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/*
** Astrolog (Version 4.10) File: formulas.c
**
** IMPORTANT NOTICE: the graphics database and chart display routines
** used in this program are Copyright (C) 1991-1994 by Walter D. Pullen
** (cruiser1@stein.u.washington.edu). Permission is granted to freely
** use and distribute these routines provided one doesn't sell,
** restrict, or profit from them in any way. Modification is allowed
** provided these notices remain with any altered or edited versions of
** the program.
**
** The main planetary calculation routines used in this program have
** been Copyrighted and the core of this program is basically a
** conversion to C of the routines created by James Neely as listed in
** Michael Erlewine's 'Manual of Computer Programming for Astrologers',
** available from Matrix Software. The copyright gives us permission to
** use the routines for personal use but not to sell them or profit from
** them in any way.
**
** The PostScript code within the core graphics routines are programmed
** and Copyright (C) 1992-1993 by Brian D. Willoughby
** (brianw@sounds.wa.com). Conditions are identical to those above.
**
** The extended accurate ephemeris databases and formulas are from the
** calculation routines in the program "Placalc" and are programmed and
** Copyright (C) 1989,1991,1993 by Astrodienst AG and Alois Treindl
** (alois@azur.ch). The use of that source code is subject to
** regulations made by Astrodienst Zurich, and the code is not in the
** public domain. This copyright notice must not be changed or removed
** by any user of this program.
**
** Initial programming 8/28,30, 9/10,13,16,20,23, 10/3,6,7, 11/7,10,21/1991.
** X Window graphics initially programmed 10/23-29/1991.
** PostScript graphics initially programmed 11/29-30/1992.
** Last code change made 3/19/1994.
*/
#include "astrolog.h"
real MC, Asc, Vtx, RA, OB, X, Y, A;
real planet1[TOTAL+1], planet2[TOTAL+1],
planetalt1[TOTAL+1], planetalt2[TOTAL+1],
house1[SIGNS+1], house2[SIGNS+1], ret1[TOTAL+1], ret2[TOTAL+1];
real FAR *datapointer;
/*
******************************************************************************
** Specific Calculations.
******************************************************************************
*/
#ifdef MATRIX
/* Given a month, day, and year, convert it into a single Julian day value, */
/* i.e. the number of days passed since a fixed reference date. */
long MdyToJulian(mon, day, yea)
int mon, day, yea;
{
#ifndef PLACALC
long im, j;
im = 12*((long)yea+4800)+(long)mon-3;
j = (2*(im%12) + 7 + 365*im)/12;
j += (long)day + im/48 - 32083;
if (j > 2299171) /* Take care of dates in */
j += im/4800 - im/1200 + 38; /* Gregorian calendar. */
return j;
#else
int greg = TRUE;
if (yea < G2JYEA || (yea == G2JYEA &&
(mon < G2JMON || (mon == G2JMON && day < 15))))
greg = FALSE;
return (long)floor(julday(mon, day, yea, 12.0, greg)+ROUND);
#endif
}
/* Take a Julian day value, and convert it back into the corresponding */
/* month, day, and year. */
void JulianToMdy(JD, mon, day, yea)
real JD;
int *mon, *day, *yea;
{
#ifndef PLACALC
long L, N, IT, JT, K, IK;
L = (long)floor(JD+ROUND)+68569L;
N = Dvd(4L*L, 146097L);
L -= Dvd(146097L*N + 3L, 4L);
IT = Dvd(4000L*(L+1L), 1461001L);
L -= Dvd(1461L*IT, 4L) - 31L;
JT = Dvd(80L*L, 2447L);
K = L-Dvd(2447L*JT, 80L);
L = Dvd(JT, 11L);
JT += 2L - 12L*L;
IK = 100L*(N-49L) + IT + L;
*mon = (int)JT; *day = (int)K; *yea = (int)IK;
#else
int greg = TRUE;
double tim;
if (JD < 2299171.0) /* October 15, 1582 */
greg = FALSE;
revjul(JD, greg, mon, day, yea, &tim);
#endif
}
