEG); -draw byAngle(G, E, F, byyellow, 0)(GEF); -draw byAngle(F, E, M, byred, 0)(FEM); +draw byAngle(N, E, G, byred, 0); +draw byAngle(G, E, F, byyellow, 0); +draw byAngle(F, E, M, byred, 0); draw byLine(E, M, byyellow, 1, 0); draw byLine(E, N, byyellow, 0, 0); draw byLine(E, F, byblue, 1, 0); @@ -5570,11 +5570,11 @@ G := 11/12[A, F]; H := (dir(angle(G-D))*r) shifted D; K := (-r, -r); -draw byAngle(C, A, D, byyellow, 0)(CAD); -draw byAngle(D, A, G, byblue, 0)(DAG); -draw byAngle(G, A, E, byred, 0)(GAE); -draw byAngle(D, C, A, black, 0)(C); -draw byAngle(A, G, D, black, 1)(G); +draw byAngle(C, A, D, byyellow, 0); +draw byAngle(D, A, G, byblue, 0); +draw byAngle(G, A, E, byred, 0); +draw byAngleWithName(D, C, A, black, 0)(C); +draw byAngleWithName(A, G, D, black, 1)(G); draw byLine(A, C, byred, 0, 0); draw byLine(D, C, byblue, 0, 0); draw byLine(D, H, byblue, 1, 0); @@ -5642,9 +5642,9 @@ forsuffixes i=A, B, D, F: i := ((i shifted -E) rotated -a) shifted E; endfor; -draw byAngle(A, B, E, byyellow, 0)(B); -draw byAngle(F, D, E, byyellow, 0)(D); -draw byAngle(F, E, A, byblue, 0)(E); +draw byAngleWithName(A, B, E, byyellow, 0)(B); +draw byAngleWithName(F, D, E, byyellow, 0)(D); +draw byAngleWithName(F, E, A, byblue, 0)(E); draw byLine(A, B, byblue, 0, 0); draw byLine(F, D, byblue, 1, 0); byLineDefine(A, D, byred, 0, 0); @@ -5704,8 +5704,8 @@ D := 6/5[C, G]; B := (dir(angle(G-F))*r) shifted F; draw byCircle(F, r, byyellow, 0, 0, 0)(F); -draw byAngle(F, C, G, byred, 0)(C); -draw byAngle(C, G, F, byyellow, 0)(G); +draw byAngleWithName(F, C, G, byred, 0)(C); +draw byAngleWithName(C, G, F, byyellow, 0)(G); byLineDefine(F, B, byred, 0, 0); byLineDefine(B, G, byred, 1, 0); byLineDefine(C, D, byblue, 1, 0); @@ -5742,8 +5742,8 @@ C := (r, 0) shifted G; E := (r, 6/5r) shifted G; F := (-1/7r, 1/2r) shifted G; -draw byAngle(A, C, F, byblue, 0)(ACF); -draw byAngle(F, C, E, byyellow, 0)(FCE); +draw byAngle(A, C, F, byblue, 0); +draw byAngle(F, C, E, byyellow, 0); draw byLine(A, C, byyellow, 0, 0); draw byLine(C, E, byblue, 0, 0); draw byLine(C, F, byred, 1, 0); @@ -5777,9 +5777,9 @@ A := (dir(80)*r) shifted E; F := (dir(80 + 180)*r) shifted E; C := (dir(-30)*r) shifted E; -draw byAngle(C, A, F, byyellow, 0)(CAF); -draw byAngle(C, E, F, byblue, 0)(CEF); -draw byAngle(E, C, A, byred, 0)(C); +draw byAngle(C, A, F, byyellow, 0); +draw byAngle(C, E, F, byblue, 0); +draw byAngleWithName(E, C, A, byred, 0)(C); draw byLine(A, C, black, 0, 1); draw byLine(E, C, black, 0, 0); draw byLine(E, F, byred, 1, 0); @@ -5808,12 +5808,12 @@ F := (dir(80 + 180)*r) shifted E; B := (dir(185)*r) shifted E; C := (dir(-30)*r) shifted E; -draw byAngle(C, A, F, byyellow, 0)(CAF); -draw byAngle(C, E, F, byblue, 0)(CEF); -draw byAngle(E, C, A, byyellow, 0)(C); -draw byAngle(B, A, F, byred, 0)(BAF); -draw byAngle(B, E, F, black, 0)(BEF); -draw byAngle(E, B, A, byred, 0)(B); +draw byAngle(C, A, F, byyellow, 0); +draw byAngle(C, E, F, byblue, 0); +draw byAngleWithName(E, C, A, byyellow, 0)(C); +draw byAngle(B, A, F, byred, 0); +draw byAngle(B, E, F, black, 0); +draw byAngleWithName(E, B, A, byred, 0)(B); draw byLine(A, C, black, 0, 1); draw byLine(E, C, black, 0, 1); draw byLine(A, B, black, 0, 1); @@ -5847,10 +5847,10 @@ C := (dir(-30)*r) shifted E; D := (dir(30)*r) shifted E; G := (dir(30 + 180)*r) shifted E; -draw byAngle(G, E, F, byblue, 0)(GEF); -draw byAngle(F, E, C, byyellow, 0)(FEC); -draw byAngle(G, D, F, black, 0)(GDF); -draw byAngle(F, D, C, byred, 0)(FDC); +draw byAngle(G, E, F, byblue, 0); +draw byAngle(F, E, C, byyellow, 0); +draw byAngle(G, D, F, black, 0); +draw byAngle(F, D, C, byred, 0); draw byLine(D, C, black, 0, 1); draw byLine(D, F, black, 0, 1); draw byLine(E, C, black, 0, 1); @@ -5886,9 +5886,9 @@ D := (dir(-90 + 50)*r) shifted F; A := (dir(90 + 25)*r) shifted F; E := (dir(90 - 35)*r) shifted F; -draw byAngle(B, A, D, byred, 0)(A); -draw byAngle(B, E, D, byblue, 0)(E); -draw byAngle(B, F, D, byyellow, 0)(F); +draw byAngleWithName(B, A, D, byred, 0)(A); +draw byAngleWithName(B, E, D, byblue, 0)(E); +draw byAngleWithName(B, F, D, byyellow, 0)(F); byLineDefine(B, F, byblue, 0, 0); byLineDefine(D, F, byred, 0, 0); draw byNamedLineSeq(0)(BF,DF); @@ -5921,10 +5921,10 @@ A := (dir(90 + 25)*r) shifted F; E := (dir(90 - 35)*r) shifted F; G := (dir(-90 + 20)*r) shifted F; -draw byAngle(B, A, G, byyellow, 0)(BAG); -draw byAngle(G, A, D, byred, 0)(GAD); -draw byAngle(B, E, G, byblue, 0)(BEG); -draw byAngle(G, E, D, black, 0)(GED); +draw byAngle(B, A, G, byyellow, 0); +draw byAngle(G, A, D, byred, 0); +draw byAngle(B, E, G, byblue, 0); +draw byAngle(G, E, D, black, 0); draw byFilledCircleSegment(F, r, xpart(cr intersectiontimes (F -- 2[F, B])), xpart(cr intersectiontimes (F -- 2[F, G])), byblue)(BG); draw byFilledCircleSegment(F, r, xpart(cr intersectiontimes (F -- 2[F, G])), 8 + xpart(cr intersectiontimes (F -- 2[F, D])), byyellow)(GD); draw byLine(G, A, byblue, 0, 0); @@ -5960,14 +5960,14 @@ B := (dir(10)*r) shifted E; C := (dir(-100)*r) shifted E; D := (dir(150)*r) shifted E; -draw byAngle(D, A, C, byred, 0)(DAC); -draw byAngle(C, A, B, byblue, 0)(CAB); -draw byAngle(A, B, D, byyellow, 0)(ABD); -draw byAngle(D, B, C, byred, 0)(DBC); -draw byAngle(B, C, A, black, 0)(BCA); -draw byAngle(A, C, D, byyellow, 0)(ACD); -draw