/*************************************************************************************************************************************/
/* */
/* D E T E R M I N A T I O N D E L ' E Q U A T I O N D ' U N E E L L I P S E : */
/* */
/* */
/* Author of '$xtc/EquationEllipse.02$vv$c' : */
/* */
/* Jean-Francois Colonna (LACTAMME, 20221011183131). */
/* */
/*************************************************************************************************************************************/
#include "INCLUDES.01.I"
extern double sqrt();
static int GenererImage=FAUX;
/* Afin de pouvoir verifier qu'il s'agit bien d'une ellipse... */
#define ZOOM \
2
#define FACTEUR \
1
#define REDUC(z) \
((z)/FACTEUR)
#define CARRE(z) \
((z)*(z))
#define CHECK(x,y) \
(CARRE(x)/CARRE(a))+(CARRE(y)/CARRE(b))
#define INFINI \
1.0e100
#define NOMBRE \
41
extern void *malloc();
static int dimX=0;
#define Xmin 0
#define Xmax (Xmin + (dimX-1))
/* Definition des abscisses. */
static int dimY=0;
#define Ymin 0
#define Ymax (Ymin + (dimY-1))
/* Definition des ordonnees. */
#define IMAGE(x,y) \
(*(image + (((y-Ymin)*dimX) + (x-Xmin)))) \
/* Acces a un point de l'image. */
#define store(n,x,y) \
{ \
IMAGE(x,y) = n; \
} \
/* Rangement d'un point valide d'une image. */
#define ELLIPSE(Lx,Ly) \
{ \
int cX=(((Lx[index]-minimum_2_X)/(maximum_2_X-minimum_2_X))*(Xmax-Xmin))+Xmin; \
int cY=(((Ly[index]-minimum_2_Y)/(maximum_2_Y-minimum_2_Y))*(Ymax-Ymin))+Ymin; \
\
cX = (((cX-Xmin)-((Xmax-Xmin)/2))/ZOOM)+(dimX/2)+Xmin; \
cY = (((cY-Ymin)-((Ymax-Ymin)/2))/ZOOM)+(dimY/2)+Ymin; \
\
store(BLANC,cX,cY); \
} \
/* Trace de l'ellipse... */
void main()
{
int index;
double Lx1[NOMBRE]={-800000000000
,-799166000064.454468
,-796663511901.509888
,-792491283632.184937
,-786647243443.405396
,-779128521231.340820
,-769931489097.738647
,-759051804715.996460
,-746484479038.770020
,-732223953778.206543
,-716264213954.533447
,-698598919432.062622
,-679221575849.836548
,-658125753714.453125
,-635305359835.672241
,-610754984887.974731
,-584470346608.554565
,-556448846633.977905
,-526690275857.960571
,-495197717087.342590
,-461978695533.236389
,-427046653020.436279
,-390422834068.982605
,-352138716161.846497
,-312239139907.355164
,-270786351349.391632
,-227865229686.255005
,-183590042709.856995
,-138113159832.700897
,-91636235028.870025
,-44424416024.877166
,+3175900065.465378
,+50715503185.226310
,+97617427472.923400
,+143150528185.577606
,+186406172868.677582
,+226286945182.115662
,+261521714723.657501
,+290725629051.373169
,+312520841585.724304
,+325716668536.934021
};
double Ly1[NOMBRE]={+1000
,+27989568947.760650
,+55921375246.897300
,+83735923255.243881
,+111373744767.720016
,+138774353113.066803
,+165875883044.374756
,+192614711478.117554
,+218925054332.794769
,+244738533244.007599
,+269983706706.834137
,+294585557945.559204
,+318464929193.731323
,+341537896320.715393
,+363715071637.104004
,+384900821220.337158
,+404992390454.005859
,+423878913452.105347
,+441440297714.340515
,+457545961486.339233
,+472053411434.564392
,+484806639343.538879
,+495634329810.908386
,+504347874400.330322
,+510739199645.671082
,+514578458131.797607
,+515611666175.225647
,+513558468956.451233
,+508110328739.113464
,+498929666769.876892
,+485650807662.503113
,+467884075341.501648
,+445225103997.960083
