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byrne.mp
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byrne.mp
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% byrne-euclid 0.2.4
% MetaPost library that implements most of the graphical
% features present in Oliver Byrne's version of Euclid's "Elements"
% Copyright 2023 Sergey Slyusarev
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http:https://www.gnu.org/licenses/>.
%
% Here we define some things of general interest
%
pi := 3.1415926;
radian := 180/pi;
lineWidth := 2pt;
lineWidthThin := 1pt;
lineWidthHair := 1/2pt;
pointMarkSize := 4pt;
pointLinesSize := 1/2cm;
defaultScaleFactor := 1;
angleSize := 1cm;
angleScale := 1;
globalRotation := 0;
magnitudeSize := 5/18cm;
magnitudeScale := 1;
magnitudeGap := 3/2lineWidth;
markLength := 3lineWidth;
rayExtension := 1/3cm;
textLabelScaleFactor := 2/5;
%
% Some symbolic constants for better readability
%
SOLID_LINE := 0;
DASHED_LINE := 1;
SOLID_SECTOR := 0;
ARC_SECTOR := 1;
DASHED_ARC_SECTOR := 2;
ALL_LABELS := 0;
OMIT_LABELS_AT_STRAIGHT_ANGLES := 1;
OMIT_FIRST_AND_LAST_LABEL := 2;
OMIT_FIRST_LABEL := 3;
OMIT_LAST_LABEL := 4;
REGULAR_WIDTH := 0;
THIN_WIDTH := 1;
HAIR_WIDTH := 2;
%
% Some common settings
%
boolean textLabels, ghostLines, autoRightAngles, omitDuplicateTextLabels, autoLabelingMode, mainPictureMode, omitSpaceRotation;
textLabels := false;
ghostLines := true;
autoRightAngles := false;
omitDuplicateTextLabels := false;
textLabelShift := lineWidth;
autoLabelingMode := false;
mainPictureMode := false;
omitSpaceRotation := false;
boolean solidAngleMode;
solidAngleMode := false;
numeric dpLength[];
dpLength0 := 2lineWidth;
dpLength1 := 2lineWidth;
dpLength2 := 3/2lineWidth;
vardef sin primary x = (sind(x*radian)) enddef;
vardef cos primary x = (cosd(x*radian)) enddef;
vardef arcsind primary x = angle((1+-+x,x)) enddef;
vardef arccosd primary x = angle((x,1+-+x)) enddef;
vardef pathToString (expr p) =
save outputString, endpoint, i;
string outputString;
if (length(p) > 0):
outputString :=
"(" & decimal(xpart(point 0 of p)) & ", " & decimal(ypart(point 0 of p)) & ")"
& ".. controls (" & decimal(xpart(postcontrol 0 of p)) & ", " & decimal(ypart(postcontrol 0 of p)) & ") and "
& "(" & decimal(xpart(precontrol 1 of p)) & ", " & decimal(ypart(precontrol 1 of p)) & ")";
if (cycle p):
endpoint := length(p) - 1;
else:
endpoint := length(p);
fi;
for i := 1 step 1 until endpoint:
outputString := outputString
& ".. (" & decimal(xpart(point i of p)) & ", " & decimal(ypart(point i of p)) & ")";
if ((i < length(p)) or (cycle p)):
outputString := outputString
& ".. controls (" & decimal(xpart(postcontrol i of p)) & ", " & decimal(ypart(postcontrol i of p)) & ") and "
& "(" & decimal(xpart(precontrol i + 1 of p)) & ", " & decimal(ypart(precontrol i + 1 of p)) & ")";
fi;
endfor;
if (cycle p):
outputString := outputString & " .. cycle";
fi;
else:
outputString :=
"(" & decimal(xpart(point 0 of p)) & ", " & decimal(ypart(point 0 of p)) & ")";
fi;
outputString
enddef;
color byred, byblue, byyellow, byblack, bygrey,
byredN, byblueN, byyellowN, byblackN, bygreyN,
