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| {$APPTYPE GUI}
{$MODE DELPHI}
program NewtonG;
{ Approximation de la racine carrée de N par la méthode de Newton ou des
tangentes. }
uses
Couleurs, Graph, SysUtils, WinCrt;
procedure SetLongWordPalette(const index: byte; const color: longWord);
{ Procédure pour utiliser les noms de couleurs de l'unité Couleurs. }
begin
SetRGBPalette(
index,
(color and $FF0000) shr 16,
(color and $FF00) shr 8,
color and $FF
);
end;
procedure ClearScreen(const color: longWord);
begin
SetLongWordPalette(0, color);
SetFillStyle(SolidFill, 0);
Bar(0, 0, GetMaxX, GetMaxY);
end;
function OpenGraph(const color: longWord): boolean;
const
title = 'Newton';
var
pilote, mode: smallInt;
begin
pilote := d8bit;
mode := m640x480;
StrCopy(windowtitle, title);
InitGraph(pilote, mode, '');
Result := GraphResult = grOk;
if Result then
ClearScreen(color);
end;
const
N = 2;
type
tFonction = function(const x: extended): extended;
function F(const x: extended): extended;
begin
F := Sqr(x) - N;
end;
procedure TraceRepere(aCouleur: longWord);
begin
SetLongWordPalette(0, aCouleur);
SetColor(0);
SetLineStyle(SolidLn, 0, NormWidth);
Line( 0, 360, 640, 360);
SetLineStyle(DottedLn, 0, NormWidth);
Line(160, 0, 160, 480);
Line(480, 0, 480, 480);
Line( 0, 120, 640, 120);
end;
procedure TraceCourbe(aFonction: tFonction; aCouleur: longWord);
const
minX = 0.5;
maxX = 2.5;
var
x, y: extended;
xEcran, yEcran: integer;
begin
SetLongWordPalette(0, aCouleur);
x := minX;
repeat
y := aFonction(x);
xEcran := Round(+320 * x - 160);
yEcran := Round(-240 * y + 360);
if (yEcran >= 0) and (yEcran < 480) then
PutPixel(xEcran, yEcran, 0);
x := x + 5E-3;
until x >= maxX;
end;
function Racine(const x: extended; aCouleur: longWord): extended;
const
minY = -0.5;
maxY = +1.5;
var
y, a, b: extended;
x1, x2: integer;
begin
y := F(x);
a := 2 * x;
b := y - a * x;
x1 := Round(320 * ((b-maxY)/-a) - 160);
x2 := Round(320 * ((b-minY)/-a) - 160);
SetLongWordPalette(0, aCouleur);
SetColor(0);
SetLineStyle(SolidLn, 0, NormWidth);
Line(x1, 0, x2, 480);
Result := b / -a;
end;
const
Epsilon = 1E-16;
var
x: extended;
t: text;
begin
if OpenGraph(DarkSlateBlue) then
begin
TraceRepere(DarkIndigo);
TraceCourbe(F, Snow);
x := N;
Assign(t, 'sortie.txt');
rewrite(t);
repeat
Write(t, x:20, ' -> ');
Delay(1000);
x := Racine(x, SlateBlue);
TraceCourbe(F, Snow);
WriteLn(t, x);
until F(x) < Epsilon;
Close(t);
SetLongWordPalette(0, Snow);
SetColor(0);
OutTextXY(10, 10, 'Appuyez sur une touche !');
ReadKey;
end;
end. |
