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calc.c
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1995-11-25
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/*
** Astrolog (Version 4.40) File: calc.c
**
** IMPORTANT NOTICE: The graphics database and chart display routines
** used in this program are Copyright (C) 1991-1995 by Walter D. Pullen
** (astara@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 1/29/1995.
*/
#include "astrolog.h"
/*
******************************************************************************
** House Cusp Calculations.
******************************************************************************
*/
/* This is a subprocedure of ComputeInHouses(). 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(rDeg)
real rDeg;
{
int i = 0;
rDeg = Mod(rDeg + 0.5/60.0/60.0);
do {
i++;
} while (!(i >= cSign ||
(rDeg >= house[i] && rDeg < house[Mod12(i+1)]) ||
(house[i] > house[Mod12(i+1)] &&
(rDeg >= house[i] || rDeg < house[Mod12(i+1)]))));
return i;
}
/* For each object in the chart, determine what house it belongs in. */
void ComputeInHouses()
{
int i;
for (i = 1; i <= cObj; i++)
inhouse[i] = HousePlaceIn(planet[i]);
}
/* 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 <= cSign; 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) - rDegQuad)/4.0;
house[sLib] = Mod(Asc+rDegHalf); house[sCap] = MC;
house[sAqu] = Mod(house[sCap] + 30.0 + delta + is.rSid);
house[sPis] = Mod(house[sAqu] + 30.0 + delta*2 + is.rSid);
house[sSag] = Mod(house[sCap] - 30.0 + delta + is.rSid);
house[sSco] = Mod(house[sSag] - 30.0 + delta*2 + is.rSid);
for (i = sAri; i < sLib; i++)
house[i] = Mod(house[i+6]-rDegHalf);
}
/* The "Whole" house system is like the Equal system with 30 degree houses, */
/* where the 1st house starts at zero degrees of the sign of the Ascendant. */
void HouseWhole()
{
int i;
for (i = 1; i <= cSign; i++)
house[i] = Mod((SFromZ(Asc)-1)*30+ZFromS(i)+is.rSid);
}
/* In "null" houses, the cusps are always fixed to start at their cor- */
/* responding sign, i.e. the 1st house is always at 0 degrees Aries, etc. */
void HouseNull()
{
int i;
for (i = 1; i <= cSign; i++)
house[i] = Mod(ZFromS(i)+is.rSid);
}
/* Calculate the house cusp positions, using the specified algorithm. */
void ComputeHouses(housesystem)
int housesystem;
{
char sz[cchSzDef];
if (RAbs(AA) > RFromD(rDegQuad-rAxis) && housesystem < 2) {
sprintf(sz,
"The %s system of houses is not defined at extreme latitudes.",
szSystem[housesystem]);
PrintError(sz);
Terminate(tcFatal);
}
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: HouseWhole(); break;
case 12: HouseNull(); break;
default: HousePlacidus();
}
}
/*
******************************************************************************
** 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 <= cStar; i++) {
x = stardata[i*6-6]; y = stardata[i*6-5]; z = stardata[i*6-4];
planet[oNorm+i] = RFromD(x*rDegMax/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[oNorm+i] = RFromD(x+y/60.0+z/60.0/60.0);
/* Convert to ecliptic zodiac coordinates. */
EquToEcl(&planet[oNorm+i], &planetalt[oNorm+i]);
planet[oNorm+i] = Mod(DFromR(planet[oNorm+i])+rEpoch2000+SD);
planetalt[oNorm+i] = DFromR(planetalt[oNorm+i]);
ret[oNorm+i] = RFromD(rDegMax/26000.0/365.25);
starname[i] = i;
}
/* Sort the index list if -Uz, -Ul, -Un, or -Ub switch in effect. */
if (us.nStar > 1) for (i = 2; i <= cStar; i++) {
j = i-1;
/* Compare star names for -Un switch. */
if (us.nStar == 'n') while (j > 0 && NCompareSz(
szObjName[oNorm+starname[j]], szObjName[oNorm+starname[j+1]]) > 0) {
SwapN(starname[j], starname[j+1]);
j--;
/* Compare star brightnesses for -Ub switch. */
} else if (us.nStar == 'b') while (j > 0 &&
starbright[starname[j]] > starbright[starname[j+1]]) {
SwapN(starname[j], starname[j+1]);
j--;
/* Compare star zodiac locations for -Uz switch. */
} else if (us.nStar == 'z') while (j > 0 &&
planet[oNorm+starname[j]] > planet[oNorm+starname[j+1]]) {
SwapN(starname[j], starname[j+1]);
j--;
/* Compare star declinations for -Ul switch. */
} else if (us.nStar == 'l') while (j > 0 &&
planetalt[oNorm+starname[j]] < planetalt[oNorm+starname[j+1]]) {
SwapN(starname[j], starname[j+1]);
j--;
