-- Graphing 3-D equations onto a 2-D graph grid         18-Sept-99 
-- Hyperbolic Paraboloid 
-- uses sizeaxis() Xfun 
~ 
The 3-D equation written in terms of X=..., Y=... and Z=... then I
calculate cross-section (trace) arrays of {x,y,z} points.  I next
convert the 3-D point arrays to corresponding 2-D point arrays and do
"plotline".  The result is a trace sketch of various quadric surfaces
in perfect perspective according to the placement of the Z-axis at an
angle of 45° between the -X axis and -Y axis. 
 
by Eric Collins 
<EricandTammyCollins@worldnet.att.net> 
~ 
 
a=1; b=4; c=1 
 
TOPtrace=8 
BOTTOMtrace=-TOPtrace 
RIGHTtrace=9 
LEFTtrace=-RIGHTtrace 
FRONTtrace=5 
POSTERIORtrace=-FRONTtrace 
GRID=22 
 
---- toggle for direcection orientation -- "0" = off, "1" = on 
pos=1 
neg=0 
 
Zax={{Xmin,Xmin}/2,{0,0},{Xmax,Xmax}/2} 
--plotline Zax 
--tic_adjuster=4 
---- Surface Equation 
fy(X,Z)=((X/a)^2-(Z/c)^2)/b 
fz(X,Y)=c*sqrt((X/a)^2-(Y*b)) 
fx(Y,Z)=a*sqrt((Y*b)+(Z/c)^2) 
 
---- Array Variables 
Zint=fz(0,B) 
Z[z]=(z-2*Zint*5-1)*.1 dim[2*Zint*10+1] 
ZRint=fz(R,B) 
ZR[z]=(z-2*ZRint*5-1)*.1 dim[2*ZRint*10+1] 
--Xint=fx(T,0)  -- X-intercept for top and bottom traces 
EX[ex]=(ex-(R-L)*5-1)*.1 dim[(R-L)*10+1] 
Yint=fy(0,T) 
 
 
---- Trace coordinate arrays equations 
YZtrace={0,fy(0,Z),Z} 
YZtraceR={R,fy(R,ZR),ZR} 
YZtraceL={L,fy(L,ZR),ZR} 
XYtrace={EX,fy(EX,0),0} 
XZtrace={EX,0,fz(EX,0)} 
XZtraceT={EX,T,fz(EX,T)} 
XZtraceT2={EX,T,-fz(EX,T)} 
XZtraceB={EX,B,fz(EX,B)} 
XZtraceB2={EX,B,-fz(EX,B)} 
T=TOPtrace 
B=BOTTOMtrace 
R=RIGHTtrace 
L=LEFTtrace 
F=FRONTtrace 
P=POSTERIORtrace 
o=pos-neg 
 
---- Array coordinate converter:  (x,y,z) to (x,y) -- 3D to 2D coordinates 
YZtracept={YZtrace[1]-YZtrace[3]/2,YZtrace[2]-YZtrace[3]/2} 
plotline YZtracept 
YZtraceptR={YZtraceR[1]-YZtraceR[3]/2,YZtraceR[2]-YZtraceR[3]/2} 
plotline YZtraceptR 
YZtraceptL={YZtraceL[1]-YZtraceL[3]/2,YZtraceL[2]-YZtraceL[3]/2} 
plotline YZtraceptL 
 
XZtracept={XZtrace[1]-XZtrace[3]/2,XZtrace[2]-XZtrace[3]/2} 
plotline XZtracept 
plotline -XZtracept 
 
XZtraceptT={XZtraceT[1]-XZtraceT[3]/2,XZtraceT[2]-XZtraceT[3]/2} 
plotline XZtraceptT 
XZtraceptT2={XZtraceT2[1]-XZtraceT2[3]/2,XZtraceT2[2]-XZtraceT2[3]/2} 
plotline XZtraceptT2 
XZtraceptB={XZtraceB[1]-XZtraceB[3]/2,XZtraceB[2]-XZtraceB[3]/2} 
plotline XZtraceptB 
XZtraceptB2={XZtraceB2[1]-XZtraceB2[3]/2,XZtraceB2[2]-XZtraceB2[3]/2} 
plotline XZtraceptB2 
 
XYtracept={XYtrace[1]-XYtrace[3]/2,XYtrace[2]-XYtrace[3]/2} 
plotline XYtracept 
 
 
ta=tic_adjuster 
tics[t]=(t-Xmax+ta)*.5  dim[2*trunc(Xmax)] 
Ztics[t]={tics[t],tics[t]} 
Ztics2[t]={tics[t]-1/8,tics[t]} 
Ztics3[t]={tics[t]-1/4,tics[t]} 
plotline {Ztics[1],Ztics2[1],Ztics3[1]} 
plotline {Ztics[2],Ztics2[2],Ztics3[2]} 
plotline {Ztics[3],Ztics2[3],Ztics3[3]} 
plotline {Ztics[4],Ztics2[4],Ztics3[4]} 
plotline {Ztics[5],Ztics2[5],Ztics3[5]} 
plotline {Ztics[6],Ztics2[6],Ztics3[6]} 
plotline {Ztics[7],Ztics2[7],Ztics3[7]} 
plotline {Ztics[8],Ztics2[8],Ztics3[8]} 
plotline {Ztics[9],Ztics2[9],Ztics3[9]} 
plotline {Ztics[10],Ztics2[10],Ztics3[10]} 
plotline {Ztics[11],Ztics2[11],Ztics3[11]} 
plotline {Ztics[12],Ztics2[12],Ztics3[12]} 
plotline {Ztics[13],Ztics2[13],Ztics3[13]} 
plotline {Ztics[14],Ztics2[14],Ztics3[14]} 
plotline {Ztics[15],Ztics2[15],Ztics3[15]} 
plotline {Ztics[16],Ztics2[16],Ztics3[16]} 
plotline {Ztics[17],Ztics2[17],Ztics3[17]} 
plotline {Ztics[18],Ztics2[18],Ztics3[18]} 
plotline {Ztics[19],Ztics2[19],Ztics3[19]} 
 
 
Xmax=GRID 
Xmin=-GRID 
Ymin=-GRID 
Ymax=GRID 
 
Xdiv=4 
Ydiv=4 
Xshowgrid=off 
Yshowgrid=off 
--Xlabel="x" 
--Ylabel="y" 
 
sizeaxis(1,(Ymax-Ymin)/(Xmax-Xmin)):