/* This is a subprocedure of CastChart(). Once we have the chart parameters, */
/* calculate a few important things related to the date, i.e. the Greenwich */
/* time, the Julian day and fractional part of the day, the offset to the */
/* sidereal, and a couple of other things. */
real ProcessInput(var)
int var;
{
real Off, Ln;
TT = Sgn(TT)*floor(dabs(TT))+FRACT(dabs(TT))*100.0/60.0+DecToDeg(ZZ);
OO = DecToDeg(OO);
AA = MIN(AA, 89.9999); /* Make sure the chart isn't being cast */
AA = MAX(AA, -89.9999); /* on the precise north or south pole. */
AA = DTOR(DecToDeg(AA));
/* if parameter 'var' isn't set, then we can assume that the true time */
/* has already been determined (as in a -rm switch time midpoint chart). */
if (var) {
JD = (real)MdyToJulian(MM, DD, YY);
if (!progress || (operation & DASHp0) > 0)
T = ((JD-2415020.0)+TT/24.0-0.5)/36525.0;
else
/* Determine actual time that a progressed chart is to be cast for. */
T = (((Jdp-JD)/progday+JD)-2415020.0+TT/24.0-0.5)/36525.0;
}
/* Compute angle that the ecliptic is inclined to the Celestial Equator */
OB = DTOR(23.452294-0.0130125*T);
Ln = Mod((933060-6962911*T+7.5*T*T)/3600.0); /* Mean lunar node */
Off = (259205536.0*T+2013816.0)/3600.0; /* Mean Sun */
Off = 17.23*sin(DTOR(Ln))+1.27*sin(DTOR(Off))-(5025.64+1.11*T)*T;
Off = (Off-84038.27)/3600.0;
SD = ((operation & DASHs) ? Off : 0.0) + addfactor;
return Off;
}
/* Convert polar to rectangular coordinates. */
void PolToRec(A, R, X, Y)
real A, R, *X, *Y;
{
if (A == 0.0)
A = SMALL;
*X = R*cos(A);
*Y = R*sin(A);
}
/* Convert rectangular to polar coordinates. */
void RecToPol(X, Y, A, R)
real X, Y, *A, *R;
{
if (Y == 0.0)
Y = SMALL;
*R = sqrt(X*X+Y*Y);
*A = Angle(X, Y);
}
/* Convert rectangular to spherical coordinates. */
real RecToSph(B, L, O)
real B, L, O;
{
real R, Q, G;
A = B; R = 1.0;
PolToRec(A, R, &X, &Y);
Q = Y; R = X; A = L;
PolToRec(A, R, &X, &Y);
G = X; X = Y; Y = Q;
RecToPol(X, Y, &A, &R);
A += O;
PolToRec(A, R, &X, &Y);
Q = ASIN(Y);
Y = X; X = G;
RecToPol(X, Y, &A, &R);
if (A < 0.0)
A += 2*PI;
G = A;
return G;
}
/* Do a coordinate transformation: Given a longitude and latitude value, */
/* return the new longitude and latitude values that the same location */
/* would have, were the equator tilted by a specified number of degrees. */
/* In other words, do a pole shift! This is used to convert among ecliptic, */
/* equatorial, and local coordinates, each of which have zero declination */
/* in different planes. In other words, take into account the Earth's axis. */
void CoorXform(azi, alt, tilt)
real *azi, *alt, tilt;
{
real x, y, a1, l1;
real sinalt, cosalt, sinazi, sintilt, costilt;
sinalt = sin(*alt); cosalt = cos(*alt); sinazi = sin(*azi);
sintilt = sin(tilt); costilt = cos(tilt);
x = cosalt * sinazi * costilt;
y = sinalt * sintilt;
x -= y;
a1 = cosalt;
y = cosalt * cos(*azi);
l1 = Angle(y, x);
a1 = a1 * sinazi * sintilt + sinalt * costilt;
a1 = ASIN(a1);
*azi = l1; *alt = a1;
}
/* This is another subprocedure of CastChart(). Calculate a few variables */
/* corresponding to the chart parameters that are used later on. The */
/* astrological vertex (object number twenty) is also calculated here. */
void ComputeVariables()
{
real R, R2, B, L, O, G;
RA = DTOR(Mod((6.6460656+2400.0513*T+2.58E-5*T*T+TT)*15.0-OO));
R2 = RA; O = -OB; B = AA; A = R2; R = 1.0;
PolToRec(A, R, &X, &Y);
X *= cos(O);
RecToPol(X, Y, &A, &R);
MC = Mod(SD+RTOD(A)); /* Midheaven */
L = R2;
G = RecToSph(B, L, O);
#if FALSE
Asc = Mod(SD+Mod(G+PI/2.0)); /* Ascendant */
#endif
L= R2+PI; B = PI/2.0-dabs(B);
if (AA < 0.0)
B = -B;
G = RecToSph(B, L, O);