outlineColor.byredN, outlineColor.byblueN, outlineColor.byyellowN, outlineColor.byblackN, outlineColor.bygreyN,
bytransparent, byDefaultAngleOptionalColor;
byred := (.85, .3, .1);
byblue := (.15, .35, .6);
byyellow := (.95, .7, 0.1);
byblack := black;
bygrey := (.8, .8, .8);
byredN := white;
byblueN := white;
byyellowN := white;
byblackN := white;
bygreyN := white;
outlineColor.byredN := byred;
outlineColor.byblueN := byblue;
outlineColor.byyellowN := byyellow;
outlineColor.byblackN := byblack;
outlineColor.bygreyN := bygrey;
bytransparent := 0.99white;
cmykcolor bylabelcolor;
bylabelcolor := (0, 0, 0, 1);
byDefaultAngleOptionalColor := white;
linecap := butt;
vardef typeOf (expr v) =
save determinedType;
string determinedType;
determinedType := "undefined";
if (boolean v):
determinedType := "boolean";
elseif (cmykcolor v):
determinedType := "cmykcolor";
elseif (color v):
determinedType := "color";
elseif (rgbcolor v):
determinedType := "rgbcolor";
elseif (numeric v):
determinedType := "numeric";
elseif (pair v):
determinedType := "pair";
elseif (path v):
determinedType := "path";
elseif (pen v):
determinedType := "pen";
elseif (picture v):
determinedType := "picture";
elseif (string v):
determinedType := "string";
elseif (transform v):
determinedType := "transform";
fi;
determinedType
enddef;
vardef sign@#(expr x) =
if str @# <> "mindZero":
if x > 0: 1 fi
if x < 0: -1 fi
if x = 0: 1 fi
else:
if x > 0: 1 fi
if x < 0: -1 fi
if x = 0: 0 fi
fi
enddef;
vardef colorLightness (expr col) =
save r, g, b;
if color col:
r := redpart(col);
g := greenpart(col);
b := bluepart(col);
elseif cmykcolor col:
r := (1 - cyanpart(col)) * (1 - blackpart(col));
g := (1 - magentapart(col)) * (1 - blackpart(col));
b := (1 - yellowpart(col)) * (1 - blackpart(col));
fi;
(0.2126*r) + (0.7152*g) + (0.0722*b) % from here https://en.wikipedia.org/wiki/Relative_luminance but it doesn't work this way; to be corrected
enddef;
vardef isWhite (expr col) =
if (colorLightness(col) = 1): % arbitrary value
true
else:
false
fi
enddef;
vardef isLight (expr col) =
if (colorLightness(col) > 0.95): % arbitrary value
true
else:
false
fi
enddef;
vardef defineColor@#(expr col) =
if (typeOf(col) = "color"):
color @#;
else:
cmykcolor @#;
fi;
@# := col;
enddef;
vardef selectOutlineColor@# =
if (typeOf(outlineColor.@#) = "color") or (typeOf(outlineColor.@#) = "cmykcolor"):
outlineColor.@#
else:
black
fi
enddef;
defineColor.oiBlack((0, 0, 0));
defineColor.oiOrange((0.9,0.6,0));
defineColor.oiSkyBlue((0.35,0.7,0.9));
defineColor.oiGreen((0,0.6,0.5));
defineColor.oiYellow((0.95,0.9,0.25));
defineColor.oiBlue((0,0.45,0.7));
defineColor.oiVermillion((0.8,0.4,0));
defineColor.oiPurple((0.8,0.6,0.7));
% CMYK variants
%defineColor.oiBlack((0,0,0,1));
%defineColor.oiOrange((0,0.5,1,0));
%defineColor.oiSkyBlue((0.8,0,0,0));
%defineColor.oiGreen((0.97,0,0.75,0));
%defineColor.oiYellow((0.1,0.05,0.9,0));
%defineColor.oiBlue((1,0.5,0,0));
%defineColor.oiVermillion((0,0.8,1,0));
%defineColor.oiPurple((0.1,0.7,0,0));
vardef cycleval (expr v, l) =
save rv;
numeric rv;
if (l > 0):
if ((v mod l) < 0):
rv := l - (v mod l);
else:
rv := (v mod l);
fi;
else:
rv := 0;
fi;
rv
enddef;
vardef angleOpticalScale (expr v) =
save va;
numeric va;