byAngle(C, D, B, byblue, 0)(CDB); -draw byAngle(B, D, A, black, 0)(BDA); +draw byAngle(D, A, C, byred, 0); +draw byAngle(C, A, B, byblue, 0); +draw byAngle(A, B, D, byyellow, 0); +draw byAngle(D, B, C, byred, 0); +draw byAngle(B, C, A, black, 0); +draw byAngle(A, C, D, byyellow, 0); +draw byAngle(C, D, B, byblue, 0); +draw byAngle(B, D, A, black, 0); draw byLine(A, B, black, 0, 1); draw byLine(B, C, black, 0, 1); draw byLine(C, D, black, 0, 1); @@ -6014,8 +6014,8 @@ B := point t2 of cr1; C := point 3/2 of cr1; D := cr2 intersectionpoint (1/2[A,C]--2[A,C]); -draw byAngle(A, C, B, byyellow, 0)(C); -draw byAngle(A, D, B, byblue, 0)(D); +draw byAngleWithName(A, C, B, byyellow, 0)(C); +draw byAngleWithName(A, D, B, byblue, 0)(D); draw byLineFull(A, D, byred, 0, 0)(B, D, 1, 0, 0); draw byLineFull(B, C, byblue, 0, 0)(A, C, 1, 0, 0); draw byLineFull(B, D, byyellow, 0, 0)(A, D, 1, 0, 0); @@ -6166,8 +6166,8 @@ D := point 5/2 of cr2; E := point t1 of cr2; F := point t2 of cr2; -draw byAngle(B, A, C, byred, 0)(A); -draw byAngle(B, G, C, byyellow, 0)(G); +draw byAngleWithName(B, A, C, byred, 0)(A); +draw byAngleWithName(B, G, C, byyellow, 0)(G); draw byFilledCircleSegment (G, r, t1, t2, byyellow)(G); draw byLine(B, C, black, 0, 0); draw byLine(A, B, black, 0, 1); @@ -6178,8 +6178,8 @@ draw byArc(G, r, t1 + 8, t2, byblue, 0, 0, 0, 0)(G); draw byArc(G, r, t1, t2, black, 0, 0, 0, 0)(Gb); byCircleDefine(G, r, byblue, 0, 0, 0)(G); -draw byAngle(E, D, F, byblue, 0)(D); -draw byAngle(E, H, F, black, 0)(H); +draw byAngleWithName(E, D, F, byblue, 0)(D); +draw byAngleWithName(E, H, F, black, 0)(H); draw byFilledCircleSegment (H, r, t1, t2, byyellow)(H); draw byLine(E, F, black, 1, 0); draw byLine(D, E, black, 0, 1); @@ -6265,10 +6265,10 @@ D := point 3/2 of cr2; E := point t1 of cr2; F := point t3 of cr2; -draw byAngle(B, A, K, byyellow, 0)(BAK); -draw byAngle(B, G, K, byyellow, 0)(BGK); -draw byAngle(K, A, C, byblue, 0)(KAC); -draw byAngle(K, G, C, byblue, 0)(KGC); +draw byAngle(B, A, K, byyellow, 0); +draw byAngle(B, G, K, byyellow, 0); +draw byAngle(K, A, C, byblue, 0); +draw byAngle(K, G, C, byblue, 0); draw byLine(A, K, black, 0, 1); draw byLine(A, B, black, 0, 1); draw byLine(A, C, black, 0, 1); @@ -6280,8 +6280,8 @@ draw byArc(G, r, t3, t1, black, 0, 0, 0, 0)(GbI); draw byArc(G, r, t2, t3, byred, 1, 0, 0, 0)(GbII); byCircleDefine(G, r, byred, 0, 0, 0)(G); -draw byAngle(E, D, F, byred, 0)(D); -draw byAngle(E, H, F, byred, 0)(H); +draw byAngleWithName(E, D, F, byred, 0)(D); +draw byAngleWithName(E, H, F, byred, 0)(H); draw byLine(D, F, black, 0, 1); draw byLine(D, E, black, 0, 1); byLineDefine(H, E, black, 0, 1); @@ -6329,7 +6329,7 @@ cr2 := (fullcircle scaled 2r) shifted L; D := point t1 of cr2; E := point t2 of cr2; -draw byAngle(A, K, B, byred, 0)(K); +draw byAngleWithName(A, K, B, byred, 0)(K); draw byLine(A, B, byred, 0, 0); byLineDefine(A, K, black, 0, 0); byLineDefine(B, K, byblue, 0, 0); @@ -6337,7 +6337,7 @@ draw byArc(K, r, t1 + 8, t2, byyellow, 0, 0, 0, 0)(K); draw byArc(K, r, t1, t2, byblue, 0, 0, 0, 0)(Kb); byCircleDefine(K, r, byyellow, 0, 0, 0)(K); -draw byAngle(D, L, E, byyellow, 0)(L); +draw byAngleWithName(D, L, E, byyellow, 0)(L); draw byLine(D, E, byred, 1, 0); byLineDefine(D, L, black, 1, 0); byLineDefine(E, L, byblue, 1, 0); @@ -6384,7 +6384,7 @@ cr2 := (fullcircle scaled 2r) shifted L; D := point t1 of cr2; E := point t2 of cr2; -draw byAngle(A, K, B, byred, 0)(K); +draw byAngleWithName(A, K, B, byred, 0)(K); draw byLine(A, B, byred, 0, 0); byLineDefine(A, K, black, 0, 0); byLineDefine(B, K, byblue, 0, 0); @@ -6392,7 +6392,7 @@ draw byArc(K, r, t1 + 8, t2, byyellow, 0, 0, 0, 0)(K); draw byArc(K, r, t1, t2, byblue, 0, 0, 0, 0)(Kb); byCircleDefine(K, r, byyellow, 0, 0, 0)(K); -draw byAngle(D, L, E, byyellow, 0)(L); +draw byAngleWithName(D, L, E, byyellow, 0)(L); draw byLine(D, E, byred, 1, 0); byLineDefine(D, L, black, 1, 0); byLineDefine(E, L, byblue, 1, 0); @@ -6437,8 +6437,8 @@ B := point t1 of cr; D := point t3 of cr; C := 1/2[A, B]; -draw byAngle(A, C, D, byblue, 0)(ACD); -draw byAngle(D, C, B, byred, 0)(DCB); +draw byAngle(A, C, D, byblue, 0); +draw byAngle(D, C, B, byred, 0); draw byLine(D, A, byblue, 0, 0); draw byLine(D, C, byyellow, 0, 0); draw byLine(D, B, byblue, 1, 0); @@ -6484,10 +6484,10 @@ A := (dir(110)*r) shifted E; B := (dir(180)*r) shifted E; C := (dir(0)*r) shifted E; -draw byAngle(A, B, C, byred, 0)(B); -draw byAngle(B, C, A, byblue, 0)(C); -draw byAngle(E, A, B, byyellow, 0)(EAB); -draw byAngle(C, A, E, black, 0)(CAE); +draw byAngleWithName(A, B, C, byred, 0)(B); +draw byAngleWithName(B, C, A, byblue, 0)(C); +draw byAngle(E, A, B, byyellow, 0); +draw byAngle(C, A, E, black, 0); draw byLine(A, E, byred, 0, 0); draw byLine(A, B, black, 0, 1); draw byLine(A, C, black, 0, 1); @@ -6515,8 +6515,8 @@ B := (dir(180 + 30)*r) shifted E; C := (dir(0 + 30)*r) shifted E; D := (dir(0 - 30)*r) shifted E; -draw byAngle(B, A, D, byblue, 0)(BAD); -draw byAngle(D, A, C, byred, 0)(DAC); +draw byAngle(B, A, D, byblue, 0); +draw byAngle(D, A, C, byred, 0); draw byLine(A, D, black, 0, 1); draw byLine(A, B, black, 0, 1); draw byLine(B, D, black, 0, 1); @@ -6546,8 +6546,8 @@ B := (dir(-110)*r) shifted E; C := (dir(5)*r) shifted E; D := (dir(80)*r) shifted E; -draw byAngle(A, D, C, byred, 