Vtx = Mod(SD+RTOD(G+PI/2.0)); /* Vertex */
}
#endif /* MATRIX */
/*
******************************************************************************
** House Cusp Calculations.
******************************************************************************
*/
/* This is a subprocedure of HousePlace(). Given a zodiac position, return */
/* which of the twelve houses it falls in. Remember that a special check */
/* has to be done for the house that spans 0 degrees Aries. */
int HousePlaceIn(point)
real point;
{
int i = 0;
point = Mod(point + 0.5/60.0/60.0);
do {
i++;
} while (!(i >= SIGNS ||
(point >= house[i] && point < house[Mod12(i+1)]) ||
(house[i] > house[Mod12(i+1)] &&
(point >= house[i] || point < house[Mod12(i+1)]))));
return i;
}
/* For each object in the chart, determine what house it belongs in. */
void HousePlace()
{
int i;
for (i = 1; i <= total; i++)
inhouse[i] = HousePlaceIn(planet[i]);
}
#ifdef MATRIX
/* The following two functions calculate the midheaven and ascendant of */
/* the chart in question, based on time and location. They are also used */
/* in some of the house cusp calculation routines as a quick way to get */
/* the 10th and 1st house cusps. */
real CuspMidheaven()
{
real MC;
MC = ATAN(tan(RA)/cos(OB));
if (MC < 0.0)
MC += PI;
if (RA > PI)
MC += PI;
return Mod(RTOD(MC)+SD);
}
real CuspAscendant()
{
real Asc;
Asc = Angle(-sin(RA)*cos(OB)-tan(AA)*sin(OB), cos(RA));
return Mod(RTOD(Asc)+SD);
}
/* These are various different algorithms for calculating the house cusps: */
real CuspPlacidus(deg, FF, neg)
real deg, FF;
bool neg;
{
real LO, R1, R2, XS;
int i;
R1 = RA+DTOR(deg);
if (neg)
X = 1.0;
else
X = -1.0;
for (i = 1; i <= 10; i++) {
/* This formula works except at 0 latitude (AA == 0.0). */
XS = X*sin(R1)*tan(OB)*tan(AA == 0.0 ? 0.0001 : AA);
XS = ACOS(XS);
if (XS < 0.0)
XS += PI;
if (neg)
R2 = RA+PI-(XS/FF);
else
R2 = RA+(XS/FF);
R1 = R2;
}
LO = ATAN(tan(R1)/cos(OB));
if (LO < 0.0)
LO += PI;
if (sin(R1) < 0.0)
LO += PI;
return RTOD(LO);
}
void HousePlacidus()
{
int i;
house[1] = Mod(Asc-SD);
house[4] = Mod(MC+DEGHALF-SD);
house[5] = CuspPlacidus(30.0, 3.0, FALSE) + DEGHALF;
house[6] = CuspPlacidus(60.0, 1.5, FALSE) + DEGHALF;
house[2] = CuspPlacidus(120.0, 1.5, TRUE);
house[3] = CuspPlacidus(150.0, 3.0, TRUE);
for (i = 1; i <= SIGNS; i++) {
if (i <= 6)
house[i] = Mod(house[i]+SD);
else
house[i] = Mod(house[i-6]+DEGHALF);
}
}
void HouseKoch()
{
real A1, A2, A3, KN, D;
int i;
A1 = sin(RA)*tan(AA)*tan(OB);
A1 = ASIN(A1);
for (i = 1; i <= SIGNS; i++) {
D = Mod(60.0+30.0*(real)i);
A2 = D/DEGQUAD-1.0; KN = 1.0;
if (D >= DEGHALF) {
KN = -1.0;
A2 = D/DEGQUAD-3.0;
}
A3 = DTOR(Mod(RTOD(RA)+D+A2*RTOD(A1)));
X = Angle(cos(A3)*cos(OB)-KN*tan(AA)*sin(OB), sin(A3));
house[i] = Mod(RTOD(X)+SD);
}
}
void HouseEqual()
{
int i;
for (i = 1; i <= SIGNS; i++)
house[i] = Mod(Asc-30.0+30.0*(real)i);
}
void HouseCampanus()
{
real KO, DN;
int i;
for (i = 1; i <= SIGNS; i++) {
KO = DTOR(60.000001+30.0*(real)i);
DN = ATAN(tan(KO)*cos(AA));
if (DN < 0.0)
DN += PI;
if (sin(KO) < 0.0)
DN += PI;
X = Angle(cos(RA+DN)*cos(OB)-sin(DN)*tan(AA)*sin(OB), sin(RA+DN));
house[i] = Mod(RTOD(X)+SD);
}
}
void HouseMeridian()
{
real D;
int i;
for (i = 1; i <= SIGNS; i++) {
D = DTOR(60.0+30.0*(real)i);
X = Angle(cos(RA+D)*cos(OB), sin(RA+D));
house[i] = Mod(RTOD(X)+SD);
}
}
void HouseRegiomontanus()