}
}
}
/*
******************************************************************************
** Chart Calculation.
******************************************************************************
*/
/* Given a zodiac degree, transform it into its Decan sign, where each */
/* sign is trisected into the three signs of its element. For example, */
/* 1 Aries -> 3 Aries, 10 Leo -> 0 Sagittarius, 25 Sagittarius -> 15 Leo. */
real Decan(deg)
real deg;
{
int sign;
real unit;
sign = SFromZ(deg);
unit = deg - ZFromS(sign);
sign = Mod12(sign + 4*((int)RFloor(unit/10.0)));
unit = (unit - RFloor(unit/10.0)*10.0)*3.0;
return ZFromS(sign)+unit;
}
/* Transform spherical to rectangular coordinates in x, y, z. */
void SphToRec(r, azi, alt, rx, ry, rz)
real r, azi, alt, *rx, *ry, *rz;
{
real rT;
*rz = r *RSinD(alt);
rT = r *RCosD(alt);
*rx = rT*RCosD(azi);
*ry = rT*RSinD(azi);
}
#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;
/* We can compute the positions of Sun through Pluto, Chiron, and the */
/* North Node using Placalc. The other objects must be done elsewhere. */
for (i = oSun; i <= oLil; i++) {
if ((i > oChi && i < oNod) || (ignore[i] && i > oMoo))
continue;
if (FPlacalcPlanet(i, t*36525.0+2415020.0, us.objCenter != oSun,
&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 + is.rSid);
planetalt[i] = r2;
ret[i] = RFromD(r3);
/* Compute x,y,z coordinates from azimuth, altitude, and distance. */
SphToRec(r4, planet[i], planetalt[i],
&spacex[i], &spacey[i], &spacez[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(fDate)
bool fDate;
{
CI ci;
real housetemp[cSign+1], Off = 0.0, vtx, j;
int i, k;
/* Hack: Time zone +/-24 means to have the time of day be in Local Mean */
/* Time (LMT). This is done by making the time zone value reflect the */
/* logical offset from GMT as indicated by the chart's longitude value. */
if (RAbs(ZZ) == 24.0)
ZZ = DecToDeg(OO)/15.0;
ci = ciCore;
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[oMC]; Asc = planet[oAsc];
} else {
for (i = 1; i <= cObj; i++) {
planet[i] = planetalt[i] = 0.0; /* On ecliptic unless we say so. */
ret[i] = 1.0; /* Direct until we say otherwise. */
}
Off = ProcessInput(fDate);
ComputeVariables(&vtx);
if (us.fGeodetic) /* Check for -G geodetic chart. */
RA = RFromD(Mod(-OO));
MC = CuspMidheaven(); /* Calculate our Ascendant & Midheaven. */
Asc = CuspAscendant();
ComputeHouses(us.nHouseSystem); /* Go calculate house cusps. */
/* Go calculate planet, Moon, and North Node positions. */
ComputePlanets();
if (!ignore[oMoo] || !ignore[oNod] || !ignore[oSou] || !ignore[oFor]) {
ComputeLunar(&planet[oMoo], &planetalt[oMoo],
&planet[oNod], &planetalt[oNod]);
ret[oNod] = -1.0;
}
/* Compute more accurate ephemeris positions for certain objects. */
#ifdef PLACALC
if (us.fPlacalc)