0)(D); -draw byAngle(C, B, A, byyellow, 0)(B); +draw byAngleWithName(A, D, C, byred, 0)(D); +draw byAngleWithName(C, B, A, byyellow, 0)(B); draw byLine(A, B, byred, 0, 0); draw byLine(B, C, byblue, 0, 0); draw byLine(C, D, black, 0, 1); @@ -6581,13 +6581,13 @@ D := (dir(30)*r) shifted O; E := (-r, -r) shifted O; F := (r, -r) shifted O; -draw byAngle(A, B, E, black, 1)(ABE); -draw byAngle(D, B, A, byblue, 0)(DBA); -draw byAngle(F, B, D, byyellow, 0)(FBD); -draw byAngle(B, A, D, byyellow, 0)(A); -draw byAngle(A, D, B, black, 0)(ADB); -draw byAngle(C, D, B, black, 1)(CDB); -draw byAngle(D, C, B, byred, 0)(C); +draw byAngle(A, B, E, black, 1); +draw byAngle(D, B, A, byblue, 0); +draw byAngle(F, B, D, byyellow, 0); +draw byAngleWithName(B, A, D, byyellow, 0)(A); +draw byAngle(A, D, B, black, 0); +draw byAngle(C, D, B, black, 1); +draw byAngleWithName(D, C, B, byred, 0)(C); draw byLine(A, D, black, 0, 1); draw byLine(D, C, black, 0, 1); draw byLine(C, B, black, 0, 1); @@ -6629,19 +6629,19 @@ E := (0, r) shifted G; D := (r, -r) shifted G; K := (-r, -r) shifted G; -draw byAngle(E, A, K, black, 1)(EAK); -draw byAngle(B, A, E, byred, 0)(BAE); -draw byAngle(D, A, B, byyellow, 0)(DAB); -draw byAngle(G, B, A, byred, 0)(B); +draw byAngle(E, A, K, black, 1); +draw byAngle(B, A, E, byred, 0); +draw byAngle(D, A, B, byyellow, 0); +draw byAngleWithName(G, B, A, byred, 0)(B); draw byLine(A, B, black, 0, 0); draw byLine(G, B, byyellow, 0, 0); draw byLine(A, G, byblue, 0, 0); draw byLine(G, E, byblue, 1, 0); draw byLineFull(K, D, byred, 0, 0)(K, D, 0, 0, 1); draw byCircle(G, r, byblue, 0, 0, 0)(G); -byAngleDefine(E, A, K, black, 1)(givenRight); -byAngleDefine(B, A, K, black, 1)(givenObtuse); -byAngleDefine(D, A, B, black, 1)(givenAcute); +byAngleDefineWithName(E, A, K, black, 1)(givenRight); +byAngleDefineWithName(B, A, K, black, 1)(givenObtuse); +byAngleDefineWithName(D, A, B, black, 1)(givenAcute); } \drawCurrentPictureInMargin \problemNP{O}{n}{a given straight line \drawUnitLine{AB} to describe a segment of a circle that shall contain an angle equal to a given angle \drawAngle{givenRight}, \drawAngle{givenObtuse}, \drawAngle{givenAcute}.} @@ -6679,11 +6679,11 @@ E := (r, -r) shifted O; F := (-r, -r) shifted O; draw byFilledCircleSegment(O, r, -2, 1, byyellow)(O); -draw byAngle(F, B, A, byblue, 0)(B); +draw byAngleWithName(F, B, A, byblue, 0)(B); draw byLine(A, B, black, 0, 0); draw byLineFull(E,F, byred, 0, 0)(E, F, 0, 0, -1); draw byCircle(O, r, byblue, 0, 0, 0)(O); -byAngleDefine(F, B, A, byred, 0)(givenAngle); +byAngleDefineWithName(F, B, A, byred, 0)(givenAngle); } \drawCurrentPictureInMargin \problemNP{T}{o}{cut off from a given circle \drawCircle{O} a segment which shall contain an angle equal to a given angle \drawAngle{givenAngle}.} @@ -6886,8 +6886,8 @@ E := cr1 intersectionpoint (subpath (4, 8) of cr2); A := (dir(angle(D-F) + 140))*r; C := cr1 intersectionpoint (D--A); -draw byAngle(D, B, F, byblue, 0)(B); -draw byAngle(F, E, D, byred, 0)(E); +draw byAngleWithName(D, B, F, byblue, 0)(B); +draw byAngleWithName(F, E, D, byred, 0)(E); draw byLine(D, C, black, 1, 0); draw byLine(C, A, black, 0, 0); draw byLine(D, F, byyellow, 0, 0); @@ -6961,10 +6961,10 @@ C := (-r, 0); D := (0, -r); O := (0, 0); -draw byAngle(A, B, C, byred, 0)(B); -draw byAngle(B, C, D, byred, 0)(C); -draw byAngle(C, D, A, byred, 0)(D); -draw byAngle(D, A, B, byred, 0)(A); +draw byAngleWithName(A, B, C, byred, 0)(B); +draw byAngleWithName(B, C, D, byred, 0)(C); +draw byAngleWithName(C, D, A, byred, 0)(D); +draw byAngleWithName(D, A, B, byred, 0)(A); byLineDefine(A, B, byred, 0, 0); byLineDefine(B, C, byred, 0, 0); byLineDefine(C, D, byred, 0, 0); @@ -7129,14 +7129,14 @@ F := F shifted d; C := (subpath (-1, 5) of cr) intersectionpoint (A -- A shifted (dir(angleValue(F, E, D))*2r)); B := (subpath (-1, 5) of cr) intersectionpoint (A -- A shifted (dir(180-angleValue(D, F, E))*2r)); -draw byAngle(C, B, A, black, 0)(B); -draw byAngle(A, C, B, black, 1)(C); -draw byAngle(G, A, B, byyellow, 0)(GAB); -draw byAngle(B, A, C, byred, 0)(BAC); -draw byAngle(C, A, H, byblue, 0)(CAH); -draw byAngle(F, E, D, byblue, 0)(E); -draw byAngle(E, D, F, byred, 0)(D); -draw byAngle(D, F, E, byyellow, 0)(F); +draw byAngleWithName(C, B, A, black, 0)(B); +draw byAngleWithName(A, C, B, black, 1)(C); +draw byAngle(G, A, B, byyellow, 0); +draw byAngle(B, A, C, byred, 0); +draw byAngle(C, A, H, byblue, 0); +draw byAngleWithName(F, E, D, byblue, 0)(E); +draw byAngleWithName(E, D, F, byred, 0)(D); +draw byAngleWithName(D, F, E, byyellow, 0)(F); draw byArbitraryFigure(B--A--C, black, 0, 1)(BAC); draw byArbitraryFigure(D--E--F--cycle, black, 0, 1)(BAC); draw byLine(B, C, byyellow, 0, 0); @@ -7185,18 +7185,18 @@ L = whatever[C, C shifted (dir(angle(C-K) + 90))] = whatever[A, A shifted (dir(angle(A-K) + 90))]; M = whatever[B, B shifted (dir(angle(B-K) + 90))] = whatever[A, L]; N = whatever[B, M] = whatever[C, L]; -draw byAngle(D, F, H, byyellow, 0)(DFH); -draw byAngle(C, K, A, byyellow, 0)(CKA); -draw byAngle(G, E, D, byblue, 0)(GED); -draw byAngle(B, K, C, byblue, 0)(BKC); -draw byAngle(M, L, N, byred, 0)(L); -draw byAngle(D, F, E, byred, 0)(DFE); -draw byAngle(L, N, M, black, 1)(N); -draw byAngle(F, E, D, black, 1)(FED); -draw byAngle(N, M, L, byred, 1)(M); -draw