{
real D;
int i;
for (i = 1; i <= SIGNS; i++) {
D = DTOR(60.0+30.0*(real)i);
X = Angle(cos(RA+D)*cos(OB)-sin(D)*tan(AA)*sin(OB), sin(RA+D));
house[i] = Mod(RTOD(X)+SD);
}
}
void HousePorphyry()
{
int i;
X = Asc-MC;
if (X < 0.0)
X += DEGREES;
Y = X/3.0;
for (i = 1; i <= 2; i++)
house[i+4] = Mod(DEGHALF+MC+i*Y);
X = Mod(DEGHALF+MC)-Asc;
if (X < 0.0)
X += DEGREES;
house[1]=Asc;
Y = X/3.0;
for (i = 1; i <= 3; i++)
house[i+1] = Mod(Asc+i*Y);
for (i = 1; i <= 6; i++)
house[i+6] = Mod(house[i]+DEGHALF);
}
void HouseMorinus()
{
real D;
int i;
for (i = 1; i <= SIGNS; i++) {
D = DTOR(60.0+30.0*(real)i);
X = Angle(cos(RA+D), sin(RA+D)*cos(OB));
house[i] = Mod(RTOD(X)+SD);
}
}
real CuspTopocentric(deg)
real deg;
{
real OA, X, LO;
OA = Mod(RA+DTOR(deg));
X = ATAN(tan(AA)/cos(OA));
LO = ATAN(cos(X)*tan(OA)/cos(X+OB));
if (LO < 0.0)
LO += PI;
if (sin(OA) < 0.0)
LO += PI;
return LO;
}
void HouseTopocentric()
{
real TL, P1, P2, LT;
int i;
modulus = 2.0*PI;
house[4] = Mod(DTOR(MC+DEGHALF-SD));
TL = tan(AA); P1 = ATAN(TL/3.0); P2 = ATAN(TL/1.5); LT = AA;
AA = P1; house[5] = CuspTopocentric(30.0) + PI;
AA = P2; house[6] = CuspTopocentric(60.0) + PI;
AA = LT; house[1] = CuspTopocentric(90.0);
AA = P2; house[2] = CuspTopocentric(120.0);
AA = P1; house[3] = CuspTopocentric(150.0);
AA = LT; modulus = DEGREES;
for (i = 1; i <= 6; i++) {
house[i] = Mod(RTOD(house[i])+SD);
house[i+6] = Mod(house[i]+DEGHALF);
}
}
#endif /* MATRIX */
/* This house system is just like the Equal system except that we start */
/* our 12 equal segments from the Midheaven instead of the Ascendant. */
void HouseEqualMidheaven()
{
int i;
for (i = 1; i <= SIGNS; i++)
house[i] = Mod(MC-270.0+30.0*(real)(i-1));
}
/* This is a new house system similar in philosophy to Porphyry houses. */
/* Instead of just trisecting the difference in each quadrant, we do a */
/* smooth sinusoidal distribution of the difference around all the cusps. */
void HousePorphyryNeo()
{
real delta;
int i;
delta = (MinDistance(MC, Asc) - DEGQUAD)/4.0;
house[_LIB] = Mod(Asc+DEGHALF); house[_CAP] = MC;
house[_AQU] = Mod(house[_CAP] + 30.0 + delta + SD);
house[_PIS] = Mod(house[_AQU] + 30.0 + delta*2 + SD);
house[_SAG] = Mod(house[_CAP] - 30.0 + delta + SD);
house[_SCO] = Mod(house[_SAG] - 30.0 + delta*2 + SD);
for (i = _ARI; i < _LIB; i++)
house[i] = Mod(house[i+6]-DEGHALF);
}
/* In "null" houses, the cusps are always fixed to start at their */
/* corresponding sign, i.e. the 1st house is always at 0 degrees Aries, etc. */
void HouseNull()
{
int i;
for (i = 1; i <= SIGNS; i++)
house[i] = Mod(STOZ(i)+SD);
}
/* Calculate the house cusp positions, using the specified algorithm. */
void ComputeHouses(housesystem)
int housesystem;
{
char string[STRING];
if (dabs(AA) > DTOR(DEGQUAD-TROPIC) && housesystem < 2) {
sprintf(string,
"The %s system of houses is not defined at extreme latitudes.",
systemname[housesystem]);
PrintError(string);
Terminate(_FATAL);
}
switch (housesystem) {
case 1: HouseKoch(); break;
case 2: HouseEqual(); break;
case 3: HouseCampanus(); break;
case 4: HouseMeridian(); break;
case 5: HouseRegiomontanus(); break;
case 6: HousePorphyry(); break;
case 7: HouseMorinus(); break;
case 8: HouseTopocentric(); break;
case 9: HouseEqualMidheaven(); break;
case 10: HousePorphyryNeo(); break;
case 11: HouseNull(); break;
default: HousePlacidus();