if (v > 60):
va := 60;
else:
va := v;
fi;
((va/60)**(-1/2))
enddef;
vardef distanceToLine (expr givenPoint, givenLine) =
save p;
pair p[];
p0 := point 0 of givenLine;
p1 := point 0 of reverse(givenLine);
p2 - givenPoint = whatever * ((p1-p0) rotated 90);
p2 = whatever[p0, p1];
p3 := p2;
arclength(givenPoint -- p3)
enddef;
vardef angleValue (expr a, b, c) =
save v;
numeric v;
v := angle(a-b) - angle(c-b);
if (v > 180): v := v - 360; fi;
if (v < -180): v := v + 360; fi;
v
enddef;
vardef lineThickness (expr th) =
if (th = 0):
lineWidth
elseif (th = 1):
lineWidthThin
elseif (th = 2):
lineWidthHair
else:
lineWidth
fi
enddef;
vardef byDashPattern (expr l, dp, endsType) =
save d, n, p;
picture p;
numeric d[], n;
n := ceiling(l/(1/3dpLength[dp]));
if (n mod 3) <> 2:
n := n - (n mod 3) + 2;
fi;
d1 := 2(l/n);
d2 := l/n;
p := dashpattern (on d1 off d2);
if (endsType = 1):
n := n - (n mod 3);
d1 := 2(l/n);
d2 := l/n;
p := dashpattern (on d1 off d2);
elseif (endsType = 2):
n := n - (n mod 3);
d1 := 2(l/n);
d2 := l/n;
p := dashpattern (off d2 on d1);
elseif (endsType = 3):
if (n mod 3) <> 1:
n := n - (n mod 3) + 1;
fi;
d1 := 2(l/n);
d2 := l/n;
p := dashpattern (off d2 on d1);
fi;
p
enddef;
def startTempScale (expr tmpScale) =
begingroup
save scaleFactor;
scaleFactor := tmpScale;
enddef;
def stopTempScale =
endgroup
enddef;
def startTempAngleScale (expr tmpAngleScale) =
begingroup
save angleScale;
angleScale := tmpAngleScale;
enddef;
def stopTempAngleScale =
endgroup
enddef;
def startGlobalRotation (expr ang) =
begingroup
save globalRotation;
globalRotation := ang;
enddef;
def stopGlobalRotation =
endgroup
enddef;
def startAutoLabeling =
begingroup
save autoLabelingMode;
boolean autoLabelingMode;
autoLabelingMode := true;
enddef;
def stopAutoLabeling =
endgroup
enddef;
def startOffspringPictureMode =
begingroup
save uniqueTextLabels, omitDuplicateTextLabels;
string uniqueTextLabels;
boolean omitDuplicateTextLabels;
omitDuplicateTextLabels := true;
uniqueTextLabels := "";
enddef;
def stopOffspringPictureMode =
endgroup
enddef;
def startMainPictureMode =
begingroup
save mainPictureMode, ghostPicture;
boolean mainPictureMode;
picture ghostPicture;
ghostPicture := image();
mainPictureMode := true;
enddef;
def stopMainPictureMode =
endgroup
enddef;
picture ghostPicture;
ghostPicture := image();
%
% This section is devoted to lists
%
vardef appendList (suffix listName)(expr valueToAdd, whereToAdd, omitDuplicates) =
if (not string listName) or (unknown listName):
string listName;
listName := "";
fi;
if length(listName) = 0:
listName := valueToAdd;
else:
save valueExists;
boolean valueExists;
valueExists := false;
if omitDuplicates:
valueExists := isInList (valueToAdd, listName);
fi;
if not valueExists:
if (whereToAdd = 1):
listName := listName & ", " & valueToAdd;
else:
listName := valueToAdd & ", " & listName;
fi;
fi;
fi;
enddef;
vardef isInList (expr valueToLookFor)(suffix listName) =
save rv, i;
boolean rv;
rv := false;
if (not string listName) or (unknown listName):
string listName;
listName := "";
fi;
forsuffixes i=scantokens(listName):
if (str i = valueToLookFor):
rv := true;
fi;
endfor;
rv
enddef;
