Balloon Calculus Drawing with LaTeX and Asymptote!

First, install Asymptote and TeXnicCenter.

Then, download the macros file and save it in C:\Program Files\Asymptote.

Then, download the balcal file and use TeXnicCenter to modify it to produce your Balloon Calculus drawings, in very little more time than it takes to type the LaTeX itself!

Use the key below to modify the balcal file. Just replace the capital letters (enclosed between dollar signs) by LaTeX expressions. Any simplifications or other improvements gratefully received by email at tom@ballooncalculus.org. Any questions, please post to the forum. Good luck!

Tom
					//	anything after double slash, on any line, is comment not code

import macros24Aug09;			//	connects to the file of this name which
					//	you have saved in c:/program files/asymptote

height = 140;				//	sets the distance between top and bottom rows









frame oneFrame = plainShape(minBox((makeText(	//	'oneFrame' because that's how it's referred to later.
					//	Copy and paste this block to create more plainShapes
					//	(called threeFrame, whatever...)

//	"$\frac{d}{dx}$", 1.4, (0,0),	//	to include this line, delete the first double slash
	"$A$", 1, (0,0)			//	1 is for size (fractions usually want to be 1.4),
					//	(0,0) is to adjust position
).fit()), 45, 30),			//	45 is horizontal minimum, 30 vertical minimum size

minBox((makeText(
//	"$\int$", 1.4, (0,0),
	"$B$", 1, (0,0)			//	follow with comma if using 'dx' (or any) frame next line
//	"$dx$", 1, (0,0)
).fit()), 45, 30),

1					//	make sure this is set to 1 (for 'oneFrame', etc.)

);					//	this marks the end of the sentence beginning 'frame oneFrame ...'








/*
//	slash-star (previous line) comments out everything up to star-slash,
//	so remove these to create the frame

frame oneFrame = plainShape(minBox((makeText(
//	"$\frac{d^2}{dx^2}$", 1.4, (0,0),
	"$C$", 1, (0,0)
).fit()), 45, 30),

minBox((makeText(
//	"$\int$", 1.4, (0,0),
//	"$\frac{d}{dx}$", 1.4, (0,0),
	"$D$", 1, (0,0)
//	"$dx$", 1, (0,0)
).fit()), 45, 30),

minBox((makeText(
//	"$\int$", 1.4, (0,0),
	"$E$", 1, (0,0)
//	"$dx$", 1, (0,0),
).fit()), 45, 30),

1
);
*/









/*
frame dashFrame1 = minBox((makeText("$F$", 1.4, (0,0))).fit(),0,14);
frame leftFrame1 = minBox((makeText("$G$", 1.4, (0,0))).fit(),0,14);
frame chainExtension1 = chainExtension(leftFrame1, dashFrame1);
*/









/*
frame twoFrame = chainShape(
0,							//	for animation - leave as zero for now!
minBox((makeText("$H$", 1.4, (0,0))).fit(),0,14),	//	bottomMultiplier - If FractionChain
minBox((makeText("$I$", 1, (0,0))).fit(),0,14),		//	bottomLeftString - or else insert
							//	chainExtension
0,							//	bottomNormalExpFracOrRootfrac... 0, 1, 2 or 3
minBox((makeText("$J$", 1, (0,0))).fit(),30,14),	//	bottomDashString
minBox((makeText("$K$", 1, (0,0))).fit(),0,14),		//	bottomRightString
minBox((makeText("$L$", 1, (0,0))).fit(),0,14),		//	bottomTopString

minBox((makeText("$M$", 1.4, (0,0))).fit(),0,14),	//	topMultiplier - If FractionChain
minBox((makeText("$N$", 1.0, (0,0))).fit(),0,14),	//	topLeftString
0,							//	topNormalExpFracOrRootfrac... 0, 1, 2 or 3
minBox((makeText("$O$", 1, (0,0))).fit(),30,14),	//	topDashString
minBox((makeText("$P$", 1, (0,0))).fit(),0,14),		//	topRightString
minBox((makeText("$Q$", 1, (0,0))).fit(),0,14),		//	topTopString