ComputePlacalc(T);
#endif
if (!us.fPlacalc) {
planet[oSou] = Mod(planet[oNod]+rDegHalf);
ret[oSou] = ret[oNod] = RFromD(-0.053);
ret[oMoo] = RFromD(12.5);
}
/* Calculate position of Part of Fortune. */
j = planet[oMoo]-planet[oSun];
if (us.nArabicNight < 0)
neg(j);
j = RAbs(j) < rDegQuad ? j : j - RSgn(j)*rDegMax;
planet[oFor] = Mod(j+Asc);
/* Fill in "planet" positions corresponding to house cusps. */
planet[oVtx] = vtx; planet[oEP] = CuspEastPoint();
for (i = 2; i <= cSign; i++)
planet[cuspLo + i - 1] = house[i];
planet[oAsc] = Asc; planet[oMC] = MC;
planet[oDes] = Mod(Asc + rDegHalf); planet[oNad] = Mod(MC + rDegHalf);
for (i = oFor; i <= cuspHi; i++)
ret[i] = RFromD(rDegMax);
}
/* Go calculate star positions if -U switch in effect. */
if (us.nStar)
ComputeStars(us.fSiderial ? 0.0 : -Off);
/* Transform ecliptic to equatorial coordinates if -sr in effect. */
if (us.fEquator)
for (i = 1; i <= cObj; i++) if (!ignore[i]) {
planet[i] = RFromD(Tropical(planet[i]));
planetalt[i] = RFromD(planetalt[i]);
EclToEqu(&planet[i], &planetalt[i]);
planet[i] = DFromR(planet[i]);
planetalt[i] = DFromR(planetalt[i]);
}
/* Now, we may have to modify the base positions we calculated above based */
/* on what type of chart we are generating. */
if (us.fProgress && us.fSolarArc) { /* Are we doing a -p0 solar arc chart? */
for (i = 1; i <= cObj; i++)
planet[i] = Mod(planet[i] + (is.JDp - is.JD) / us.rProgDay);
for (i = 1; i <= cSign; i++)
house[i] = Mod(house[i] + (is.JDp - is.JD) / us.rProgDay);
}
if (us.nHarmonic > 1) /* Are we doing a -x harmonic chart? */
for (i = 1; i <= cObj; i++)
planet[i] = Mod(planet[i] * (real)us.nHarmonic);
if (us.objOnAsc) {
if (us.objOnAsc > 0) /* Is -1 put on Ascendant in effect? */
j = planet[us.objOnAsc]-Asc;
else /* Or -2 put object on Midheaven switch? */
j = planet[-us.objOnAsc]-MC;
for (i = 1; i <= cSign; 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 <= cObj; i++)
if (force[i] != 0.0) {
planet[i] = force[i]-rDegMax;
planetalt[i] = ret[i] = 0.0;
}
ComputeInHouses(); /* Figure out what house everything falls in. */
/* If -f domal chart switch in effect, switch planet and house positions. */
if (us.fFlip) {
for (i = 1; i <= cObj; i++) {
k = inhouse[i];
inhouse[i] = SFromZ(planet[i]);
planet[i] = ZFromS(k)+MinDistance(house[k], planet[i]) /
MinDistance(house[k], house[Mod12(k+1)])*30.0;
}
for (i = 1; i <= cSign; i++) {
k = HousePlaceIn(ZFromS(i));
housetemp[i] = ZFromS(k)+MinDistance(house[k], ZFromS(i)) /
MinDistance(house[k], house[Mod12(k+1)])*30.0;
}
for (i = 1; i <= cSign; i++)
house[i] = housetemp[i];
}
/* If -3 decan chart switch in effect, edit planet positions accordingly. */
if (us.fDecan) {
for (i = 1; i <= cObj; i++)
planet[i] = Decan(planet[i]);
ComputeInHouses();
}
ciCore = ci;
return T;