vardef setAttribute@#(expr attrGenus, attrSpecies, attrName, attrValue) =
save finName;
string finName;
if not string scantokens(attrGenus & "Synonym").scantokens(attrName):
finName := attrName;
else:
finName := scantokens(attrGenus & "Synonym").scantokens(attrName);
if (boolean scantokens(attrGenus & "SynonymPartial").scantokens(attrName)):
if scantokens(attrGenus & "SynonymPartial").scantokens(attrName):
finName := attrName;
fi;
fi;
fi;
if str @# = "":
scantokens(typeOf(attrValue)) scantokens(attrGenus & attrSpecies).scantokens(finName);
elseif (typeOf(scantokens(attrGenus & attrSpecies).scantokens(finName)0) <> typeOf(attrValue)):
scantokens(typeOf(attrValue)) scantokens(attrGenus & attrSpecies).scantokens(finName)[];
fi;
scantokens(attrGenus & attrSpecies).scantokens(finName)@# := attrValue;
enddef;
vardef getAttribute@#(expr attrGenus, attrSpecies, attrName) =
save finName;
string finName;
if not string scantokens(attrGenus & "Synonym").scantokens(attrName):
finName := attrName;
else:
finName := scantokens(attrGenus & "Synonym").scantokens(attrName);
if (boolean scantokens(attrGenus & "SynonymPartial").scantokens(attrName)):
if scantokens(attrGenus & "SynonymPartial").scantokens(attrName):
if known scantokens(attrGenus & attrSpecies).scantokens(attrName)@#:
finName := attrName;
fi;
fi;
fi;
fi;
scantokens(attrGenus & attrSpecies).scantokens(finName)@#
enddef;
vardef attributeExists (expr attrGenus, attrSpecies, attrName) =
save rv;
boolean rv;
if known scantokens(attrGenus & attrSpecies).scantokens(attrName):
rv := true;
else:
rv := false;
fi;
rv
enddef;
setAttribute("line", "Color", "noLine", white);
setAttribute("line", "Dashed", "noLine", 0);
setAttribute("line", "EndAName", "noLine", "noLine");
setAttribute("line", "EndBName", "noLine", "noLine");
setAttribute("line", "EndA", "noLine", inf);
setAttribute("line", "EndB", "noLine", inf);
setAttribute("line", "Synonym", "noLine", "noLine");
setAttribute("line", "Color", "dummyLine", bygrey);
setAttribute("line", "Dashed", "dummyLine", 0);
setAttribute("line", "Thin", "dummyLine", 1);
%
% Some general 3D stuff
%
color projectionAngle;
projectionAngle := (0, 0, 0);
color rotationAxisB.X, rotationAxisE.X, rotationAxisB.Y, rotationAxisE.Y, rotationAxisB.Z, rotationAxisE.Z;
string rotationAxisPart.X, rotationAxisPart.Y, rotationAxisPart.Z;
rotationAxisB.X := (0, 0, 0);
rotationAxisE.X := (1, 0, 0);
rotationAxisPart.X := "redpart";
rotationAxisB.Y := (0, 0, 0);
rotationAxisE.Y := (0, 1, 0);
rotationAxisPart.Y := "greenpart";
rotationAxisB.Z := (0, 0, 0);
rotationAxisE.Z := (0, 0, 1);
rotationAxisPart.Z := "bluepart";
primarydef somecolor colorrotated someangle =
rotateColor(somecolor, someangle)
enddef;
% Rotation order can be selected like this rotateColor.XYZ,
% or by setting defaultRotationOrder
string defaultRotationOrder;
defaultRotationOrder := "ZYX";
vardef rotateColor@#(expr somecolor, someangle) =
save rotationOrder, argumentString, rv;
string rotationOrder[], argumentString;
color rv;
argumentString := str @#;
if argumentString = "":
argumentString := defaultRotationOrder;
fi;
for i := 0 step 1 until length(argumentString) - 1:
rotationOrder[i] = substring (i, i + 1) of argumentString;