byAngle(E, D, F, byred, 1)(D); -draw byAngle(K, A, L, black, 0)(A); -draw byAngle(L, C, K, black, 0)(C); +draw byAngle(D, F, H, byyellow, 0); +draw byAngle(C, K, A, byyellow, 0); +draw byAngle(G, E, D, byblue, 0); +draw byAngle(B, K, C, byblue, 0); +draw byAngleWithName(M, L, N, byred, 0)(L); +draw byAngle(D, F, E, byred, 0); +draw byAngleWithName(L, N, M, black, 1)(N); +draw byAngle(F, E, D, black, 1); +draw byAngleWithName(N, M, L, byred, 1)(M); +draw byAngleWithName(E, D, F, byred, 1)(D); +draw byAngleWithName(K, A, L, black, 0)(A); +draw byAngleWithName(L, C, K, black, 0)(C); draw byArbitraryFigure(F--D--E, black, 0, 1)(FDE); byLineDefine(N, L, byblue, 0, 0); byLineDefine(L, M, byyellow, 0, 0); @@ -7259,13 +7259,13 @@ F = whatever[D, D shifted ((B-C) rotated 90)] = whatever[B, C]; G = whatever[D, D shifted ((C-A) rotated 90)] = whatever[A, C]; r := abs(E-D); -draw byAngle(B, E, D, byred, 0)(E); -draw byAngle(D, F, B, byred, 0)(F); -draw byAngle(E, B, D, byblue, 0)(EBD); -draw byAngle(D, B, F, byyellow, 0)(DBF); -draw byAngle(G, C, D, black, 0)(GCD); -draw byAngle(D, C, F, black, 1)(DCF); -draw byAngle(E, D, F, black, 1)(EDF); +draw byAngleWithName(B, E, D, byred, 0)(E); +draw byAngleWithName(D, F, B, byred, 0)(F); +draw byAngle(E, B, D, byblue, 0); +draw byAngle(D, B, F, byyellow, 0); +draw byAngle(G, C, D, black, 0); +draw byAngle(D, C, F, black, 1); +draw byAngle(E, D, F, black, 1); draw byLine(E, D, byyellow, 1, 0); draw byLine(G, D, byred, 1, 0); draw byLine(F, D, black, 1, 0); @@ -7331,8 +7331,8 @@ C := (dir(c)*r) shifted F; D := 1/2[A, B]; E := 1/2[A, C]; -draw byAngle(A, D, F, byred, 0)(ADF); -draw byAngle(F, D, B, black, 0)(FDB); +draw byAngle(A, D, F, byred, 0); +draw byAngle(F, D, B, black, 0); draw byLine(D, F, byyellow, 0, 0); draw byLine(E, F, byyellow, 1, 0); draw byLine(A, F, black, 1, 0); @@ -7396,10 +7396,10 @@ B := (-r, 0); C := (0, -r); D := (r, 0); -draw byAngle(D, A, B, byyellow, 0)(A); -draw byAngle(C, D, A, black, 0)(D); -draw byAngle(A, E, B, byblue, 0)(AEB); -draw byAngle(D, E, A, byred, 0)(DEA); +draw byAngleWithName(D, A, B, byyellow, 0)(A); +draw byAngleWithName(C, D, A, black, 0)(D); +draw byAngle(A, E, B, byblue, 0); +draw byAngle(D, E, A, byred, 0); draw byLine(B, E, byred, 1, 0); draw byLine(D, E, byblue, 1, 0); draw byLine(A, E, black, 1, 0); @@ -7451,12 +7451,12 @@ G := (-r, r); H := (-r, -r); K := (r, -r); -draw byAngle(F, G, H, byred, 0)(G); -draw byAngle(G, H, K, byred, 0)(H); -draw byAngle(H, K, F, byred, 0)(K); -draw byAngle(K, F, G, byred, 0)(F); -draw byAngle(B, E, C, black, 0)(E); -draw byAngle(E, C, H, byyellow, 0)(C); +draw byAngleWithName(F, G, H, byred, 0)(G); +draw byAngleWithName(G, H, K, byred, 0)(H); +draw byAngleWithName(H, K, F, byred, 0)(K); +draw byAngleWithName(K, F, G, byred, 0)(F); +draw byAngleWithName(B, E, C, black, 0)(E); +draw byAngleWithName(E, C, H, byyellow, 0)(C); draw byLine(A, C, byred, 1, 0); draw byLine(B, D, byblue, 1, 0); byLineDefine(F, G, black, 0, 0); @@ -7560,10 +7560,10 @@ D := (dir(45+360)*r) shifted E; draw byPolygon(A--C--D--cycle, byred)(ACD); draw byPolygon(A--B--C--cycle, byyellow)(ABC); -draw byAngle(D, A, E, byyellow, 0)(DAE); -draw byAngle(E, A, B, black, 0)(EAB); -draw byAngle(A, B, E, byred, 0)(ABE); -draw byAngle(E, B, C, byblue, 0)(EBC); +draw byAngle(D, A, E, byyellow, 0); +draw byAngle(E, A, B, black, 0); +draw byAngle(A, B, E, byred, 0); +draw byAngle(E, B, C, byblue, 0); draw byLine(A, E, byblue, 0, 0); draw byLine(E, C, byblue, 1, 0); draw byLine(B, E, black, 0, 0); @@ -7613,11 +7613,11 @@ F = whatever[1/2[A, C], 1/2[A, C] shifted ((A-C) rotated 90)] = whatever[1/2[A, D], 1/2[A, D] shifted ((A-D) rotated 90)]; r3 := abs(F-A); -draw byAngle(D, A, B, black, 1)(A); -draw byAngle(C, D, A, black, 0)(CDA); -draw byAngle(B, D, C, byyellow, 0)(BDC); -draw byAngle(D, C, B, byblue, 0)(C); -draw byAngle(C, B, D, byred, 0)(B); +draw byAngleWithName(D, A, B, black, 1)(A); +draw byAngle(C, D, A, black, 0); +draw byAngle(B, D, C, byyellow, 0); +draw byAngleWithName(D, C, B, byblue, 0)(C); +draw byAngleWithName(C, B, D, byred, 0)(B); draw byLine(A, D, byyellow, 0, 0); draw byLine(B, D, byblue, 0, 0); draw byLine(C, D, byred, 0, 0); @@ -7674,17 +7674,17 @@ E := (dir(90+4/5(360))*r) shifted O; draw byArbitraryFigure(C--E--B--D, black, 0, 1)(pg); draw byPolygon(A--C--D--cycle, byyellow)(ACD); -draw byAngle(E, A, B, black, -1)(A); -draw byAngle(A, B, C, black, -1)(B); -draw byAngle(B, C, D, black, -1)(C); -draw byAngle(C, D, E, black, -1)(D); -draw byAngle(D, E, A, black, -1)(E); -draw byAngle(C, A, D, black, 0)(CAD); -draw byAngle(E, C, A, byyellow, 0)(ECA); -draw byAngle(E, C, A, black, -1)(ECAb); -draw byAngle(D, C, E, byblue, 0)(DCE); -draw byAngle(A, D, B, black, 1)(ADB); -draw byAngle(B, D, C, byred, 0)(BDC); +draw byAngleWithName(E, A, B, black, -1)(A); +draw byAngleWithName(A, B, C, black, -1)(B); +draw byAngleWithName(B, C, D, black, -1)(C); +draw byAngleWithName(C, D, E, black, -1)(D); +draw byAngleWithName(D, E, A, black, -1)(E); +draw byAngle(C, A, D, black, 0); +draw byAngle(E, C, A, byyellow, 0); +draw byAngleWithName(E, C, A, black, -1)(ECAb); +draw byAngle(D, C, E, byblue, 0); +draw byAngle(A, D, B, black, 1); +draw byAngle(B, D, C, byred, 0); draw byNamedAngleDummySides(ADB,BDC); byLineDefine(A, B, byblue, 