minBox((makeText("$R$", 1, (0,0))).fit(),25,30),	//	byProdString
2
);
*/









/*
frame twoFrame = chainShape(
0,
minBox((makeText("$S$", 1.4, (0,0))).fit(),0,14),
minBox((makeText("$T$", 1, (0,0))).fit(),0,14),
1,
minBox((makeText("$U$", 1, (0,0))).fit(),30,14),
minBox((makeText("$V$", 1, (0,0))).fit(),0,14),
minBox((makeText("$W$", 1, (0,0))).fit(),0,14),

minBox((makeText("$X$", 1.4, (0,0))).fit(),0,14),
minBox((makeText("$Y$", 1.0, (0,0))).fit(),0,14),
1,
minBox((makeText("$Z$", 1, (0,0))).fit(),30,14),
minBox((makeText("$A$", 1, (0,0))).fit(),0,14),
minBox((makeText("$B$", 1, (0,0))).fit(),0,14),

minBox((makeText("$C$", 1, (0,0))).fit(),25,30),
2
);
*/





/*
frame twoFrame = chainShape(
0,
minBox((makeText("$D$", 1.4, (0,0))).fit(),0,14),
minBox((makeText("$E$", 1, (0,0))).fit(),0,14),
2,
minBox((makeText("$F$", 1, (0,0))).fit(),30,14),
minBox((makeText("$G$", 1, (0,0))).fit(),0,14),
minBox((makeText("$H$", 1, (0,0))).fit(),0,14),

minBox((makeText("$I$", 1.4, (0,0))).fit(),0,14),
minBox((makeText("$J$", 1.0, (0,0))).fit(),0,14),
3,
minBox((makeText("$K$", 1, (0,0))).fit(),30,14),
minBox((makeText("$L$", 1, (0,0))).fit(),0,14),
minBox((makeText("$M$", 1, (0,0))).fit(),0,14),

minBox((makeText("$N$", 1, (0,0))).fit(),25,30),
2
);
*/









/*
frame twoFrame = prodShapeIn(
false,						//	legs crossed?
minBox((makeText("$O$", 1, (0,0))).fit(),23,12),//	oneLeft
minBox((makeText("$P$", 1, (0,0))).fit(),23,12),//	oneRight
minBox((makeText("$Q$", 1, (0,0))).fit(),23,12),//	twoLeft
minBox((makeText("$R$", 1, (0,0))).fit(),23,12),//	twoRight
minBox((makeText("$S$", 1, (0,0))).fit(),23,12),//	threeLeft
minBox((makeText("$T$", 1, (0,0))).fit(),23,12),//	threeRight
2
);
*/









/*
frame twoFrame = prodShapeInLeft(
true,
minBox((makeText("$U$", 1.4, (0,0))).fit(),0,14),	//	bottomMultiplier - If FractionChain
minBox((makeText("$V$", 1, (0,0))).fit(),0,14),		//	bottomLeftString
0,							//	bottomNormalExpFracOrRootfrac
minBox((makeText("$W$", 1, (0,0))).fit(),30,14),	//	bottomDashString
minBox((makeText("$X$", 1, (0,0))).fit(),0,14),		//	bottomRightString
minBox((makeText("$Y$", 1, (0,0))).fit(),0,14),		//	bottomTopString

minBox((makeText("$Z$", 1.4, (0,0))).fit(),0,14),	//	topMultiplier - If FractionChain
minBox((makeText("$A$", 1, (0,0))).fit(),0,14),		//	topLeftString
0,							//	topNormalExpFracOrRootfrac
minBox((makeText("$B$", 1, (0,0))).fit(),30,14),	//	topDashString
minBox((makeText("$C$", 1, (0,0))).fit(),0,14),		//	topRightString
minBox((makeText("$D$", 1, (0,0))).fit(),0,14),		//	topTopString

minBox((makeText("$E$", 1, (0,0))).fit(),30,20),	//	byProdString

minBox((makeText("$F$", 1, (0,0))).fit(),30,14),	//	oneRight
minBox((makeText("$G$", 1, (0,0))).fit(),30,14),	//	twoRight
minBox((makeText("$H$", 1, (0,0))).fit(),30,14),	//	threeLeft
minBox((makeText("$I$", 1, (0,0))).fit(),30,14),	//	threeRight

