#Code to turn a 3d function in R into a stl file for molding and casting something BIG
#Laura Perovich Nov 2012

#Same stl building block functions as other weeks
#Load package misc3d that includes surfaceTriangles function
library(misc3d)
library(plotrix)

#Define character constants used in the stl files
tristart1<-"facet normal 0 0 0"
tristart2<-" outer loop"
triend1<-" endloop"
triend2<-"endfacet"
startline1<-"+"
startline2<-" solid LAURA"
endline<-" endsolid LAURA"

#Make a function that will make each facet from data returned from surfaceTriangles applied to a function
#(probably a more elegant way to do this?)
makefacet<-function(data){
facetvector<-c()
for (i in 1:nrow(data[[1]])){
v1<-paste("  vertex", as.character(data[[1]][i, 1]), as.character(data[[1]][i, 2]), as.character(data[[1]][i, 3]), sep=" ")
v2<-paste("  vertex", as.character(data[[2]][i, 1]), as.character(data[[2]][i, 2]), as.character(data[[2]][i, 3]), sep=" ")
v3<-paste("  vertex", as.character(data[[3]][i, 1]), as.character(data[[3]][i, 2]), as.character(data[[3]][i, 3]), sep=" ")
facetvector<-c(facetvector, tristart1, tristart2, v1, v2, v3, triend1, triend2) 
}
return(facetvector)
}

#Make a function that puts the facets together with the file headers and writes it out
makestl<-function(location, facetvector){
fileConn<-file(location)
writeLines(c(startline1, startline2, facetvector, endline), fileConn)
close(fileConn)
}


##########################################################################
######################## TABLE SURFACE ###################################
##########################################################################
#square edge; four legs on outside corners, each on a local maxima
#Bottom of the table is a curve, top of the table is mostly flat with contour plot etched in.

#Define some constants to use in the function
aa<-2
kk<-3
bb<-function(x) (cos(x)/kk)
cc<-function(y) (cos(y)/kk)

#Add ledges and edges for molding and casting
#define edge amounts
ee<-.3
dd<-.7

#Dimensions:
#I want the top of the table to be roughly two feet square
#It need to be less that this because the width of the piece is only 2 ft and I need border space
#Scale the whole thing to 22", make sure the depth must be less than 4 inches--aim for 3.5.

rOverI<-2*(pi+ee+dd)/22
iOverR<-1/rOverI
#each inch is 0.3765 R units
#each R unit is 2.656 inches

#Functions for all the pieces of the mold
#Just the function for the contours to etch (internal)
mytableInternal<-function(x,y) (ifelse(x<pi &x>-pi &y<pi & y >-pi, -(cc(y)*cos(y*aa)+bb(x)*cos(x*aa)), ifelse(x<pi+dd &x>-pi-dd &y<pi+dd &y>-pi-dd, NA, NA)))

#Estimate the max and min of the function to figure out approximate limits for the contours
w<-seq(-pi-ee-dd,pi+ee+dd,len=90)
q<-seq(-pi-ee-dd,pi+ee+dd,len=90)
Tmin<-min(outer(w,q, mytableInternal), na.rm=TRUE)
Tmax<-ma(outer(w,q, mytableInternal), na.rm=TRUE)

#The bottom surface of the table, plus the edges for molding/casting:
mytableSquare<-function(x,y) (ifelse(x<pi &x>-pi &y<pi & y >-pi, -(cc(y)*cos(y*aa)+bb(x)*cos(x*aa)), ifelse(x<pi+dd &x>-pi-dd &y<pi+dd &y>-pi-dd, 1.2*Tmax, 1.35*Tmax)))
drawScene(surfaceTriangles(seq(-pi-ee-dd,pi+ee+dd,len=90), seq(-pi-ee-dd,pi+ee+dd,len=90),
                           mytableSquare, color2 = "green"))

#The top surface of the table, plus the edges, minus the contours:
mytableJustSquare<-function(x,y) (ifelse(x<pi &x>-pi &y<pi & y >-pi, 1.4*Tmax, ifelse(x<pi+dd &x>-pi-dd &y<pi+dd &y>-pi-dd, 1.35*Tmax, 1.2*Tmax)))
drawScene(surfaceTriangles(seq(-pi-ee-dd,pi+ee+dd,len=90), seq(-pi-ee-dd,pi+ee+dd,len=90),
                           mytableJustSquare, color2 = "green"))