0, 0); byLineDefine(B, C, byred, 0, 0); @@ -7723,16 +7723,16 @@ C := 1/2[K, L]; D := 1/2[L, M]; r2 := abs(F-B); -draw byAngle(B, F, K, byred, 0)(BFK); -draw byAngle(K, F, C, byyellow, 0)(KFC); -draw byAngle(C, F, L, byblue, 0)(CFL); -draw byAngle(L, F, D, byred, 0)(LFD); -draw byAngle(F, K, B, byyellow, 1)(FKB); -draw byAngle(C, K, F, black, 0)(CKF); -draw byAngle(F, C, K, byblue, 1)(FCK); -draw byAngle(L, C, F, byblue, 1)(LCF); -draw byAngle(F, L, C, black, 0)(FLC); -draw byAngle(D, L, F, black, 1)(DLF); +draw byAngle(B, F, K, byred, 0); +draw byAngle(K, F, C, byyellow, 0); +draw byAngle(C, F, L, byblue, 0); +draw byAngle(L, F, D, byred, 0); +draw byAngle(F, K, B, byyellow, 1); +draw byAngle(C, K, F, black, 0); +draw byAngle(F, C, K, byblue, 1); +draw byAngle(L, C, F, byblue, 1); +draw byAngle(F, L, C, black, 0); +draw byAngle(D, L, F, black, 1); draw byLine(F, K, byblue, 0, 0); draw byLine(F, C, black, 1, 0); draw byLine(F, L, black, 0, 0); @@ -7824,16 +7824,16 @@ L := 1/2[D, E]; M := 1/2[E, A]; r2 := abs(F-G); -draw byAngle(G, B, F, byyellow, 0)(GBF); -draw byAngle(F, B, H, byyellow, 0)(FBH); -draw byAngle(F, H, C, black, 0)(H); -draw byAngle(H, C, F, byblue, 0)(HCF); -draw byAngle(F, C, K, byblue, 0)(FCK); -draw byAngle(C, K, F, black, 0)(K); -draw byAngle(K, D, F, byred, 0)(KDF); -draw byAngle(F, D, E, byred, 0)(FDE); -draw byAngle(D, E, F, black, 1)(DEF); -draw byAngle(F, E, M, black, 1)(FEM); +draw byAngle(G, B, F, byyellow, 0); +draw byAngle(F, B, H, byyellow, 0); +draw byAngleWithName(F, H, C, black, 0)(H); +draw byAngle(H, C, F, byblue, 0); +draw byAngle(F, C, K, byblue, 0); +draw byAngleWithName(C, K, F, black, 0)(K); +draw byAngle(K, D, F, byred, 0); +draw byAngle(F, D, E, byred, 0); +draw byAngle(D, E, F, black, 1); +draw byAngle(F, E, M, black, 1); draw byLine(F, G, black, 0, 1); draw byLine(F, M, black, 0, 1); draw byLine(F, A, black, 0, 1); @@ -7930,12 +7930,12 @@ C := (dir(90+2/5(360))*r) shifted F; D := (dir(90+3/5(360))*r) shifted F; E := (dir(90+4/5(360))*r) shifted F; -draw byAngle(C, F, B, byblue, 0)(CFB); -draw byAngle(D, F, C, black, 1)(DFC); -draw byAngle(B, C, F, black, 0)(BCF); -draw byAngle(F, C, D, byyellow, 0)(FCD); -draw byAngle(C, D, F, byyellow, 0)(CDF); -draw byAngle(F, D, E, byred, 0)(FDE); +draw byAngle(C, F, B, byblue, 0); +draw byAngle(D, F, C, black, 1); +draw byAngle(B, C, F, black, 0); +draw byAngle(F, C, D, byyellow, 0); +draw byAngle(C, D, F, byyellow, 0); +draw byAngle(F, D, E, byred, 0); draw byLine(F, A, byyellow, 1, 0); draw byLine(F, C, byred, 1, 0); draw byLine(F, D, byblue, 1, 0); @@ -8000,12 +8000,12 @@ E := (dir(330)*r) shifted G; F := (dir(30)*r) shifted G; H := (dir(270)*r) shifted D; -draw byAngle(A, G, F, black, -1)(AGF); -draw byAngle(B, G, A, black, -1)(BGA); -draw byAngle(C, G, B, black, -1)(CGB); -draw byAngle(D, G, C, byred, 0)(DGC); -draw byAngle(E, G, D, byblue, 0)(EGD); -draw byAngle(F, G, E, black, 0)(FGE); +draw byAngle(A, G, F, black, -1); +draw byAngle(B, G, A, black, -1); +draw byAngle(C, G, B, black, -1); +draw byAngle(D, G, C, byred, 0); +draw byAngle(E, G, D, byblue, 0); +draw byAngle(F, G, E, black, 0); draw byLine(D, H, byred, 0, 0); draw byLine(A, D, black, 0, 0); draw byLine(B, E, byyellow, 0, 0); @@ -10509,11 +10509,11 @@ C = whatever[A, A + dir(220+a)] = whatever[B, B shifted dir(0)]; D = whatever[A, A + dir(220+1/2a)] = whatever[B, C]; E = whatever[A, B] = whatever[C, C shifted (A-D)]; -draw byAngle(B, A, D, byyellow, 0)(BAD); -draw byAngle(D, A, C, black, 0)(DAC); -draw byAngle(C, A, E, black, 1)(CAE); -draw byAngle(A, E, C, byblue, 0)(E); -draw byAngle(E, C, A, byred, 0)(C); +draw byAngle(B, A, D, byyellow, 0); +draw byAngle(D, A, C, black, 0); +draw byAngle(C, A, E, black, 1); +draw byAngleWithName(A, E, C, byblue, 0)(E); +draw byAngleWithName(E, C, A, byred, 0)(C); draw byLine(C, A, byyellow, 0, 0); draw byLine(A, D, byblue, 0, 0); byLineDefine(A, E, byred, 1, 0); @@ -10574,12 +10574,12 @@ D := (A scaled 4/3) shifted (C-B); E := (C scaled 4/3) shifted (C-B); F = whatever[A, B] = whatever[D, E]; -draw byAngle(A, B, C, byyellow, 0)(B); -draw byAngle(B, C, A, byblue, 0)(BCA); -draw byAngle(C, A, B, black, 1)(A); -draw byAngle(D, C, E, byred, 0)(DCE); -draw byAngle(C, E, D, black, 0)(E); -draw byAngle(E, D, C, byred, 1)(D); +draw byAngleWithName(A, B, C, byyellow, 0)(B); +draw byAngle(B, C, A, byblue, 0); +draw byAngleWithName(C, A, B, black, 1)(A); +draw byAngle(D, C, E, byred, 0); +draw byAngleWithName(C, E, D, black, 0)(E); +draw byAngleWithName(E, D, C, byred, 1)(D); draw byLine(C, A, byred, 0, 0); draw byLine(C, D, byblue, 1, 0); byLineDefine(A, F, byyellow, 1, 0); @@ -10635,9 +10635,9 @@ B := (0, 0); A := (2u, 5/2u); C := (3u, 0); -draw byAngle(B, A, C, byyellow, 0)(A); -draw byAngle(A, B, C, byblue, 0)(B); -draw byAngle(B, C, A, byred, 0)(C); +draw byAngleWithName(B, A, C, byyellow, 0)(A); +draw byAngleWithName(A, B, C, byblue, 0)(B); +draw byAngleWithName(B, C, A, byred, 0)(C); byLineDefine(A, B, byred, 1, 0); byLineDefine(B, C, black, 1, 0); byLineDefine(C, A, byblue, 1, 0); @@ -10647,12 +10647,12 @@ E := B shifted d; F := C shifted d; G := (A yscaled -1) shifted d; -draw byAngle(F, D, E, black, 0)(D); -draw byAngle(D, E, F, byyellow, 0)(DEF); -draw byAngle(E, F, D, byred, 