```// File: SPLINE1.BCPL
// P.Baudelaire & R.Flegal
// December 5, 1977  4:45 PM

// The procedure ParametricSpline implements the algorithm (1.2.7) described in
//		"Spline Curve Techniques"
//		by P.Baudelaire, R.Flegal, & R.Sproull
//		Xerox Internal Report  (May 1977)

//  Uses MICROCODE floating point routines

// outgoing procedures:

external [
ParametricSpline
PSerror
]

// outgoing statics:

external [
PSzone
]

static [
PSzone=0		// storage zone
]

// incoming procedures:

external [
FLD; FAD; FML; FST	// microFLOAT (Alto floating point package)
FLDI; FSB; FDV; FCM; FNEG
//	FPSetup

Allocate		// Alto SYSTEM
Free
Zero
]

// incoming statics:

external [
FPwork		// microFLOAT (Alto floating point package)
]

// local definitions:

manifest [
naturalSpline=0
periodicSpline=1
// floating point registers: 1 to 4
ac1=1; ac2=2; ac3=3; ac4=4
// constants:
zero=5; one=6; two=7; six=8
numFPacs=9
]

structure PSVEC [
FPworkSave word
FPworkNew word
fpx word
fpy word
a word
b word
c word
r word
s word
]

manifest lPSVEC=size PSVEC/16

// local statics:

static [
PSvec=0
]

let ParametricSpline(n,x,y,p1x,p2x,p3x,p1y,p2y,p3y,splineType,w; numargs nargs) = valof [

// default arguments, get storage, check various things
let tempVec= vec lPSVEC
if PSinit(tempVec) eq 0 resultis 0

let p1,p2,p3,p=nil,nil,nil,nil
let c,r,s=0,0,0

if n ls 0 then [
// convert coordinates from integer to floating point
n=-n
let fpx=PSallocate(lv(PSvec>>PSVEC.fpx), 2*n)
let fpy=PSallocate(lv(PSvec>>PSVEC.fpy), 2*n)
if (fpx eq 0) % (fpy eq 0) resultis 0
for i=0 to n-1 do [
FST(FLDI(ac1, x!i), fpx+2*i)
FST(FLDI(ac1, y!i), fpy+2*i)
]
x=fpx
y=fpy
]

switchon nargs into [
case 9:
splineType=naturalSpline
case 10:
w=0
case 11:
if splineType ne naturalSpline &
splineType ne periodicSpline resultis PSquit(PSerror(3))
if n ls 3 then splineType=naturalSpline
endcase
default:
resultis PSquit(PSerror(4))
]

if splineType eq periodicSpline then [
if ((FCM(FLD(ac1,x), x+2*(n-1)) ne 0) %
(FCM(FLD(ac2,y), y+2*(n-1)) ne 0)) resultis PSquit(PSerror(2))
c=PSallocate(lv(PSvec>>PSVEC.c), 2*n)
r=PSallocate(lv(PSvec>>PSVEC.r), 2*n)
s=PSallocate(lv(PSvec>>PSVEC.s), 2*n)
if (c eq 0) % (r eq 0) % (s eq 0) resultis 0
]

let a=PSallocate(lv(PSvec>>PSVEC.a), 2*n)
let b=PSallocate(lv(PSvec>>PSVEC.b), 2*n)
if (a eq 0) % (b eq 0) resultis 0

// a(0)=w(0)
FST(FLDI(ac1, (w ? (w!1)+4,  4)), a)

//a(i)=w(i)-1/a(i-1)  {i=1,2,...,n-3}
//w(i) defaults to 4.   {1=0,1,...,n-3}
for i=1 to n-3 do [
FST( FSB (FLDI(ac4,(w ? (w!(i+1))+4, 4)), FDV(FLDI(ac2,1), ac1)), a+i*2)
FLD(ac1,ac4)
]

if splineType eq periodicSpline then [
// c(0)=1
FST(one, c)
// c(i)=-c(i-1)/a(i-1)   {i=1,2,...,n-3}
for i=1 to n-3 do
FST(FNEG(FDV(FLD(ac1, c+2*(i-1)), a+2*(i-1))), c+2*i)
]

//do everything twice to get x(t)  and y(t).
