3.6 Интерполяция сплайнами
3.6.1 Листинг
unit Unit1;
interface
uses
Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
Dialogs, StdCtrls, Grids, ExtCtrls, jpeg;
type
TForm1 = class(TForm)
StringGrid1: TStringGrid;
Edit1: TEdit;
Image1: TImage;
Button2: TButton;
Button1: TButton;
Memo1: TMemo;
Label1: TLabel;
Label2: TLabel;
Edit2: TEdit;
Button3: TButton;
Panel1: TPanel;
Panel2: TPanel;
Label3: TLabel;
Label4: TLabel;
lbl7: TLabel;
bvl1: TBevel;
Image2: TImage;
lbl10: TLabel;
lbl1: TLabel;
lbl2: TLabel;
lbl3: TLabel;
lbl4: TLabel;
lbl5: TLabel;
lbl6: TLabel;
Image3: TImage;
lbl9: TLabel;
procedure Button2Click(Sender: TObject);
procedure Button1Click(Sender: TObject);
procedure Button3Click(Sender: TObject);
procedure FormCreate(Sender: TObject);
private
{ Private declarations }
public
{ Public declarations }
end;
type
Mas=array[0..100] of Extended;
var
Form1: TForm1;
Xmax,Xmin,Ymax,Ymin:extended;
i,j,n,k,raz,nn : integer;
Q,P :Mas;
xx,a,b,c,d,y,cc,h,aa,bb:Mas;
st:string;
R:real;
yy:real;
PX,PY,Lg,Rg:integer;
x,XXmax,XXmin: extended;
implementation
{$R *.dfm}
procedure TForm1.Button1Click(Sender: TObject);
begin
n:=StrToInt(Edit1.text);
StringGrid1.ColCount:=n;
StringGrid1.Width:=(n)*67;
StringGrid1.Visible:=true;
end;
function S(x: Extended; i:Integer; a,y,xx,c,b,d:Mas ; var Xmax,Xmin,Ymax,Ymin:extended):Extended;
var
Sum, Mng: extended;
begin
Sum:=0;
Sum:=a[i]+b[i]*(x-xx[i-1])+c[i]*(x-xx[i-1])*(x-xx[i-1])+d[i]*(x-xx[i-1])*(x-xx[i-1])*(x-xx[i-1]);
S:=Sum;
Xmax:=10;
Xmin:=-10;
Ymax:=10;
Ymin:=-10;
end;
procedure TForm1.Button2Click(Sender: TObject);
begin
memo1.Text:='';
Panel1.Visible:=true;
Panel2.Visible:=true;
nn:=StrToInt(Edit1.text);
n:=nn-1;
for j:=0 to n do
begin
xx[j]:=StrToFloat(StringGrid1.Cells[j,0]);
y[j]:=StrToFloat(StringGrid1.Cells[j,1]);
end;
for i:=1 to n do
h[i]:=xx[i]-xx[i-1];
c[1]:=0;
aa[2]:=0;
Q[1]:=0;
p[1]:=0;
for i:=2 to n do
begin // Нахождение коэф с[i] методом прогонки
bb[i]:=2*(h[i-1]+h[i]);
cc[i]:=h[i];
aa[i+1]:=h[i];
d[i]:=3*((y[i]-y[i-1])/h[i]-(y[i-1]-y[i-2])/h[i-1]); {y[0]}
P[i]:=(-cc[i])/(bb[i]+aa[i]*P[i-1]);
Q[i]:=(d[i]-aa[i]*Q[i-1])/(bb[i]+aa[i]*P[i-1]);
end;
c[n+1]:=0;
for i:=n downto 2 do
begin
c[i]:=P[i]*c[i+1]+Q[i];
end;
c[n+1]:=0;
for i:=1 to n do
begin
b[i]:=((y[i]-y[i-1])/h[i]-(1/3)*h[i]*(c[i+1]+2*c[i]));
d[i]:=(c[i+1]-c[i])/(3*h[i]);
a[i]:=y[i-1];
end;
for i:=1 to n do
begin
With Form1.Memo1.Lines do
begin
Add('a = '+FloatToStrF(a[i],fffixed,4,2));
Add('b = '+FloatToStrF(b[i],fffixed,4,2));
Add('c = '+FloatToStrF(c[i],fffixed,4,2));
Add('d = '+FloatToStrF(d[i],fffixed,4,2));
Add('----------------');
end;
end;
image1.Canvas.MoveTo(0,Image1.height div 2);
image1.Canvas.LineTo(Image1.width,Image1.height div 2);
image1.Canvas.MoveTo(Image1.width div 2,0);
image1.Canvas.LineTo(Image1.width div 2,Image1.height);
for i:=1 to n do
begin
XXmax:=xx[i];
XXmin:=xx[i-1];
x:=XXmin;
yy:=(S(x,i,a,y,xx,c,b,d,Xmax,Xmin,Ymax,Ymin));
image1.Canvas.MoveTo(Trunc((XXmin-Xmin)*(Image1.Width/(Xmax-Xmin))),trunc(Image1.Height-(yy-Ymin)*Image1.height/(Ymax-Ymin)));
Image1.Canvas.Pixels[Trunc((XXmin-Xmin)*(Image1.Width/(Xmax-Xmin))),trunc(Image1.Height-(yy-Ymin)*Image1.height/(Ymax-Ymin))]:=clRed;
Rg:=trunc((xx[i]-xx[i-1])*(Image1.Width/(Xmax-Xmin)));
for PX:=0 to Rg do
Begin
x:=XXmin+PX*(Xmax-Xmin)/Image1.Width;
yy:=(S(x,i,a,y,xx,c,b,d,Xmax,Xmin,Ymax,Ymin));
PY:=trunc(Image1.Height-(yy-Ymin)*Image1.height/(Ymax-Ymin));
Image1.Canvas.Pen.Color:=clRed;
Lg:=trunc((x-Xmin)*(Image1.Width/(Xmax-Xmin)));
Image1.Canvas.LineTo(Lg,PY);
end;
end;
memo1.Visible:=TRUE;
end;
procedure TForm1.Button3Click(Sender: TObject);
begin
x:=StrToFloat(Edit2.text);
for i:=1 to n do
if (x>=xx[i-1]) and (x<=xx[i]) then
begin
yy:=(S(x,i,a,y,xx,c,b,d,Xmax,Xmin,Ymax,Ymin));
Form1.memo1.lines.add('Значение функции в точке '+FloatToStr(x)+'= '+FloatToStr(yy));
Exit;
end;
end;
procedure TForm1.FormCreate(Sender: TObject);
begin
{ image1.Canvas.MoveTo(0,Image1.height div 2);
image1.Canvas.LineTo(Image1.width,Image1.height div 2);
image1.Canvas.MoveTo(Image1.width div 2,0);
image1.Canvas.LineTo(Image1.width div 2,Image1.height); }
end;
end.