1)(EFD); -draw byAngle(E, G, F, black, 0)(G); -draw byAngle(G, E, F, byblue, 0)(GEF); -draw byAngle(E, F, G, byred, 0)(EFG); +draw byAngleWithName(F, D, E, black, 0)(D); +draw byAngle(D, E, F, byyellow, 0); +draw byAngle(E, F, D, byred, 1); +draw byAngleWithName(E, G, F, black, 0)(G); +draw byAngle(G, E, F, byblue, 0); +draw byAngle(E, F, G, byred, 0); draw byLine(E, F, black, 0, 0); byLineDefine(F, G, byyellow, 1, 0); byLineDefine(G, E, byyellow, 0, 0); @@ -10697,9 +10697,9 @@ A := (0, 0); B := (2u, 5/2u); C := (3u, 0); -draw byAngle(A, B, C, byyellow, 0)(B); -draw byAngle(B, A, C, byblue, 0)(A); -draw byAngle(A, C, B, byred, 0)(C); +draw byAngleWithName(A, B, C, byyellow, 0)(B); +draw byAngleWithName(B, A, C, byblue, 0)(A); +draw byAngleWithName(A, C, B, byred, 0)(C); byLineDefine(A, B, byred, 1, 0); byLineDefine(C, A, black, 1, 0); byLineDefine(B, C, byblue, 1, 0); @@ -10709,12 +10709,12 @@ E := B shifted d; F := C shifted d; G := (B yscaled -1) shifted d; -draw byAngle(F, D, E, byblue, 1)(FDE); -draw byAngle(D, E, F, byyellow, 1)(E); -draw byAngle(E, F, D, byred, 1)(EFD); -draw byAngle(F, D, G, byblue, 0)(FDG); -draw byAngle(G, F, D, byred, 0)(GFD); -draw byAngle(D, G, F, black, 0)(G); +draw byAngle(F, D, E, byblue, 1); +draw byAngleWithName(D, E, F, byyellow, 1)(E); +draw byAngle(E, F, D, byred, 1); +draw byAngle(F, D, G, byblue, 0); +draw byAngle(G, F, D, byred, 0); +draw byAngleWithName(D, G, F, black, 0)(G); draw byLine(E, F, black, 0, 0); byLineDefine(F, G, byyellow, 1, 0); byLineDefine(G, D, byyellow, 0, 0); @@ -10759,21 +10759,21 @@ D := (A scaled 4/5) shifted d; E := (B scaled 4/5) shifted d; F := (C scaled 4/5) shifted d; -draw byAngle(B, C, A, byblue, 0)(C); -draw byAngle(C, A, B, byred, 0)(A); -draw byAngle(A, B, G, black, 0)(ABG); -draw byAngle(G, B, C, black, 1)(GBC); -draw byAngle(C, G, B, byyellow, 0)(CGB); -draw byAngle(B, G, A, byred, 0)(BGA); +draw byAngleWithName(B, C, A, byblue, 0)(C); +draw byAngleWithName(C, A, B, byred, 0)(A); +draw byAngle(A, B, G, black, 0); +draw byAngle(G, B, C, black, 1); +draw byAngle(C, G, B, byyellow, 0); +draw byAngle(B, G, A, byred, 0); draw byLine(B, G, byblue, 0, 0); byLineDefine(A, B, byyellow, 0, 0); byLineDefine(B, C, byred, 0, 0); byLineDefine(C, A, black, 0, 0); draw byNamedLineSeq(0)(AB,BC,CA); -draw byAngle(D, E, F, byblue, 1)(E); -draw byAngle(E, F, D, byyellow, 1)(F); -draw byAngle(F, D, E, byred, 1)(D); -draw byAngle(D, E, F, byblue, 1)(E); +draw byAngleWithName(D, E, F, byblue, 1)(E); +draw byAngleWithName(E, F, D, byyellow, 1)(F); +draw byAngleWithName(F, D, E, byred, 1)(D); +draw byAngleWithName(D, E, F, byblue, 1)(E); byLineDefine(D, E, byyellow, 1, 0); byLineDefine(E, F, byred, 1, 0); byLineDefine(F, D, byblue, 1, 0); @@ -10816,12 +10816,12 @@ D := (xpart(A), ypart(B)); draw byPolygon((A--B--D--cycle), byyellow)(ABD); draw byPolygon((A--D--C--cycle), byred)(ADC); -draw byAngle(A, B, C, black, 0)(B); -draw byAngle(B, C, A, byblue, 1)(C); +draw byAngleWithName(A, B, C, black, 0)(B); +draw byAngleWithName(B, C, A, byblue, 1)(C); draw byNamedAngleDummySides(C); -draw byAngle(B, D, A, byblue, 0)(D); -draw byAngle(D, A, B, byred, 0)(DAB); -draw byAngle(C, A, D, byyellow, 0)(CAD); +draw byAngleWithName(B, D, A, byblue, 0)(D); +draw byAngle(D, A, B, byred, 0); +draw byAngle(C, A, D, byyellow, 0); draw byLine(A, D, black, 0, 0); } \drawCurrentPictureInMargin @@ -11068,7 +11068,7 @@ O := 1/2[A, C]; q := (fullcircle scaled 2r) shifted O; D := q intersectionpoint (B--(B shifted (0, r))); -draw byAngle(A, D, C, byblue, 0)(D); +draw byAngleWithName(A, D, C, byblue, 0)(D); byLineDefine(A, C, black, 0, 1); byLineStylize(A, C, 0, 0, -1)(AC); draw byMarkLine(1/2, byblue)(AC); @@ -11171,8 +11171,8 @@ draw byPolygon((D--A--B--cycle), byblue)(DAB); draw byPolygon((D--A--E--cycle), byred)(DAE); draw byPolygon((A--B--C--cycle), byyellow)(ABC); -draw byAngle(D, A, E, byblue, 0)(DAE); -draw byAngle(B, A, C, byred, 0)(BAC); +draw byAngle(D, A, E, byblue, 0); +draw byAngle(B, A, C, byred, 0); byLineDefine(B, D, black, 1, 0); byLineDefine(D, A, byyellow, 0, 0); byLineDefine(B, A, black, 0, 0); @@ -11362,12 +11362,12 @@ draw byPolygon((D--C--F--cycle), byyellow)(DCF); draw byPolygon((D--F--E--cycle), byblue)(DFE); draw byPolygon((D--E--L--cycle), byred)(DEL); -draw byAngleExtended(D, F, E, byred, 1)(F)(black); -draw byAngleExtended(D, E, L, byyellow, 1)(E)(byred); -draw byAngle(D, C, F, byred, 1)(C); -draw byAngle(F, D, C, byblue, 1)(FDC); -draw byAngle(E, D, F, black, 1)(EDF); -draw byAngle(L, D, E, byyellow, 1)(LDE); +draw byAngleExtendedWithName(D, F, E, byred, 1)(F)(black); +draw byAngleExtendedWithName(D, E, L, byyellow, 1)(E)(byred); +draw byAngleWithName(D, C, F, byred, 1)(C); +draw byAngle(F, D, C, byblue, 1); +draw byAngle(E, D, F, black, 1); +draw byAngle(L, D, E, byyellow, 1); draw byLine(D, F, byred, 1, 0); byLineDefine(D, E, byyellow, 1, 0); byLineDefine(C, D, black, 1, 0); @@ -11386,12 +11386,12 @@ draw byPolygon((B--A--G--cycle), byyellow)(BAG); draw byPolygon((B--G--H--cycle), byblue)(BGH); draw byPolygon((B--H--K--cycle), byred)(BHK); -draw byAngleExtended(B, G, H, black, 1)(G)(byred); -draw byAngleExtended(B, H, K, byyellow, 1)(H)(byred); -draw byAngle(B, A, G, byred, 0)(A); -draw byAngle(G, B, A, byblue, 0)(GBA); -draw