2
);
*/
















/*
frame twoFrame = prodShapeInRight(
true,
minBox((makeText("$J$", 1, (0,0))).fit(),30,14),	//	oneLeft
minBox((makeText("$K$", 1, (0,0))).fit(),30,14),	//	oneRight
minBox((makeText("$L$", 1, (0,0))).fit(),30,14),	//	twoLeft
minBox((makeText("$M$", 1, (0,0))).fit(),30,14),	//	threeLeft

minBox((makeText("$O$", 1.4, (0,0))).fit(),0,14),	//	bottomMultiplier - If FractionChain
minBox((makeText("$P$", 1, (0,0))).fit(),0,14),		//	bottomLeftString
0,							//  bottomNormalExpFracOrRootfrac
minBox((makeText("$Q$", 1, (0,0))).fit(),30,14),	//	bottomDashString
minBox((makeText("$R$", 1, (0,0))).fit(),0,14),		//	bottomRightString
minBox((makeText("$S$", 1, (0,0))).fit(),0,14),		//	bottomTopString

minBox((makeText("$T$", 1.4, (0,0))).fit(),0,14),	//	topMultiplier - If FractionChain
minBox((makeText("$U$", 1, (0,0))).fit(),0,14),		//	topLeftString
0,							//  topNormalExpFracOrRootfrac
minBox((makeText("$V$", 1, (0,0))).fit(),30,14),	//	topDashString
minBox((makeText("$W$", 1, (0,0))).fit(),0,14),		//	topRightString
minBox((makeText("$X$", 1, (0,0))).fit(),0,14),		//	topTopString

minBox((makeText("$Y$", 1, (0,0))).fit(),30,20),	//	byProdString
2
);
*/














/*
frame twoFrame = prodShapeInBoth(
true,
minBox((makeText("$Z$", 1.4, (0,0))).fit(),0,14),	//	leftBottomMultiplier - If FractionChain
minBox((makeText("$A$", 1, (0,0))).fit(),0,14),		//	leftBottomLeftString
0,							//	leftBottomNormalExpFracOrRootfrac
minBox((makeText("$B$", 1, (0,0))).fit(),30,14),	//	leftBottomDashString
minBox((makeText("$C$", 1, (0,0))).fit(),0,14),		//	leftBottomRightString
minBox((makeText("$D$", 1, (0,0))).fit(),0,14),		//	leftBottomTopString

minBox((makeText("$E$", 1.4, (0,0))).fit(),0,14),	//	leftTopMultiplier - If FractionChain
minBox((makeText("$F$", 1, (0,0))).fit(),0,14),		//	leftTopLeftString
0,							//	leftTopNormalExpFracOrRootfrac
minBox((makeText("$G$", 1, (0,0))).fit(),30,14),	//	leftTopDashString
minBox((makeText("$H$", 1, (0,0))).fit(),0,14),		//	leftTopRightString
minBox((makeText("$I$", 1, (0,0))).fit(),0,14),		//	leftTopTopString

minBox((makeText("$J$", 1, (0,0))).fit(),30,20),	//	leftByProdString


minBox((makeText("$K$", 1, (0,0))).fit(),40,14),	//	oneRight
minBox((makeText("$L$", 1, (0,0))).fit(),40,14),	//	threeLeft


minBox((makeText("$M$", 1.4, (0,0))).fit(),0,14),	//	rightBottomMultiplier - If FractionChain
minBox((makeText("$N$", 1, (0,0))).fit(),0,14),		//	rightBottomLeftString
0,							//	rightBottomNormalExpFracOrRootfrac
minBox((makeText("$O$", 1, (0,0))).fit(),30,14),	//	rightBottomDashString
minBox((makeText("$P$", 1, (0,0))).fit(),0,14),		//	rightBottomRightString
minBox((makeText("$Q$", 1, (0,0))).fit(),0,14),		//	rightBottomTopString

minBox((makeText("$R$", 1.4, (0,0))).fit(),0,14),	//	rightTopMultiplier - If FractionChain
minBox((makeText("$S$", 1, (0,0))).fit(),0,14),		//	rightTopLeftString
0,							//	rightTopNormalExpFracOrRootfrac
minBox((makeText("$T$", 1, (0,0))).fit(),30,14),	//	rightTopDashString
minBox((makeText("$U$", 1, (0,0))).fit(),0,14),		//	rightTopRightString
minBox((makeText("$V$", 1, (0,0))).fit(),0,14),		//	rightTopTopString

minBox((makeText("$W$", 1, (0,0))).fit(),30,20),	//	rightByProdString

2
);
*/














//			then we paste the various frames into a picture, pik

picture pik;