endfor;
rv := somecolor;
rv := byRotateAroundAxis(
rotationAxisB.scantokens(rotationOrder0),
rotationAxisE.scantokens(rotationOrder0),
scantokens(rotationAxisPart.scantokens(rotationOrder0))(someangle), rv);
rv := byRotateAroundAxis(
rotationAxisB.scantokens(rotationOrder1),
rotationAxisE.scantokens(rotationOrder1),
scantokens(rotationAxisPart.scantokens(rotationOrder1))(someangle), rv);
rv := byRotateAroundAxis(
rotationAxisB.scantokens(rotationOrder2),
rotationAxisE.scantokens(rotationOrder2),
scantokens(rotationAxisPart.scantokens(rotationOrder2))(someangle), rv);
rv
enddef;
primarydef colorone crossproduct colortwo =
begingroup
save xp, yp, zp;
numeric xp[], yp[], zp[];
xp1 := (redpart colorone)/cm;
yp1 := (greenpart colorone)/cm;
zp1 := (bluepart colorone)/cm;
xp2 := (redpart colortwo)/cm;
yp2 := (greenpart colortwo)/cm;
zp2 := (bluepart colortwo)/cm;
xp3 := ((yp1*zp2) - (zp1*yp2))*cm;
yp3 := ((zp1*xp2) - (xp1*zp2))*cm;
zp3 := ((xp1*yp2) - (yp1*xp2))*cm;
(xp3, yp3, zp3)
endgroup
enddef;
primarydef colorone dotprodXYZ colortwo =
begingroup
save xp, yp, zp;
numeric xp[], yp[], zp[];
xp1 := (redpart colorone);
yp1 := (greenpart colorone);
zp1 := (bluepart colorone);
xp2 := (redpart colortwo);
yp2 := (greenpart colortwo);
zp2 := (bluepart colortwo);
xp1*xp2 + yp1*yp2 + zp1*zp2
endgroup
enddef;
vardef isInPlane (expr colPoint, colPlaneA, colPlaneB, colPlaneC) =
save vecsToCompare, rv;
color vecsToCompare[];
boolean rv;
rv := false;
if (colPoint = colPlaneA)
or (colPoint = colPlaneB)
or (colPoint = colPlaneC):
rv := true;
else:
vecsToCompare1 := colPlaneA-colPlaneB;
vecsToCompare2 := colPlaneC-colPlaneB;
vecsToCompare3 := colPoint-colPlaneB;
fi;
if not rv:
if ((absXYZ(unitvectorXYZ(vecsToCompare1) - unitvectorXYZ(vecsToCompare3)) < 1/100)
or (absXYZ(unitvectorXYZ(vecsToCompare1) + unitvectorXYZ(vecsToCompare3)) < 1/100)
or (absXYZ(unitvectorXYZ(vecsToCompare2) - unitvectorXYZ(vecsToCompare3)) < 1/100)
or (absXYZ(unitvectorXYZ(vecsToCompare2) + unitvectorXYZ(vecsToCompare3)) < 1/100)):
rv := true;
else:
vecsToCompare4 := unitvectorXYZ(vecsToCompare1 crossproduct vecsToCompare2);
vecsToCompare5 := unitvectorXYZ(vecsToCompare3 crossproduct vecsToCompare2);
if ((absXYZ(vecsToCompare4 - vecsToCompare5) < 1/100)
or (absXYZ(vecsToCompare4 + vecsToCompare5) < 1/100)):
rv := true;
else:
rv := false;
fi;
fi;
fi;
rv
enddef;
vardef unitvectorXYZ (expr somecolor) =
save vecLength;
numeric vecLength;
vecLength := absXYZ(somecolor);
if (vecLength > 0):
somecolor/vecLength
else:
errmessage("Can't construct a unit vector from a zero-length vector");
fi
enddef;
vardef absXYZ (expr somecolor) =
(sqrt(
((redpart somecolor)/1cm)**2
+ ((greenpart somecolor)/1cm)**2
+ ((bluepart somecolor)/1cm)**2)*1cm)
enddef;
vardef lineAndPlaneIntersection (expr lineA, lineB, planeA, planeB, planeC) =
save planeNormal, planeOrigin, lineD;
color planeNormal, planeOrigin;
numeric lineD;
planeNormal := normalToPlane(planeA, planeB, planeC);
planeOrigin := planeB;
lineD := ((planeNormal/cm) dotprodXYZ ((planeOrigin - lineA)/cm))
/((planeNormal/cm) dotprodXYZ ((lineB - lineA)/cm));
lineA + ((lineB-lineA)*lineD)
enddef;
vardef normalToPlane (expr planeA, planeB, planeC) =