byAngle(H, B, G, black, 0)(HBG); -draw byAngle(K, B, H, byyellow, 0)(KBH); +draw byAngleExtendedWithName(B, G, H, black, 1)(G)(byred); +draw byAngleExtendedWithName(B, H, K, byyellow, 1)(H)(byred); +draw byAngleWithName(B, A, G, byred, 0)(A); +draw byAngle(G, B, A, byblue, 0); +draw byAngle(H, B, G, black, 0); +draw byAngle(K, B, H, byyellow, 0); byLineDefine(B, G, byred, 0, 0); byLineDefine(A, B, black, 0, 0); byLineDefine(A, G, byblue, 0, 0); @@ -11447,14 +11447,14 @@ G := B shifted (unitvector(C-B) scaled ((abs(E-F)/abs(B-C))*abs(E-F))); draw byPolygon((A--B--G--cycle), byblue)(ABG); draw byPolygon((A--G--C--cycle), byred)(AGC); -draw byAngle(A, B, C, byred, 0)(B); +draw byAngleWithName(A, B, C, byred, 0)(B); draw byLine(A, G, byyellow, 1, 0); byLineDefine(A, B, byyellow, 0, 0); byLineDefine(B, G, black, 1, 0); byLineDefine(G, C, black, 0, 0); draw byNamedLineSeq(0)(AB,BG,GC); draw byPolygon((D--E--F--cycle), byyellow)(DEF); -draw byAngle(D, E, F, black, 0)(E); +draw byAngleWithName(D, E, F, black, 0)(E); byLineDefine(D, E, byred, 0, 0); byLineDefine(E, F, byblue, 0, 0); draw byNamedLineSeq(0)(DE,EF); @@ -11493,9 +11493,9 @@ draw byPolygon((B--E--A--cycle), byblue)(BEA); draw byPolygon((B--D--E--cycle), byred)(BDE); draw byPolygon((B--C--D--cycle), byyellow)(BCD); -draw byAngle(B, D, E, byblue, 0)(BDE); -draw byAngle(B, C, D, black, 0)(C); -draw byAngle(B, D, C, byred, 0)(BDC); +draw byAngle(B, D, E, byblue, 0); +draw byAngleWithName(B, C, D, black, 0)(C); +draw byAngle(B, D, C, byred, 0); draw byLine(B, D, black, 1, 0); byLineDefine(B, E, black, 0, 0); byLineDefine(B, C, byblue, 0, 0); @@ -11514,9 +11514,9 @@ draw byPolygon((G--L--F--cycle), byblue)(GLF); draw byPolygon((G--K--L--cycle), byred)(GKL); draw byPolygon((G--H--K--cycle), byyellow)(GHK); -draw byAngle(G, K, L, byblue, 1)(GKL); -draw byAngle(G, H, K, black, 1)(H); -draw byAngle(G, K, H, byred, 1)(GKH); +draw byAngle(G, K, L, byblue, 1); +draw byAngleWithName(G, H, K, black, 1)(H); +draw byAngle(G, K, H, byred, 1); draw byLine(G, K, black, 1, 1); byLineDefine(G, L, black, 0, 1); byLineDefine(G, H, byred, 0, 1); @@ -11687,9 +11687,9 @@ draw byPolygon((A--B--C--D--cycle), byyellow)(ABCD); draw byPolygon((E--F--G--C--cycle), byblue)(EFGC); draw byPolygon((C--D--H--G--cycle), byred)(CDHG); -draw byAngle(B, C, D, byred, 0)(BCD); -draw byAngle(D, C, G, byyellow, 0)(DCG); -draw byAngle(G, C, E, black, 0)(GCE); +draw byAngle(B, C, D, byred, 0); +draw byAngle(D, C, G, byyellow, 0); +draw byAngle(G, C, E, black, 0); draw byLine(D, C, black, 0, 0); draw byLine(C, E, byred, 0, 0); draw byLine(B, C, byblue, 0, 0); @@ -11801,7 +11801,7 @@ L := (xpart(B), -1/2ypart(A)); E := (xpart(C), ypart(L)); draw byPolygon((B--C--E--L--cycle), byblue)(BCEL); -draw byAngle(C, B, L, byred, 0)(B); +draw byAngleWithName(C, B, L, byred, 0)(B); pair Da, Db, Dc, Dd, De; Da := dir(0) scaled 1/2u; Db := dir(72) scaled 2/5u; @@ -11822,7 +11822,7 @@ F := C shifted (l, 0); M := E shifted (l, 0); draw byPolygon((C--F--M--E--cycle), white)(CFME); -draw byAngle(F, C, E, byyellow, 0)(C); +draw byAngleWithName(F, C, E, byyellow, 0)(C); draw byLine(C, E, byred, 0, 0); draw byLine(B, C, byyellow, 0, 0); draw byLine(C, F, black, 1, 0); @@ -11887,7 +11887,7 @@ K = whatever[A, B] = whatever[H, H shifted d2]; draw byPolygon((F--H--K--E--cycle), byred)(FHKE); draw byPolygon((G--D--C--B--E--F--cycle), byblue)(GDCBEF); -draw byAngle(B, A, D, byyellow, 0)(A); +draw byAngleWithName(B, A, D, byyellow, 0)(A); draw byLine(K, H, byyellow, 0, 0); draw byLine(G, H, byyellow, 1, 0); draw byLine(A, C, black, 0, 1); @@ -12202,12 +12202,12 @@ s := 3/5; D := (A scaled s) shifted C; E := (C scaled s) shifted C; -draw byAngle(C, A, B, byyellow, 0)(A); -draw byAngle(A, B, C, byred, 0)(B); -draw byAngle(B, C, A, byblue, 0)(BCA); -draw byAngle(E, D, C, black, 0)(D); -draw byAngle(D, C, E, black, 1)(DCE); -draw byAngle(A, C, D, byyellow, 0)(ACD); +draw byAngleWithName(C, A, B, byyellow, 0)(A); +draw byAngleWithName(A, B, C, byred, 0)(B); +draw byAngle(B, C, A, byblue, 0); +draw byAngleWithName(E, D, C, black, 0)(D); +draw byAngle(D, C, E, black, 1); +draw byAngle(A, C, D, byyellow, 0); byLineDefine(A, B, byblue, 0, 0); byLineDefine(B, C, byyellow, 0, 0); byLineDefine(C, E, byyellow, 1, 0); @@ -12275,10 +12275,10 @@ C := (dir(ba + a1)*r) shifted G; K := (dir(ba + 2a1)*r) shifted G; L := (dir(ba + 3a1)*r) shifted G; -draw byAngle(B, A, C, byyellow, 0)(A); -draw byAngle(B, G, C, black, 0)(BC); -draw byAngle(C, G, K, byred, 0)(CK); -draw byAngle(K, G, L, byblue, 0)(KL); +draw byAngleWithName(B, A, C, byyellow, 0)(A); +draw byAngleWithName(B, G, C, black, 0)(BC); +draw byAngleWithName(C, G, K, byred, 0)(CK); +draw byAngleWithName(K, G, L, byblue, 0)(KL); draw byLine(A, B, black, 0, 1); draw byLine(A, C, black, 0, 1); draw byLine(G, C, black, 0, 1); @@ -12297,10 +12297,10 @@ F := (dir(ba + a2)*r) shifted H; M := (dir(ba + 2a2)*r) shifted H; N := (dir(ba + 3a2)*r) shifted H; -draw byAngle(E, D, F, byyellow, 1)(D); -draw byAngle(E, H, F, black, 1)(EF); -draw byAngle(F, H, M, byred, 1)(FM); -draw byAngle(M, H, N, byblue, 1)(MN); +draw byAngleWithName(E, D, F, byyellow, 1)(D); +draw byAngleWithName(E, H, F, black, 1)(EF); +draw byAngleWithName(F, H, M, byred, 1)(FM); +draw byAngleWithName(M, H, N, byblue, 