}
}
#ifdef MATRIX
/*
******************************************************************************
** Planetary Position Calculations.
******************************************************************************
*/
/* Read the next three values from the planet data stream, and return them */
/* combined as the coefficients of a quadratic equation in the chart time. */
real ReadThree()
{
real S0, S1, S2;
S0 = ReadPlanetData(); S1 = ReadPlanetData();
S2 = ReadPlanetData();
return S0 = DTOR(S0+S1*T+S2*T*T);
}
/* Another coordinate transformation. This is used by the ComputePlanets() */
/* procedure to rotate rectangular coordinates by a certain amount. */
real RecToSph2(AP, AN, IN)
real AP, AN, IN;
{
real R, D, G;
RecToPol(X, Y, &A, &R); A += AP; PolToRec(A, R, &X, &Y);
D = X; X = Y; Y = 0.0; RecToPol(X, Y, &A, &R);
A += IN; PolToRec(A, R, &X, &Y);
G = Y; Y = X; X = D; RecToPol(X, Y, &A, &R); A += AN;
if (A < 0.0)
A += 2.0*PI;
PolToRec(A, R, &X, &Y);
return G;
}
/* Calculate some harmonic delta error correction factors to add onto the */
/* coordinates of Jupiter through Pluto, for better accuracy. */
void ErrorCorrect(ind, x, y, z)
int ind;
real *x, *y, *z;
{
real U, V, W, S0, T0[4];
int IK, IJ, errorindex;
errorindex = errorcount[ind];
for (IK = 1; IK <= 3; IK++) {
if (ind == 6 && IK == 3) {
T0[3] = 0.0;
break;
}
if (IK == 3)
errorindex--;
S0 = ReadThree(); A = 0.0;
for (IJ = 1; IJ <= errorindex; IJ++) {
U = ReadPlanetData(); V = ReadPlanetData(); W = ReadPlanetData();
A = A+DTOR(U)*cos((V*T+W)*PI/DEGHALF);
}
T0[IK] = RTOD(S0+A);
}
*x += T0[2]; *y += T0[1]; *z += T0[3];
}
/* Another subprocedure of the ComputePlanets() routine. Convert the final */
/* rectangular coordinates of a planet to zodiac position and declination. */
void ProcessPlanet(ind, aber)
int ind;
real aber;
{
real ang, rad;
RecToPol(spacex[ind], spacey[ind], &ang, &rad);
planet[ind] = Mod(RTOD(ang) /*+ NU*/ - aber + SD);
RecToPol(rad, spacez[ind], &ang, &rad);
if (centerplanet == _SUN && ind == _SUN)
ang = 0.0;
planetalt[ind] = RTOD(ang);
}
/* This is probably the heart of the whole program of Astrolog. Calculate */
/* the position of each body that orbits the Sun. A heliocentric chart is */
/* most natural; extra calculation is needed to have other central bodies. */
void ComputePlanets()
{
real helio[BASE+1], helioalt[BASE+1], helioret[BASE+1],
heliox[BASE+1], helioy[BASE+1], helioz[BASE+1];
real aber = 0.0, AU, E, EA, E1, M, XW, YW, AP, AN, IN, G, XS, YS, ZS;
int ind = 1, i;
datapointer = planetdata;
while (ind <= (operation & DASHu ? BASE : PLANETS+1)) {
modulus = 2.0*PI;
EA = M = Mod(ReadThree()); /* Calculate mean anomaly */
E = RTOD(ReadThree()); /* Calculate eccentricity */
for (i = 1; i <= 5; i++)
EA = M+E*sin(EA); /* Solve Kepler's equation */
AU = ReadPlanetData(); /* Semi-major axis */
E1 = 0.01720209/(pow(AU, 1.5)*
(1.0-E*cos(EA))); /* Begin velocity coordinates */
XW = -AU*E1*sin(EA); /* Perifocal coordinates */
YW = AU*E1*pow(1.0-E*E,0.5)*cos(EA);
AP = ReadThree(); AN = ReadThree();
IN = ReadThree(); /* Calculate inclination */
X = XW; Y = YW; G = RecToSph2(AP, AN, IN); /* Rotate velocity coords */
heliox[ind] = X; helioy[ind] = Y;
helioz[ind] = G; /* Helio ecliptic rectangtular */