unitvectorXYZ((planeA-planeB) crossproduct (planeC-planeB))
enddef;
vardef spaceRotated (suffix somepath)(expr someangle) =
save rv, tv, spacepoint, op, rp, tp;
path rv, tv;
color spacepoint[];
pair op[], rp[], tp[];
if (typeOf(thirdDimension.somepath) <> "path"):
path thirdDimension.somepath;
thirdDimension.somepath := somepath scaled 0;
fi;
for i := 0 step 1 until length(somepath):
op0 := point i of somepath;
spacepoint0 :=
(xpart(op0), ypart(op0),
xpart(point i of thirdDimension.somepath)
) colorrotated someangle;
rp0 := (redpart(spacepoint0), greenpart(spacepoint0));
tp0 := (bluepart(spacepoint0), 0);
if (i = 0):
rv := rp0;
tv := tp0;
else:
op1 := postcontrol (i-1) of somepath;
spacepoint1 :=
(xpart(op1), ypart(op1),
xpart(postcontrol (i-1) of thirdDimension.somepath)
) colorrotated someangle;
rp1 := (redpart(spacepoint1), greenpart(spacepoint1));
tp1 := (bluepart(spacepoint1), 0);
op2 := precontrol i of somepath;
spacepoint2 :=
(xpart(op2), ypart(op2),
xpart(precontrol i of thirdDimension.somepath)
) colorrotated someangle;
rp2 := (redpart(spacepoint2), greenpart(spacepoint2));
tp2 := (bluepart(spacepoint2), 0);
rv := rv .. controls rp1 and rp2 ..
if ((i < length(somepath)) or (not cycle somepath)):
rp0
else:
cycle
fi;
tv := tv .. controls tp1 and tp2 ..
if ((i < length(somepath)) or (not cycle somepath)):
tp0
else:
cycle
fi;
fi;
endfor;
thirdDimension.somepath := tv;
rv
enddef;
vardef bySetProjection@#(expr xa, ya, za) =
projectionAngle := (xa, ya, za);
byRotatePoints@#(xa, ya, za, false)();
if str @# <> "":
defaultRotationOrder := str @#;
fi;
enddef;
vardef byPutPointsInSpace (text pL) =
byRotatePoints(0, 0, 0, true)(pL);
enddef;
% Gets a either a 2d or a 3d point and returns a 3d point
vardef byGetPointXYZ (suffix givenPoint) =
if (typeOf(givenPoint) = "color"):
givenPoint
elseif (typeOf(pointXYZ.givenPoint) = "color"):
pointXYZ.givenPoint
else:
errmessage("Point " & str givenPoint & " has no representation in space");
fi
enddef;
vardef byRotateAroundAxis (expr lineEndA, lineEndB, a, pointA) =
save vecA, vecB, rV, q;
color vecA, vecB, rV;
cmykcolor q[];
vecA := pointA - lineEndA;
vecB := unitvectorXYZ(lineEndB - lineEndA);
q1 := (0, redpart(vecA), greenpart(vecA), bluepart(vecA));
q2 := (cosd(a/2), sind(a/2)*redpart(vecB), sind(a/2)*greenpart(vecB), sind(a/2)*bluepart(vecB));
q3 := (cyanpart(q2), -magentapart(q2), -yellowpart(q2), -blackpart(q2));
q4 := (q2 hamiltonProduct q1) hamiltonProduct q3;
rV := (magentapart(q4), yellowpart(q4), blackpart(q4)) + lineEndA;
rV
enddef;
vardef byRotatePointsAroundAxis (suffix lineEndA, lineEndB)(expr a)(text pointsList) =
save lineEndAxyz, lineEndBxyz, pN;
color lineEndAxyz, lineEndBxyz;
if (typeOf(lineEndA) = "color"):
lineEndAxyz := lineEndA;
else:
byPutPointsInSpace(lineEndA);
lineEndAxyz := pointXYZ.lineEndA;
fi;
if (typeOf(lineEndB) = "color"):
lineEndBxyz := lineEndB;
else:
byPutPointsInSpace(lineEndB);
lineEndBxyz := pointXYZ.lineEndB;
fi;
forsuffixes pN := pointsList:
if (typeOf(pN) = "color"):
pN := byRotateAroundAxis(lineEndAxyz, lineEndBxyz, a, pN);
elseif (typeOf(pN) = "pair"):
byPutPointsInSpace(pN);