1)(MN); draw byLine(D, E, black, 0, 1); draw byLine(D, F, black, 0, 1); draw byLine(H, F, black, 0, 1); @@ -12365,13 +12365,13 @@ F := 4/3[A, C]; D = whatever[A, B] = whatever[C, C shifted 1/2[unitvector(F-C), unitvector(B-C)]]; E = whatever[A, C] = whatever[B, B shifted (C-D)]; -draw byAngle(C, E, B, byyellow, 0)(E); -draw byAngle(E, B, C, byblue, 1)(EBC); -draw byAngle(C, B, D, byred, 0)(CBD); -draw byAngle(B, D, C, byyellow, 1)(D); -draw byAngle(B, C, E, black, 1)(BCE); -draw byAngle(D, C, B, byblue, 0)(DCB); -draw byAngle(F, C, D, black, 0)(FCD); +draw byAngleWithName(C, E, B, byyellow, 0)(E); +draw byAngle(E, B, C, byblue, 1); +draw byAngle(C, B, D, byred, 0); +draw byAngleWithName(B, D, C, byyellow, 1)(D); +draw byAngle(B, C, E, black, 1); +draw byAngle(D, C, B, byblue, 0); +draw byAngle(F, C, D, black, 0); draw byLine(B, E, byred, 0, 0); draw byLine(B, C, byyellow, 0, 0); byLineDefine(A, B, byblue, 0, 0); @@ -12418,10 +12418,10 @@ C := (dir(-10)*r) shifted O; D = whatever[B, C] = whatever[A, A shifted 1/2[unitvector(B-A), unitvector(C-A)]]; E := (subpath (0, -4) of c) intersectionpoint (A--4[A, D]); -draw byAngle(A, B, C, byyellow, 0)(B); -draw byAngle(A, E, C, black, 0)(E); -draw byAngle(C, A, E, byblue, 0)(CAE); -draw byAngle(E, A, B, byred, 0)(EAB); +draw byAngleWithName(A, B, C, byyellow, 0)(B); +draw byAngleWithName(A, E, C, black, 0)(E); +draw byAngle(C, A, E, byblue, 0); +draw byAngle(E, A, B, byred, 0); draw byLine(A, B, byblue, 0, 0); draw byLine(B, D, byred, 1, 0); draw byLine(D, C, byred, 0, 0); @@ -12465,12 +12465,12 @@ C := (dir(5)*r) shifted O; D = whatever[B, C] = whatever[A, A shifted ((B-C) rotated 90)]; E := (dir(60 + 180)*r) shifted O; -draw byAngle(A, B, C, byyellow, 1)(B); -draw byAngle(A, E, C, byred, 1)(E); -draw byAngle(B, D, A, byblue, 0)(D); -draw byAngle(B, C, A, byblue, 1)(BCA); -draw byAngle(E, C, B, byyellow, 0)(ECB); -draw byAngle(C, A, B, byred, 0)(A); +draw byAngleWithName(A, B, C, byyellow, 1)(B); +draw byAngleWithName(A, E, C, byred, 1)(E); +draw byAngleWithName(B, D, A, byblue, 0)(D); +draw byAngle(B, C, A, byblue, 1); +draw byAngle(E, C, B, byyellow, 0); +draw byAngleWithName(C, A, B, byred, 0)(A); draw byLine(A, E, byblue, 0, 0); draw byLine(C, E, black, 0, 0); draw byLine(A, D, byyellow, 1, 0); @@ -12515,13 +12515,13 @@ C := (dir(a3)*r) shifted O; D := (dir(a4)*r) shifted O; E = whatever[B, D] = whatever[A, A shifted dir((a1-180)-(a3-(a1-180)))]; -draw byAngle(B, C, A, byyellow, 0)(BCA); -draw byAngle(A, C, D, byred, 1)(ACD); -draw byAngle(B, D, A, byblue, 1)(D); -draw byAngle(A, B, D, byyellow, 1)(B); -draw byAngle(E, A, B, byblue, 0)(EAB); -draw byAngle(C, A, E, black, 0)(CAE); -draw byAngle(D, A, C, byred, 0)(DAC); +draw byAngle(B, C, A, byyellow, 0); +draw byAngle(A, C, D, byred, 1); +draw byAngleWithName(B, D, A, byblue, 1)(D); +draw byAngleWithName(A, B, D, byyellow, 1)(B); +draw byAngle(E, A, B, byblue, 0); +draw byAngle(C, A, E, black, 0); +draw byAngle(D, A, C, byred, 0); draw byLine(A, E, byyellow, 1, 0); draw byLine(A, C, byblue, 0, 0); draw byLine(B, E, byred, 1, 0); diff --git a/byrne_euclid_man.tex b/byrne_euclid_man.tex index 966f65d..d24d495 100644 --- a/byrne_euclid_man.tex +++ b/byrne_euclid_man.tex @@ -322,7 +322,7 @@ \stopsection \startsection[title={Angles}] -\startsubsection[title={byAngleDefine(suffix a, b, c) (expr col, sty) (suffix angleName)}] +\startsubsection[title={byAngleDefineWithName(suffix a, b, c) (expr col, sty) (suffix angleName)}] Defines a new angle with a given name. Returns nothing. {\tt a, b, c} — of suffix type, coordinates of angle points. @@ -333,18 +333,27 @@ {\tt angleName} — of suffix type, angle name. \stopsubsection -\startsubsection[title={byAngle(suffix a, b, c) (expr col, sty) (suffix angleName)}] +\startsubsection[title={byAngleDefine(suffix a, b, c) (expr col, sty)}] +Same as {\tt byAngleDefineWithName}, but name is assigned automatically (in form of {\tt abc}). +\stopsubsection +\startsubsection[title={byAngleWithName(suffix a, b, c) (expr col, sty) (suffix angleName)}] Defines a new angle with a given name. Returns a picture of that angle. -a, b, c, col, sty, angleName — same as byAngleDefine. +a, b, c, col, sty, angleName — same as byAngleDefineWithName. +\stopsubsection +\startsubsection[title={byAngle(suffix a, b, c) (expr col, sty)}] +Same as {\tt byAngleWithName}, but name is assigned automatically (in form of {\tt abc}). \stopsubsection -\startsubsection[title={byAngleExtended(suffix a, b, c) (expr col, sty) (suffix angleName) (text optionalColors)}] +\startsubsection[title={byAngleExtendedWithName(suffix a, b, c) (expr col, sty) (suffix angleName) (text optionalColors)}] Defines a new angle with a given name with additional colors. Returns a picture of that angle. {\tt optionalColors} — of text type, a list of additional colors (currently only affects angles with sty = 1). {\tt a, b, c, col, sty, angleName} — same as {\tt byAngleDefine}. \stopsubsection +\startsubsection[title={byAngleExtended(suffix a, b, c) (expr col, sty) (text optionalColors)}] +Same as {\tt byAngleExtendedWithName}, but name is assigned automatically (in form of {\tt abc}). +\stopsubsection \startsubsection[title={byNamedAngle(text anglesList)}] Produces already defined angles. Returns a picture of that angles.