,+417272362288.405457
,+383656913569.580444
,+344089133453.590576
,+298426404636.323669
,+246761858210.234467
,+189524738428.388153
,+127567417275.454803
,+62198223006.654739
};
double Lx2[NOMBRE]={+329515043551.962524
,+323674532868.917603
,+308564150133.509460
,+285081892772.509705
,+254475501947.702972
,+218137658787.323669
,+177436906761.184479
,+133610597143.845917
,+87716052194.003341
,+40622578393.841774
,-6973667863.918034
,-54525136275.164947
,-101606497534.667068
,-147890330250.330505
,-193126365338.586426
,-237124520192.660980
,-279741380978.299683
,-320869592701.490845
,-360429601866.614075
,-398363259766.155457
,-434628874995.758789
,-469197382259.000793
,-502049380352.338501
,-533172829268.901184
,-562561259638.667480
,-590212378315.997192
,-616126969700.465210
,-640308042395.343994
,-662760159839.397949
,-683488909924.952026
,-702500482089.756958
,-719801340182.548706
,-735397962263.524780
,-749296632401.443970
,-761503277891.523193
,-772023340802.756470
,-780861679188.498535
,-788022488122.065308
,-793509238390.982666
,-797324630363.287231
,-799470563564.701050
};
double Ly2[NOMBRE]={-4882226246.836296
,-71755092708.735641
,-136528805597.224564
,-197575237592.599060
,-253681601590.071869
,-304090926985.294800
,-348453819930.926392
,-386735626516.374207
,-419117050514.681030
,-445909525249.911804
,-467492196848.978088
,-484269211220.109741
,-496642941958.444824
,-504998521330.766052
,-509695854117.710144
,-511066339505.118835
,-509412401795.952881
,-505008611894.748901
,-498103619840.776733
,-488922441210.968323
,-477668816546.808472
,-464527498768.808533
,-449666385627.008789
,-433238466668.945557
,-415383573394.559753
,-396229942333.709900
,-375895603252.519348
,-354489608547.058411
,-332113120234.844666
,-308860374532.823303
,-284819536244.112122
,-260073461792.595642
,-234700379460.007568
,-208774502202.248444
,-182366580523.182190
,-155544404924.997314
,-128373267044.422150
,-100916386548.792847
,-73235308198.392166
,-45390273860.971466
,-17440583527.914199
};
/* Ces listes {x1,y1} et {x2,Y2} sont des points "diametralement opposes" d'une ellipse */
/* obtenue par integration des equations de Newton ('v $xiirk/NCOS_81' et aussi */
/* 'v $xiirk/$Fnota Debut_listG_NCOS_81_coordonnees_XY')... */
double minimum_1_X=+INFINI,maximum_1_X=-INFINI;
double minimum_1_Y=+INFINI,maximum_1_Y=-INFINI;
double Translation_X;
double Translation_Y;
for (index=0 ; index<NOMBRE ; index++)
{
minimum_1_X = MIN2(Lx1[index],minimum_1_X);
minimum_1_X = MIN2(Lx2[index],minimum_1_X);
maximum_1_X = MAX2(Lx1[index],maximum_1_X);
maximum_1_X = MAX2(Lx2[index],maximum_1_X);
minimum_1_Y = MIN2(Ly1[index],minimum_1_Y);
minimum_1_Y = MIN2(Ly2[index],minimum_1_Y);
maximum_1_Y = MAX2(Ly1[index],maximum_1_Y);
maximum_1_Y = MAX2(Ly2[index],maximum_1_Y);
/* Premier calcul des extrema des coordonnees afin de centrer l'ellipse... */
}
Translation_X = (maximum_1_X+minimum_1_X)/2;
Translation_Y = (maximum_1_Y+minimum_1_Y)/2;
for (index=0 ; index<NOMBRE ; index++)
{
Lx1[index]=Lx1[index]-Translation_X;
Ly1[index]=Ly1[index]-Translation_Y;
Lx2[index]=Lx2[index]-Translation_X;
Ly2[index]=Ly2[index]-Translation_Y;
/* Operation de centrage de l'ellipse afin que son equation soit "canonique"... */
}
if (GenererImage == FAUX)
{
double moyenne_a=0;