modulus = DEGREES;
X = AU*(cos(EA)-E); /* Perifocal coordinates for */
Y = AU*sin(EA)*pow(1.0-E*E,0.5); /* rectangular position coordinates */
G = RecToSph2(AP, AN, IN); /* Rotate for rectangular */
XS = X; YS = Y; ZS = G; /* position coordinates */
if (ind >= _JUP && ind <= _PLU)
ErrorCorrect(ind, &XS, &YS, &ZS);
ret[ind] = /* Helio daily motion */
(XS*helioy[ind]-YS*heliox[ind])/(XS*XS+YS*YS);
spacex[ind] = XS; spacey[ind] = YS; spacez[ind] = ZS;
ProcessPlanet(ind, 0.0);
ind += (ind == 1 ? 2 : (ind != PLANETS+1 ? 1 : 10));
}
spacex[0] = spacey[0] = spacez[0] = 0.0;
if (!centerplanet) {
if (exdisplay & DASHv0)
for (i = 0; i <= BASE; i++) /* Use relative velocity */
ret[i] = DTOR(1.0); /* if -v0 is in effect */
return;
}
#endif /* MATRIX */
/* A second loop is needed for geocentric charts or central bodies other */
/* than the Sun. For example, we can't find the position of Mercury in */
/* relation to Pluto until we know the position of Pluto in relation to */
/* the Sun, and since Mercury is calculated first, another pass needed. */
ind = centerplanet;
for (i = 0; i <= BASE; i++) {
helio[i] = planet[i];
helioalt[i] = planetalt[i];
helioret[i] = ret[i];
if (i != _MOO && i != ind) {
spacex[i] -= spacex[ind];
spacey[i] -= spacey[ind];
spacez[i] -= spacez[ind];
}
}
spacex[ind] = spacey[ind] = spacez[ind] = 0.0;
SwapReal(&spacex[0], &spacex[ind]);
SwapReal(&spacey[0], &spacey[ind]); /* Do some swapping - we want */
SwapReal(&spacez[0], &spacez[ind]); /* the central body to be in */
SwapReal(&spacex[1], &spacex[ind]); /* object position number zero. */
SwapReal(&spacey[1], &spacey[ind]);
SwapReal(&spacez[1], &spacez[ind]);
for (i = 1; i <= (operation & DASHu ? BASE : PLANETS+1);
i += (i == 1 ? 2 : (i != PLANETS+1 ? 1 : 10))) {
XS = spacex[i]; YS = spacey[i]; ZS = spacez[i];
if (ind != _SUN || i != _SUN)
ret[i] = (XS*(helioy[i]-helioy[ind])-YS*(heliox[i]-heliox[ind]))/
(XS*XS+YS*YS);
if (ind == _SUN)
aber = 0.0057756*sqrt(XS*XS+YS*YS+ZS*ZS)*RTOD(ret[i]); /* Aberration */
ProcessPlanet(i, aber);
if (exdisplay & DASHv0) /* Use relative velocity */
ret[i] = DTOR(ret[i]/helioret[i]); /* if -v0 is in effect */
}
}
#ifdef MATRIX
/*
******************************************************************************
** Lunar Position Calculations
******************************************************************************
*/
/* Calculate the position and declination of the Moon, and the Moon's North */
/* Node. This has to be done separately from the other planets, because they */
/* all orbit the Sun, while the Moon orbits the Earth. */
void ComputeLunar(moonlo, moonla, nodelo, nodela)
real *moonlo, *moonla, *nodelo, *nodela;
{
real LL, G, N, G1, D, L, ML, L1, MB, T1, M = 3600.0;
LL = 973563.0+1732564379.0*T-4.0*T*T; /* Compute mean lunar longitude */
G = 1012395.0+6189.0*T; /* Sun's mean longitude of perigee */
N = 933060.0-6962911.0*T+7.5*T*T; /* Compute mean lunar node */
G1 = 1203586.0+14648523.0*T-37.0*T*T; /* Mean longitude of lunar perigee */
D = 1262655.0+1602961611.0*T-5.0*T*T; /* Mean elongation of Moon from Sun */
L = (LL-G1)/M; L1 = ((LL-D)-G)/M; /* Some auxiliary angles */
T1 = (LL-N)/M; D = D/M; Y = 2.0*D;