pointXYZ.pN := byRotateAroundAxis(lineEndAxyz, lineEndBxyz, a, pointXYZ.pN);
fi;
endfor;
enddef;
primarydef colorone hamiltonProduct colortwo =
begingroup
save a, b, c, d;
numeric a[], b[], c[], d[];
a1 := cyanpart(colorone);
b1 := magentapart(colorone);
c1 := yellowpart(colorone);
d1 := blackpart(colorone);
a2 := cyanpart(colortwo);
b2 := magentapart(colortwo);
c2 := yellowpart(colortwo);
d2 := blackpart(colortwo);
(
(a1*a2) - (b1*b2) - (c1*c2) - (d1*d2),
(a1*b2) + (b1*a2) + (c1*d2) - (d1*c2),
(a1*c2) - (b1*d2) + (c1*a2) + (d1*b2),
(a1*d2) + (b1*c2) - (c1*b2) + (d1*a2)
)
endgroup
enddef;
vardef isRightAngle (suffix a, b, c) =
save d, rv;
numeric d;
boolean rv;
if (attributeExists("point", "XYZ", str a)
and attributeExists("point", "XYZ", str b)
and attributeExists("point", "XYZ", str c)):
d := unitvectorXYZ(pointXYZ.a - pointXYZ.b) dotprodXYZ unitvectorXYZ(pointXYZ.c - pointXYZ.b);
else:
d := unitvector(a - b) dotprod unitvector(c - b);
fi;
if (abs(d) < 1/1000):
rv := true;
else:
rv := false;
fi;
rv
enddef;
%
% This section is dedicated to lines
%
vardef byLineRender (expr a, b, col, dp, th, c, d, ct, dt, dpt, s, sf) =
save p, la, lineItself, lineBleeding, clippingPath, cutAngle, linePerp, lineStyShift, currentLineWidth, clippingPathPoint, aS, bS;
picture p;
path lineItself, lineBleeding, clippingPath;
pair cutAngle[], linePerp, lineStyShift, clippingPathPoint[], aS, bS;
la := angle(b-a);
aS := a*sf;
bS := b*sf;
lineStyShift := (0, 0);
currentLineWidth := lineThickness(th);
cutAngle1 := unitvector(b-a) rotated -90;
if (abs(c-a) > 0):
if (abs(unitvector(c-a)-unitvector(a-b)) > 1/100):
if (ct = 0):
cutAngle1 := unitvector(1/2[unitvector(b-a), unitvector(c-a)]);
elseif (ct = 1):
cutAngle1 := unitvector(1[unitvector(b-a), unitvector(c-a)]);
fi;
fi;
fi;
cutAngle2 := unitvector(a-b) rotated 90;
if (abs(d-b) > 0):
if (abs(unitvector(d-b)-unitvector(b-a)) > 1/100):
if (dt = 0):
cutAngle2 := unitvector(1/2[unitvector(a-b), unitvector(d-b)]);
elseif (dt = 1):
cutAngle2 := unitvector(1[unitvector(a-b), unitvector(d-b)]);
fi;
fi;
fi;
if (sign(ypart(cutAngle2 rotated -la)) <> sign(ypart(cutAngle1 rotated -la))):
cutAngle2 := cutAngle2 rotated 180;
fi;
lineItself := (a--b) scaled sf;
linePerp := unitvector((point 0 of lineItself)-(point 1 of lineItself)) rotated 90;
lineBleeding :=
((point 0 of lineItself) shifted (unitvector((point 0 of lineItself) - (point 1 of lineItself)) scaled 2dpLength[dp])) --
lineItself -- ((point 1 of lineItself) shifted (unitvector((point 1 of lineItself) - (point 0 of lineItself)) scaled 2dpLength[dp]));
lineStyShift := (linePerp scaled (1/2currentLineWidth*s));
p := image(
pickup pencircle scaled currentLineWidth;
if (dp > 0):
draw (lineItself shifted lineStyShift) withcolor white;
draw (lineItself shifted lineStyShift) withcolor col
dashed byDashPattern(arclength(lineItself), dp, dpt);
if ((dpt = 0) or (dpt = 1)):
draw (subpath(0, 1) of lineBleeding shifted lineStyShift) withcolor col;
fi;
if ((dpt = 0) or (dpt = 2)):
draw (subpath(2, 3) of lineBleeding shifted lineStyShift) withcolor col;
fi;
else:
draw (lineBleeding shifted lineStyShift) withcolor col;
fi;
if (th < 0):