#Check that the depth here is okay.
.2*Tmax
#Gives 0.133 R units which is 0.35 inches so no problem
#The real life size of this piece should be 22" square, check:
2*(pi+ee+dd)/rOverI==22

#Write out the stl files:
#NOTE: These planes need to be made into 3D surfaces.  Can do this in meshlab--see trials and tribulations and week 4 instructions.
triA<-surfaceTriangles(seq(-pi-ee-dd, pi+ee+dd,len=150), seq(-pi-ee-dd, pi+ee+dd,len=150), mytableSquare)
fv<-makefacet(triA)
makestl("/media/6AD8BBE2D8BBAAA9/Users/perovich/Documents/MIT/HTMAA/week8/squareTable.stl", fv)

triA<-surfaceTriangles(seq(-pi-ee-dd, pi+ee+dd,len=150), seq(-pi-ee-dd, pi+ee+dd,len=150), mytableJustSquare)
fv<-makefacet(triA)
makestl("/media/6AD8BBE2D8BBAAA9/Users/perovich/Documents/MIT/HTMAA/week8/squareTableContour.stl", fv)

#Now come up with an image for the contour plot that will be the top of the table:
#Just the inside here, not the molding/casting edges--can re-z zero here with the shopbot (?)
bmp("/media/6AD8BBE2D8BBAAA9/Users/perovich/Documents/MIT/HTMAA/week8/contourOnly.bmp", width=960, height=960)
contour(w, q, outer(w,q, mytableInternal), drawlabels=FALSE, axes=FALSE, asp=1)
#Add lines so I know exactly where to crop the image to get my expected dimensions
#Should go from -pi to pi
abline(h=-pi)
abline(h=pi)
abline(v=-pi)
abline(v=pi)
dev.off()
#Dimensions this should scale to:
2*pi/rOverI
#16.688 inches square

#Make a ("22 inch") square file to cut out molds as needed for assembly
bmp("/media/6AD8BBE2D8BBAAA9/Users/perovich/Documents/MIT/HTMAA/week8/square.bmp", width=960, height=960)
plot(0,0, xlim=c(0, 22), ylim=c(0, 22), type="n", axes=FALSE, asp=1, xlab="", ylab="")
polygon(c(0, 22, 22, 0),c(0, 0, 22, 22))
dev.off()

#Table legs
#Want about 20" of height.  Equivalent to ~45 circles per leg. 180 circles total (!!)
#There should be enough wood.  So assume width of 0.46"
#Circle discs will go on a dowel.  
#Dowel diameter is 7/16th. Make the hole just a smidgen bigger 15/32nd.  
#Diameters of overall circles from about 2 to 4 inches should give nice range.  Make incremental.
#Cut on the wood so we have 48" to play with in width, minus some for edge space.  Up to 8 ft for y. (96" ->94")
#Make sure to space them out some.

#All the external circle radiuses
Lrad<-seq(2/2, 4/2, .2/2)
#Constant internal circle radius
Lradint<-(15/32)/2

#Put one circle every 5 inches--should leave enough material space for things to stay in place(?)
cstartx<-3
cstarty<-3
cposx<-seq(cstartx, 46-cstartx, 5)
cposy<-seq(cstarty, 94-cstarty, 5)
#This gives us 9 by 18 or 162 circles.  This will have to do (short ~two inches per leg)

#Plot away.
rcount<-1
bmp("/media/6AD8BBE2D8BBAAA9/Users/perovich/Documents/MIT/HTMAA/week8/circleLegs.bmp", width=960, height=960)
plot(0,0, asp=1, xlim=c(0, 94), ylim=c(0, 94), type="n", axes=FALSE, xlab="", ylab="")
for (i in 1:length(cposx)){
  for (j in 1:length(cposy)){
    draw.circle(cposx[i],cposy[j],Lradint,nv=100,border=NULL,col=NA,lty=1,lwd=1)
    draw.circle(cposx[i],cposy[j],Lrad[rcount %% length(Lrad)+1],nv=100,border=NULL,col=NA,lty=1,lwd=1)
    #Made sure to mod plus one since we don't have a zero spot in the radius list.
    rcount<-(rcount+1) 
  }
}
#Draw lines so I know exactly where to crop the image for scaling purposes.
#0 to 96 and 0 to 48 (inches)
#Note that things end up a bit off centered since we don't have exactly nice dividing with the circle dimensions.
abline(h=0)
abline(h=96)
abline(v=0)
abline(v=48)
dev.off()