/* Compute Moon's perturbations. */
ML = 22639.6*SIND(L)-4586.4*SIND(L-Y)+2369.9*SIND(Y)+769.0*SIND(2.0*L)-
669.0*SIND(L1)-411.6*SIND(2.0*T1)-212.0*SIND(2.0*L-Y)-206.0*SIND(L+L1-Y);
ML += 192.0*SIND(L+Y)-165.0*SIND(L1-Y)+148.0*SIND(L-L1)-125.0*SIND(D)-110.0*
SIND(L+L1)-55.0*SIND(2.0*T1-Y)-45.0*SIND(L+2.0*T1)+40.0*SIND(L-2.0*T1);
*moonlo = G = Mod((LL+ML)/M+SD); /* Lunar longitude */
/* Compute lunar latitude. */
MB = 18461.5*SIND(T1)+1010.0*SIND(L+T1)-999.0*SIND(T1-L)-624.0*SIND(T1-Y)+
199.0*SIND(T1+Y-L)-167.0*SIND(L+T1-Y);
MB += 117.0*SIND(T1+Y)+62.0*SIND(2.0*L+T1)-
33.0*SIND(T1-Y-L)-32.0*SIND(T1-2.0*L)-30.0*SIND(L1+T1-Y);
*moonla = MB =
Sgn(MB)*((dabs(MB)/M)/DEGREES-floor((dabs(MB)/M)/DEGREES))*DEGREES;
/* Compute position of the north node. One can compute the true North */
/* Node here if they like, but the Mean Node seems to be the one used */
/* in astrology, so that's the one Astrolog returns by default. */
#ifdef TRUENODE
N = N+5392.0*SIND(2.0*T1-Y)-541.0*SIND(L1)-442.0*SIND(Y)+423.0*SIND(2.0*T1)-
291.0*SIND(2.0*L-2.0*T1);
#endif
*nodelo = Mod(N/M+SD);
*nodela = 0.0;
}
#endif /* MATRIX */
/*
******************************************************************************
** Star Position Calculations
******************************************************************************
*/
/* This is used by the chart calculation routine to calculate the positions */
/* of the fixed stars. Since the stars don't move in the sky over time, */
/* getting their positions is mostly just reading info from an array and */
/* converting it to the correct reference frame. However, we have to add */
/* in the correct precession for the tropical zodiac, and sort the final */
/* index list based on what order the stars are supposed to be printed in. */
void ComputeStars(SD)
real SD;
{
int i, j;
real x, y, z;
/* Read in star positions. */
for (i = 1; i <= STARS; i++) {
x = stardata[i*6-6]; y = stardata[i*6-5]; z = stardata[i*6-4];
planet[BASE+i] = DTOR(x*DEGREES/24.0+y*15.0/60.0+z*0.25/60.0);
x = stardata[i*6-3]; y = stardata[i*6-2]; z = stardata[i*6-1];
planetalt[BASE+i] = DTOR(x+y/60.0+z/60.0/60.0);
EquToEcl(&planet[BASE+i], &planetalt[BASE+i]); /* Convert to */
planet[BASE+i] = Mod(RTOD(planet[BASE+i])+SD2000+SD); /* ecliptic. */
planetalt[BASE+i] = RTOD(planetalt[BASE+i]);
starname[i] = i;
}
/* Sort the index list if -Uz, -Ul, -Un, or -Ub switch in effect. */
if (universe > 1) for (i = 2; i <= STARS; i++) {
j = i-1;
/* Compare star names for -Un switch. */
if (universe == 'n') while (j > 0 && StringCmp(
objectname[BASE+starname[j]], objectname[BASE+starname[j+1]]) > 0) {
SWAP(starname[j], starname[j+1]);
j--;
/* Compare star brightnesses for -Ub switch. */
} else if (universe == 'b') while (j > 0 &&
starbright[starname[j]] > starbright[starname[j+1]]) {
SWAP(starname[j], starname[j+1]);
j--;
/* Compare star zodiac locations for -Uz switch. */
} else if (universe == 'z') while (j > 0 &&
planet[BASE+starname[j]] > planet[BASE+starname[j+1]]) {
SWAP(starname[j], starname[j+1]);
j--;
/* Compare star declinations for -Ul switch. */
} else if (universe == 'l') while (j > 0 &&
planetalt[BASE+starname[j]] < planetalt[BASE+starname[j+1]]) {
SWAP(starname[j], starname[j+1]);
j--;