draw (lineBleeding shifted (lineStyShift + (linePerp scaled 1/4currentLineWidth))) withpen pencircle scaled 1/2currentLineWidth withcolor black;
fi;
);
clippingPathPoint1
= whatever[aS shifted (linePerp*1/2lineWidth) shifted lineStyShift,
bS shifted (linePerp*1/2lineWidth) shifted lineStyShift]
= whatever[aS, aS shifted cutAngle1];
clippingPathPoint2
= whatever[aS shifted (linePerp*-1/2lineWidth) shifted lineStyShift,
bS shifted (linePerp*-1/2lineWidth) shifted lineStyShift]
= whatever[aS, aS shifted cutAngle1];
clippingPathPoint3
= whatever[aS shifted (linePerp*-1/2lineWidth) shifted lineStyShift,
bS shifted (linePerp*-1/2lineWidth) shifted lineStyShift]
= whatever[bS, bS shifted cutAngle2];
clippingPathPoint4
= whatever[aS shifted (linePerp*1/2lineWidth) shifted lineStyShift,
bS shifted (linePerp*1/2lineWidth) shifted lineStyShift]
= whatever[bS, bS shifted cutAngle2];
clippingPath := clippingPathPoint1 -- clippingPathPoint2 -- clippingPathPoint3 -- clippingPathPoint4 -- cycle;
clip p to clippingPath;
if mainPictureMode and ghostLines:
save gP;
picture gP;
gP := ghostPicture;
ghostPicture := image(
draw gP;
begingroup;
save ghostLines;
boolean ghostLines;
ghostLines := false;
draw byLineRender (a, b, white, dp, 2, c, d, ct, dt, dpt, s, sf);
% draw byLineRender (a, b, col, dp, 2, c, d, ct, dt, dpt, s, sf);
endgroup;
);
fi;
p rotated globalRotation
enddef;
vardef byReturnLineLength (suffix a, b) =
if byIsPointInSpace(a, b):
absXYZ(pointXYZ.a - pointXYZ.b)
else:
abs(a-b)
fi
enddef;
vardef byLineDefine@#(suffix a, b)(expr col, dp, th) =
if str @# = "":
byLineDefine.scantokens(str a & str b)(a, b)(col, dp, th);
else:
save lA;
if mainPictureMode:
appendList(allLinesList, str @#, 1, true);
fi;
if byIsPointInSpace(a, b):
if (typeOf(a) = "pair") and (typeOf(b) = "pair"):
if (a <> b):
lA := angle(b-a);
else:
lA := 0;
fi;
else:
lA := 0;
fi;
else:
if (a <> b):
lA := angle(b-a);
else:
lA := 0;
fi;
fi;
setAttribute("line", "Angle", str @#, lA);
setAttribute("line", "Color", str @#, col);
setAttribute("line", "Dashed", str @#, dp);
setAttribute("line", "Thin", str @#, th);
setAttribute("line", "EndA", str @#, a);
setAttribute("line", "EndB", str @#, b);
setAttribute("line", "Shift", str @#, 0);
setAttribute("line", "DirA", str @#, a);
setAttribute("line", "DirB", str @#, b);
setAttribute("line", "EndAType", str @#, 0);
setAttribute("line", "EndBType", str @#, 0);
setAttribute("line", "EndAName", str @#, str a);
setAttribute("line", "EndBName", str @#, str b);
setAttribute("line", "DirAName", str @#, str a);
setAttribute("line", "DirBName", str @#, str b);
setAttribute("line", "UseLineLabel", str @#, false);
setAttribute("line", "Label", str @#, str @#);
setAttribute("line", "Synonym", str @#, str @#);
fi;
enddef;
vardef byLineStylize (suffix c, d)(expr ct, dt, s) (suffix lineName) =
setAttribute("line", "Shift", str lineName, s);
setAttribute("line", "DirA", str lineName, c);
setAttribute("line", "DirB", str lineName, d);
setAttribute("line", "DirAName", str lineName, str c);
setAttribute("line", "DirBName", str lineName, str d);
setAttribute("line", "EndAType", str lineName, ct);
setAttribute("line", "EndBType", str lineName, dt);
enddef;
vardef byLine@#(suffix a, b)(expr col, dp, th) =