for t=1 to 2 do [
test ( t eq 1 )
ifso [ p=x; p1=p1x; p2=p2x; p3=p3x ]
ifnot [ p=y; p1=p1y; p2=p2y; p3=p3y ]

computebc:
if n ge 3 then test splineType eq naturalSpline
ifso [
//b(0)=6*(p(2)-2*p(1)+p(0))
FST(FML(FAD(FSB(FSB(FLD(ac1, p+4), p+2), p+2), p), six), b)

//b(i)=6*(p(i+2)-2*p(i+1)+p(i))-b(i-1)/a(i-1)  {i=1,2,...,n-3}
for i=1 to n-3 do [
FML(FLD(ac2, p+2*(i+1)), two)
FST(FSB(ac1, FDV(FLD(ac2, b+2*(i-1)), a+(i-1)*2)), b+i*2)
]
]
ifnot [
// b(0)=6*(p(1)-2*p(0)+p(n-2))
FST(FML(FAD(FSB(FSB(FLD(ac1, p+2), p), p), p+2*(n-2)), six), b)

// b(i)=6*(p(i+1)-2*p(i)+p(i-1))-b(i-1)/a(i-1)  {i=1,2,...,n-3}
for i=1 to n-3 do [
FML(FLD(ac2, p+2*i), two)
FST(FSB(ac1, FDV(FLD(ac2, b+2*(i-1)), a+(i-1)*2)), b+i*2)
]

// r(n-2)=1  and  s(n-2)=0
FST(one, r+2*(n-2))
FST(zero, s+2*(n-2), 0)
// r(i)=-(r(i+1)+c(i))/a(i)   {i=n-3,...,1,0}
// s(i)=(b(i)-s(i+1))/a(i)   {i=n-3,...,1,0}
for i=n-3 to 0 by -1 do [
FST(FDV(FSB(FLD(ac1, b+2*i), s+2*(i+1)), a+2*i), s+2*i)
]
]

computep2:
// COMPUTE SECOND DERIVATIVES
test splineType eq naturalSpline
ifso [
// p2(0)=p2(n-1)=0
FST(zero, p2); FST(zero, p2+2*(n-1))
// p2(i)=(b(i-1)-p2(i+1))/a(i-1)  {i= n-2,...,2,1}
for i=n-2 to 1 by -1 do
FST(FDV(FSB(FLD(ac1, b+2*(i-1)), p2+(i+1)*2), a+(i-1)*2), p2+2*i)
]
ifnot [
// D2=p(n-1)-2*p(n-2)+p(n-3)
// ac1=p2(n-2)=(6*D2-s(0)-s(n-3))/(r(0)+r(n-3)+4)
FAD(FSB(FLD(ac1, p+2*(n-1)), FML(FLD(ac3, p+2*(n-2)), two)), p+2*(n-3))
FST(FDV(FSB(FSB(FML(ac1, six), s), s+2*(n-3)), ac2), p2+2*(n-2))

// p2(i)=r(i)*p2(n-2) + s(i)   {i=0,1,2,...,n-3}
for i=0 to n-3 do

// p2(n-1)=p2(0)
FST(FLD(ac1, p2), p2+2*(n-1))
]

computep1p3:
// COMPUTE FIRST & THIRD DERIVATIVES
// p1(i)=p(i+1)-p(i)-(2*p2(i)+p2(i+1))/6
// p3(i)=p2(i+1)-p2(i)  {i=0,1,2,...,n-2}
for i=0 to n-2 do [
FSB(FLD(ac1, p+2*(i+1)), p+2*i)
FST(FSB(ac1, FDV(ac2, six)), p1+i*2)
FST(FSB(FLD(ac1, p2+(i+1)*2), p2+i*2), p3+i*2)
]
]

resultis PSquit(true)
]

and PSinit(psv) = valof [
if PSzone eq 0 resultis PSerror(0)
PSvec=psv
Zero(PSvec, lPSVEC)
// new floating point work area
let cnst=FPwork!0-4*FPwork!1
let FPworkNew= Allocate(PSzone, 4*numFPacs+cnst)
if FPworkNew eq 0 resultis PSerror(1)
PSvec>>PSVEC.FPworkSave=FPwork
PSvec>>PSVEC.FPworkNew=FPworkNew
FPworkNew!1=numFPacs
//	FPSetup(FPworkNew)
FPwork=FPworkNew
FLDI(zero,0); FLDI(one, 1); FLDI(two,2); FLDI(six,6)
resultis true
]

and PSallocate(location, m) = valof [
let b=Allocate(PSzone, m)
if b eq 0 resultis PSquit(PSerror(1))
@location=b
resultis b
]

and PSerror(errorCode,a1,a2,a3,a4) = valof [
(table[#77403; #1401]) ("PS.ERRORS", lv errorCode)
resultis 0
]

and PSquit(result) = valof [
if PSvec eq 0 resultis result
//	FPSetup(PSvec>>PSVEC.FPworkSave)
FPwork=PSvec>>PSVEC.FPworkSave
PSvec>>PSVEC.FPworkSave=0
for i=0 to lPSVEC-1 do if PSvec!i ne 0 then Free(PSzone, PSvec!i)
PSvec=0
resultis result
]

```