лаба №1 крэс-05 / spline_1

{Џа®Ја ¬¬  Ї®бв஥­Ёп Ї®«Ё­®¬  ‹ Ја ­¦  Ё ‘Ї« ©­ 
ђ Ў®вг ўлЇ®«­Ё«Ё ‹лвЄЁ­ Џ.‚., ‹г§Ё­ Њ.Њ. Ја Ђ’-01-2}
program Interpolition;
uses graph;
const n=8;
var x,y:array[0..n]of real;
i,j,sp,t,m,b:integer;
w:real;

function lagr(x1:real):real;
var i,j:integer;
ln,q,p:real;
begin
ln:=0;
for i:=0 to n do
begin
q:=1;
p:=1;
for j:=0 to n do
begin
if not (i=j) then p:=p*(x1-x[j]);
if not (i=j) then q:=q*(x[i]-x[j]);
end;
ln:=ln+y[i]*p/q;
end;
lagr:=ln;
end;

function spline(x1:real):real;
var MM,H,GG,FF,AA,BB,CC,DD:array[0..n]of real;
U:real;
ii,l,j,i,k:integer;
begin
MM[0]:=0;
MM[n]:=0;
i:=1;
while i<=n do
begin
H[i]:=X[i]-X[i-1];
i:=i+1;
end;
GG[1]:=2*(H[1]+H[2]);
FF[1]:=6*((y[2]-y[1])/H[2]-(y[1]-y[0])/H[1]);
i:=2;
while i<=(n-1) do
begin
GG[i]:=2*(H[i]-H[i+1])-sqr(H[i])/GG[i-1];
FF[i]:=6*((y[i+1]-y[i])/H[i+1]-(y[i]-y[i-1])/H[i])-FF[i-1]*H[i-1]/GG[i-1];
i:=i+1;
end;
MM[N-1]:=FF[N-1]/GG[N-1];
j:=1;
while j<=(n-2) do
begin
i:=n-1-j;
MM[i]:=(FF[i]-H[i+1]*MM[i+1])/GG[i];
j:=j+1
end;
i:=1;
while i<=N do
begin
AA[i]:=MM[i-1]/(6*H[i]);
BB[i]:=MM[i]/(6*H[i]);
CC[i]:=(Y[i-1]-(1/6)*MM[i-1]*sqr(H[i]))/H[i];
DD[i]:=(Y[i]-(1/6)*MM[i]*sqr(H[i]))/H[i];
i:=i+1;
end;
U:=x[i]+(x[i+1]-x[i])/2;
i:=1;
j:=N+1;
L:=1;
while L<=2 do
begin
k:=trunc((i+j)/2);
if u>=X[k] then i:=k else j:=k;
if J>i+1 then l:=l-1;
L:=l+1;
end;
k:=j;
{ii:=4+trunc(x1);}
spline:=AA[i]*sqr(X[i]-x1)*(X[i]-x1)+BB[i]*sqr(x1-X[i-1])*(x1-X[i-1])+CC[i]*(X[i]-x1)+DD[i]*(x1-X[i-1]);
end;

begin
for i:=0 to n do x[i]:=-4+i;
y[0]:=0;
y[1]:=0;
y[2]:=1;
y[3]:=0;
y[4]:=0;
y[5]:=0;
y[6]:=-1;
y[7]:=0;
y[8]:=0;

m:=detect;
initgraph(m,b,'d:\bormanpascal\bgi');
line(360,0,360,340);
line(0,170,720,170);
for i:=50 to 700 do
begin
t:=round(-170*(lagr(6*i/360-6))/4+170);
putpixel(i,t,3);
sp:=round(-170*(spline(6*i/360-6))/4+170);
putpixel(i,sp,4);
end;
readln;
closegraph;
end.