real oneMax = xpart(max(oneFrame));
add(pik,oneFrame,(0,0));


real twoMin = xpart(min(twoFrame));
real twoMax = xpart(max(twoFrame));
shapeShift[2] = oneMax + 60 - twoMin;
add(pik,twoFrame,(shapeShift[2],0));
/*
//			uncomment from here if you have created a 'threeFrame'
real threeMin = xpart(min(threeFrame));
real threeMax = xpart(max(threeFrame));
shapeShift[3] = shapeShift[2] + twoMax + 60 - threeMin;
add(pik,threeFrame,(shapeShift[3],0));
/*
//			likewise for 'fourFrame'... copy and modify for further frames
real fourMin = xpart(min(fourFrame));
real fourMax = xpart(max(fourFrame));
shapeShift[4] = shapeShift[3] + threeMax + 40 - fourMin;
add(pik,fourFrame,(shapeShift[4],0));
*/




	label(pik,scale(textScale)*"$=$",(bottomSign(1,2,1,2), 0));
			//	places = sign between frames 1 and 2, at fraction 1 over 2
	label(pik,scale(textScale)*"$=$",(topSign(1,2,1,2), height));
			//	same

/*
			//	un-comment for more signs as needed between shapes
	label(pik,scale(textScale)*"$-$",(bottomSign(2,3,1,3), 0));
			//	places - sign between frames 2 and 3, at fraction 1 over 3
	label(pik,scale(textScale)*"$-$",(topSign(2,3,1,3) + 10, height));

	label(pik,scale(1.4*textScale)*"$[$",(bottomSign(2,3,2,3), 0));
			//	places [ sign between frames 2 and 3, at fraction 2 over 3
	label(pik,scale(1.4*textScale)*"$[$",(topSign(2,3,2,3) + 20, height));

	label(pik,scale(textScale)*"$-$",(bottomSign(3,4,1,2), 0));
			//	places - sign half-way between frames 3 and 4
	label(pik,scale(textScale)*"$-$",(topSign(3,4,1,2), height));

	label(pik,scale(textScale)*"$=$",(bottomSign(4,5,1,2), 0));
	label(pik,scale(textScale)*"$=$",(topSign(4,5,1,2), height));

	label(pik,scale(1.4*textScale)*"$]$",(shapeShift[4] + bottomRight[4] + 20,0));
	label(pik,scale(1.4*textScale)*"$]$",(shapeShift[4] + topRight[4] + 40,height));
*/


	label(pik,scale(textScale)*"$+\ \ \ \ c$",(shapeShift[2] + topRight[2] + 80,height));
		//	places +\ \ \ \ c text some way (80) past top right end of second frame



/*
		// un-comment this block to create mapping arrows for 'internal' substitution

	pik.add(new void(frame f, transform t) {
		pair bottomBase = (shapeShift[2] + bottomArrowX[2], bottomArrowY[2] - 20);
		pair bottomHead = (shapeShift[2] + shapeShift[3] + bottomArrowX[3], bottomArrowY[3] - 30);
		path bottomLine=shift(5,9)*bottomBase
															--shift(7,0)*bottomBase
															--shift(-7,0)*bottomHead
															--shift(-5,9)*bottomHead;
		draw(f,bottomLine,Arrow(6bp));
		label(f,scale(textScale*3/4)*"$x \mapsto \arctan t$",shift(0,-20)*(bottomBase + bottomHead)/2);
		pair topBase = (topArrowX[1], height + topArrowY[1] + 30);
		pair topHead = (shapeShift[2] + shapeShift[3] + topArrowX[3], height + topArrowY[3] + 30);
		path topLine=shift(5,-9)*topBase
															--shift(7,0)*topBase
															--shift(-7,0)*topHead
															--shift(-5,-9)*topHead;
		draw(f,topLine,Arrow(6bp));
		label(f,scale(textScale*3/4)*"$x \mapsto \arctan t$",shift(0,20)*(topBase + topHead)/2);
	});
*/


frame pikFrame = pik.fit();
label(pikFrame, scale(0.7)*"drawn with: Asymptote", shift(45,-17)*min(pikFrame));//	please include these
label(pikFrame, scale(0.7)*"and Balloon Calculus", shift(40,-5)*min(pikFrame));	//	... or better!
box(pikFrame, 5mm,5mm, invisible);
add(pikFrame,(0,0));
Guide to balcal.asy