}
/*
******************************************************************************
** Aspect Calculations.
******************************************************************************
*/
/* Set up the aspect/midpoint grid. Allocate memory for this array, if not */
/* already done. Allocation is only done once, first time this is called. */
bool FEnsureGrid()
{
if (grid != NULL)
return fTrue;
grid = (GridInfo FAR *)PAllocate(sizeof(GridInfo), fFalse, "grid");
return grid != NULL;
}
/* Indicate whether some aspect between two objects should be shown. */
bool FAcceptAspect(obj1, asp, obj2)
int obj1, asp, obj2;
{
int fSupp;
if (ignorea(asp)) /* If the aspect restricted, reject immediately. */
return fFalse;
if (us.fSmartCusp) {
/* Allow only conjunctions to the minor house cusps. */
if ((FMinor(obj1) || FMinor(obj2)) && asp > aCon)
return fFalse;
/* Prevent any simultaneous aspects to opposing angle cusps, */
/* e.g. if conjunct one, don't be opposite the other; if trine */
/* one, don't sextile the other; don't square both at once, etc. */
fSupp = (asp == aOpp || asp == aSex || asp == aSSx || asp == aSes);
if ((FAngle(obj1) || FAngle(obj2)) &&
(fSupp || (asp == aSqu &&
(obj1 == oDes || obj2 == oDes || obj1 == oNad || obj2 == oNad))))
return fFalse;
/* Prevent any simultaneous aspects to the North and South Node. */
if (fSouthNode) {
if (((obj1 == oNod || obj2 == oNod) && fSupp) ||
((obj1 == oSou || obj2 == oSou) && (fSupp || asp == aSqu)))
return fFalse;
}
}
return fTrue;
}
/* This is a subprocedure of FCreateGrid() and FCreateGridRelation(). */
/* Given two planets, determine what aspect, if any, is present between */
/* them, and save the aspect name and orb in the specified grid cell. */
void GetAspect(planet1, planet2, ret1, ret2, i, j)
real *planet1, *planet2, *ret1, *ret2;
int i, j;
{
int k;
real l, m;
grid->v[i][j] = grid->n[i][j] = 0;
l = MinDistance(planet2[i], planet1[j]);
for (k = us.nAsp; k >= 1; k--) {
if (!FAcceptAspect(i, k, j))
continue;
m = l-aspectangle[k];
if (RAbs(m) < GetOrb(i, j, k)) {
grid->n[i][j] = k;
/* If -ga switch in effect, then change the sign of the orb to */
/* correspond to whether the aspect is applying or separating. */
/* To do this, we check the velocity vectors to see if the */
/* planets are moving toward, away, or are overtaking each other. */
if (us.fAppSep)
m = RSgn2(ret1[j]-ret2[i])*
RSgn2(MinDifference(planet2[i], planet1[j]))*RSgn2(m)*RAbs(m);
grid->v[i][j] = (int)(m*60.0);
}
}
}
/* Very similar to GetAspect(), this determines if there is a parallel or */
/* contraparallel aspect between the given two planets, and stores the */
/* result as above. The settings and orbs for conjunction are used for */
/* parallel and those for opposition are used for contraparallel. */
void GetParallel(planet1, planet2, planetalt1, planetalt2, i, j)
real *planet1, *planet2, *planetalt1, *planetalt2;
int i, j;
{
int k;
real l, alt1, alt2;
l = RFromD(planet1[j]); alt1 = RFromD(planetalt1[j]);
EclToEqu(&l, &alt1); alt1 = DFromR(alt1);
l = RFromD(planet2[i]); alt2 = RFromD(planetalt2[i]);