double moyenne_b=0;
int nombre=0;
for (index=0 ; index<NOMBRE ; index++)
{
Lx1[index]=REDUC(Lx1[index]);
Ly1[index]=REDUC(Ly1[index]);
Lx2[index]=REDUC(Lx2[index]);
Ly2[index]=REDUC(Ly2[index]);
/* Operation eventuelle de reduction des coordonnees au cas ou elles seraient vraiment */
/* trop grandes... */
}
for (index=0 ; index<NOMBRE ; index++)
{
double x1=Lx1[index];
double y1=Ly1[index];
double x2=Lx2[index];
double y2=Ly2[index];
/* Les points {x1,y1} et {x2,Y2} sont deux points quasiment "diametralement opposes"... */
double X1=CARRE(x1);
double Y1=CARRE(y1);
double X2=CARRE(x2);
double Y2=CARRE(y2);
if ((X1 != X2) && (Y1 != Y2))
/* Ce test est necessaire car, en effet, les coordonnees sont recentrees par rapport a */
/* leurs extrema. Il peut donc y avoir deux points "opposees" dont les coordonnees sont */
/* opposees et donc leurs carres sont egaux. Cela donnerait donc des 'iA's et/ou des 'iB's */
/* nuls... */
{
double a,A,iA;
double b,B,iB;
double determinant=((Y2*X1)-(Y1*X2));
/* Les coordonnees ayant ete "centrees", on peut utiliser l'equation "canonique" de */
/* l'ellipse... */
/* */
/* On va travailler simplement sur les carres en passant de : */
/* */
/* 2 2 2 2 */
/* x1 y1 x2 y2 */
/* ----- + ----- = 1 ----- + ----- = 1 */
/* 2 2 2 2 */
/* a b a b */
/* */
/* a : */
/* */
/* X1 Y1 X2 Y2 */
/* ---- + ---- = 1 ---- + ---- = 1 */
/* A B A B */
/* */
/* puis a : */
/* */
/* iA.X1 + iB.Y1 = 1 iA.X2 + iB.Y2 = 1 */
/* */
/* {iA,iB} etant les inverses de {A,B}. On est donc en presence d'un systeme lineaire de */
/* deux equations a deux inconnues trivial a resoudre... */
iB = (X1-X2)/determinant;
iA = (Y2-Y1)/determinant;
A = 1/iA;
B = 1/iB;
a = sqrt(A);
b = sqrt(B);
moyenne_a = moyenne_a+a;
moyenne_b = moyenne_b+b;
printf("{{%+f,%+f},{%+f,%+f}} a=%+f b=%+f",x1,y1,x2,y2,a,b);
printf(" Check=(%+f,%+f)\n"
,CHECK(x1,y1)
,CHECK(x2,y2)
);
nombre++;
}
else
{
}
}
moyenne_a = moyenne_a/nombre;
moyenne_b = moyenne_b/nombre;
printf("\n");
printf("Moyenne : a=%+f b=%+f sur %d couples de points.\n",moyenne_a,moyenne_b,nombre);
}
else
{
int x,y;
/* Definition des coordonnees des points de l'image. */
unsigned char *image;
/* Definition de l'image a generer... */
double minimum_2_X=+INFINI,maximum_2_X=-INFINI;
double minimum_2_Y=+INFINI,maximum_2_Y=-INFINI;
Get(dimX,"dimX");
Get(dimY,"dimY");
/* Recuperation des dimensions en 'X' et en 'Y' de l'image a generer. */
image=(unsigned char*)malloc(dimY*dimX);
/* Definition de l'image a generer... */
for (y=Ymin ; y<=Ymax ; y++)
{
for (x=Xmin ; x<=Xmax ; x++)
{
store(NOIR,x,y);
/* Initialisation de l'image finale... */
}
}
for (index=0 ; index<NOMBRE ; index++)
{
minimum_2_X = MIN2(Lx1[index],minimum_2_X);
minimum_2_X = MIN2(Lx2[index],minimum_2_X);
maximum_2_X = MAX2(Lx1[index],maximum_2_X);
maximum_2_X = MAX2(Lx2[index],maximum_2_X);
minimum_2_Y = MIN2(Ly1[index],minimum_2_Y);
minimum_2_Y = MIN2(Ly2[index],minimum_2_Y);
maximum_2_Y = MAX2(Ly1[index],maximum_2_Y);
maximum_2_Y = MAX2(Ly2[index],maximum_2_Y);
/* Deuxieme calcul des extrema des coordonnees afin de centrer l'image... */
}
for (index=0 ; index<NOMBRE ; index++)
{
ELLIPSE(Lx1,Ly1);
ELLIPSE(Lx2,Ly2);
}
write(1,image,dimX*dimY);
/* Sortie de l'image afin de verifier qu'il s'agit bien d'une ellipse... */
}
}