}
}
}
/*
******************************************************************************
** Chart Calculation.
******************************************************************************
*/
#ifdef PLACALC
/* Compute the positions of the planets at a certain time using the Placalc */
/* accurate formulas and ephemeris. This will superseed the Matrix routine */
/* values and is only called with the -b switch is in effect. Not all */
/* objects or modes are available using this, but some additional values */
/* such as Moon and Node velocities not available without -b are. (This is */
/* the one place in Astrolog which calls the Placalc package functions.) */
void ComputePlacalc(t)
real t;
{
int i;
real r1, r2, r3, r4, r;
/* We can compute the positions of Sun through Pluto, Chiron, and the */
/* North Node using Placalc. The other object must be done elsewhere. */
for (i = _SUN; i <= _NOD; i++) if (i <= _CHI || i >= _NOD) {
if (PlacalcPlanet(i, t*36525.0+2415020.0, centerplanet != _SUN,
&r1, &r2, &r3, &r4)) {
/* Note that this can't compute charts with central planets other */
/* than the Sun or Earth or relative velocities in current state. */
planet[i] = Mod(r1 + SD);
planetalt[i] = r2;
ret[i] = DTOR(r3);
/* Compute x,y,z coordinates from azimuth, altitude, and distance. */
spacez[i] = r4*SIND(planetalt[i]);
r = r4*COSD(planetalt[i]);
spacex[i] = r*COSD(planet[i]);
spacey[i] = r*SIND(planet[i]);
}
}
}
#endif
/* This is probably the main routine in all of Astrolog. It generates a */
/* chart, calculating the positions of all the celestial bodies and house */
/* cusps, based on the current chart information, and saves them for use */
/* by any of the display routines. */
real CastChart(var)
int var;
{
int i, k;
real housetemp[SIGNS+1], Off = 0.0, j;
if (MM == -1) {
/* Hack: If month is negative, then we know chart was read in through a */
/* -o0 position file, so the planet positions are already in the arrays. */
MC = planet[_MC]; Asc = planet[_ASC]; Vtx = planet[_VTX];
} else {
Off = ProcessInput(var);
ComputeVariables();
if (operation & DASHG) /* Check for -G geodetic chart. */
RA = DTOR(Mod(-OO));
MC = CuspMidheaven(); /* Calculate our Ascendant & Midheaven. */
Asc = CuspAscendant();
ComputeHouses(housesystem); /* Go calculate house cusps. */
for (i = 1; i <= total; i++) {
planetalt[i] = 0.0; /* Assume on ecliptic unless we say so. */
ret[i] = 1.0; /* Assume direct until we say otherwise. */
}
/* Go calculate planet, Moon, and North Node positions. */
ComputePlanets();
ComputeLunar(&planet[_MOO], &planetalt[_MOO],
&planet[_NOD], &planetalt[_NOD]);
ret[_NOD] = -1.0;
/* Compute more accurate ephemeris positions for certain objects. */
#ifdef PLACALC
if (placalc)
ComputePlacalc(T);
#endif
/* Calculate position of Part of Fortune. */
j = planet[_MOO]-planet[_SUN];
j = dabs(j) < DEGQUAD ? j : j - Sgn(j)*DEGREES;
planet[_FOR] = Mod(j+Asc);
/* Fill in "planet" positions corresponding to house cusps. */
planet[_MC] = MC; planet[_ASC] = Asc; planet[_VTX] = Vtx;
planet[C_LO] = house[11]; planet[C_LO+1] = house[12];
planet[C_LO+2] = house[2]; planet[C_LO+3] = house[3];
}
/* Go calculate star positions if -U switch in effect. */
if (universe)
ComputeStars(operation & DASHs ? 0.0 : -Off);
/* Now, we may have to modify the base positions we calculated above based */
/* on what type of chart we are generating. */
if (operation & DASHp0) { /* Are we doing a -p0 solar arc chart? */
for (i = 1; i <= total; i++)
planet[i] = Mod(planet[i] + (Jdp - JD) / progday);
for (i = 1; i <= SIGNS; i++)
house[i] = Mod(house[i] + (Jdp - JD) / progday);
}
if (multiplyfactor > 1) /* Are we doing a -x harmonic chart? */
for (i = 1; i <= total; i++)
planet[i] = Mod(planet[i] * (real)multiplyfactor);
if (onasc) {
if (onasc > 0) /* Is -1 put on Ascendant in effect? */
j = planet[onasc]-Asc;
else /* Or -2 put object on Midheaven switch? */
j = planet[-onasc]-MC;
for (i = 1; i <= SIGNS; i++) /* If so, rotate the houses accordingly. */
house[i] = Mod(house[i]+j);
}
/* Check to see if we are -F forcing any objects to be particular values. */
for (i = 1; i <= total; i++)
if (force[i] != 0.0) {
planet[i] = force[i]-DEGREES;
planetalt[i] = ret[i] = 0.0;
}
HousePlace(); /* Figure out what house everything falls in. */
/* If -f domal chart switch in effect, switch planet and house positions. */
if (operation & DASHf) {
for (i = 1; i <= total; i++) {
k = inhouse[i];
inhouse[i] = ZTOS(planet[i]);
planet[i] = STOZ(k)+MinDistance(house[k], planet[i]) /
MinDistance(house[k], house[Mod12(k+1)])*30.0;
}
for (i = 1; i <= SIGNS; i++) {
k = HousePlaceIn(STOZ(i));
housetemp[i] = STOZ(k)+MinDistance(house[k], STOZ(i)) /
MinDistance(house[k], house[Mod12(k+1)])*30.0;
}
for (i = 1; i <= SIGNS; i++)
house[i] = housetemp[i];
}
/* If -3 decan chart switch in effect, edit planet positions accordingly. */
if (operation & DASH3)
for (i = 1; i <= total; i++) {
k = ZTOS(planet[i]);
j = planet[i] - STOZ(k);
k = Mod12(k + 4*((int)floor(j/10.0)));
j = (j - floor(j/10.0)*10.0)*3.0;
planet[i] = STOZ(k)+j;
HousePlace();
}
return T;
}
/* formulas.c */
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.