EclToEqu(&l, &alt2); alt2 = DFromR(alt2);
grid->v[i][j] = grid->n[i][j] = 0;
for (k = Min(us.nAsp, aOpp); k >= 1; k--) {
if (!FAcceptAspect(i, k, j))
continue;
l = RAbs(k == aCon ? alt1 - alt2 : RAbs(alt1) - RAbs(alt2));
if (l < GetOrb(i, j, k)) {
grid->n[i][j] = k;
grid->v[i][j] = (int)(l*60.0);
}
}
}
/* Fill in the aspect grid based on the aspects taking place among the */
/* planets in the present chart. Also fill in the midpoint grid. */
bool FCreateGrid(fFlip)
bool fFlip;
{
int i, j, k;
real l;
if (!FEnsureGrid())
return fFalse;
for (j = 1; j <= cObj; j++) if (!ignore[j])
for (i = 1; i <= cObj; i++) if (!ignore[i])
/* The parameter 'flip' determines what half of the grid is filled in */
/* with the aspects and what half is filled in with the midpoints. */
if (fFlip ? i > j : i < j) {
if (us.fParallel)
GetParallel(planet, planet, planetalt, planetalt, i, j);
else
GetAspect(planet, planet, ret, ret, i, j);
} else if (fFlip ? i < j : i > j) {
l = Mod(Midpoint(planet[i], planet[j])); k = (int)l; /* Calculate */
grid->n[i][j] = k/30+1; /* midpoint. */
grid->v[i][j] = (int)((l-(real)(k/30)*30.0)*60.0);
} else {
grid->n[i][j] = SFromZ(planet[j]);
grid->v[i][j] = (int)(planet[j]-(real)(grid->n[i][j]-1)*30.0);
}
return fTrue;
}
/* This is similar to the previous function; however, this time fill in the */
/* grid based on the aspects (or midpoints if 'acc' set) taking place among */
/* the planets in two different charts, as in the -g -r0 combination. */
bool FCreateGridRelation(fMidpoint)
bool fMidpoint;
{
int i, j, k;
real l;
if (!FEnsureGrid())
return fFalse;
for (j = 1; j <= cObj; j++) if (!ignore[j])
for (i = 1; i <= cObj; i++) if (!ignore[i])
if (!fMidpoint) {
if (us.fParallel)
GetParallel(cp1.obj, cp2.obj, cp1.alt, cp2.alt, i, j);
else
GetAspect(cp1.obj, cp2.obj, cp1.dir, cp2.dir, i, j);
} else {
l = Mod(Midpoint(cp2.obj[i], cp1.obj[j])); k = (int)l; /* Calculate */
grid->n[i][j] = k/30+1; /* midpoint. */
grid->v[i][j] = (int)((l-(real)(k/30)*30.0)*60.0);
}
return fTrue;
}
/* Fill out tables based on the number of unrestricted planets in signs by */
/* element, signs by mode, as well as other values such as the number of */
/* objects in yang vs. yin signs, in various house hemispheres (north/south */
/* and east/west), and the number in first six signs vs. second six signs. */
/* This is used by the -v chart listing and the sidebar in graphics charts. */
void CreateElemTable(pet)
ET *pet;
{
int i, s;
ClearB((lpbyte)pet, (int)sizeof(ET));
for (i = 1; i <= cObj; i++) if (!ignore[i]) {
pet->coSum++;
s = SFromZ(planet[i]);
pet->coSign[s-1]++;
pet->coElemMode[(s-1)&3][(s-1)%3]++;
pet->coElem[(s-1)&3]++; pet->coMode[(s-1)%3]++;
pet->coYang += (s & 1);
pet->coLearn += (s < sLib);
if (!FCusp(i)) {
pet->coHemi++;
s = inhouse[i];
pet->coHouse[s-1]++;
pet->coModeH[(s-1)%3]++;
pet->coMC += (s >= sLib);
pet->coAsc += (s < sCan || s >= sCap);
}
}
pet->coYin = pet->coSum - pet->coYang;
pet->coShare = pet->coSum - pet->coLearn;
pet->coDes = pet->coHemi - pet->coAsc;
pet->coIC = pet->coHemi - pet->coMC;
}
/* calc.c */