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calc.cpp
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/*
** Astrolog (Version 7.20) File: calc.cpp
**
** IMPORTANT NOTICE: Astrolog and all chart display routines and anything
** not enumerated below used in this program are Copyright (C) 1991-2021 by
** Walter D. Pullen ([email protected], http://www.astrolog.org/astrolog.htm).
** Permission is granted to freely use, modify, and distribute these
** routines provided these credits and notices remain unmodified with any
** altered or distributed versions of the program.
**
** The main ephemeris databases and calculation routines are from the
** library SWISS EPHEMERIS and are programmed and copyright 1997-2008 by
** Astrodienst AG. The use of that source code is subject to the license for
** Swiss Ephemeris Free Edition, available at http://www.astro.com/swisseph.
** This copyright notice must not be changed or removed by any user of this
** program.
**
** Additional 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 ([email protected]). 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.
**
** The original planetary calculation routines used in this program have
** been copyrighted and the initial core of this program was mostly a
** conversion to C of the routines created by James Neely as listed in
** 'Manual of Computer Programming for Astrologers', by Michael Erlewine,
** available from Matrix Software.
**
** Atlas composed using data from https://www.geonames.org/ licensed under a
** Creative Commons Attribution 4.0 License. Time zone changes composed using
** public domain TZ database: https://data.iana.org/time-zones/tz-link.html
**
** The PostScript code within the core graphics routines are programmed
** and Copyright (C) 1992-1993 by Brian D. Willoughby ([email protected]).
**
** More formally: This program is free software; you can redistribute it
** and/or modify it under the terms of the GNU General Public License as
** published by the Free Software Foundation; either version 2 of the
** License, or (at your option) any later version. This program is
** distributed in the hope that it will be useful and inspiring, but
** WITHOUT ANY WARRANTY; without even the implied warranty of
** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
** General Public License for more details, a copy of which is in the
** LICENSE.HTM file included with Astrolog, and at http://www.gnu.org
**
** Initial programming 8/28-30/1991.
** X Window graphics initially programmed 10/23-29/1991.
** PostScript graphics initially programmed 11/29-30/1992.
** Last code change made 4/11/2021.
*/
#include "astrolog.h"
/*
******************************************************************************
** Julian Day Calculations.
******************************************************************************
*/
// 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(int mon, int day, int yea)
{
#ifdef MATRIX
if (!us.fEphemFiles)
return MatrixMdyToJulian(mon, day, yea);
#endif
#ifdef EPHEM
int fGreg = fTrue;
double jd;
if (yea < ciGreg.yea || (yea == ciGreg.yea &&
(mon < ciGreg.mon || (mon == ciGreg.mon && day < ciGreg.day))))
fGreg = fFalse;
#ifdef SWISS
if (!us.fPlacalcPla)
jd = SwissJulDay(mon, day, yea, 12.0, fGreg) + rRound;
#endif
#ifdef PLACALC
if (us.fPlacalcPla)
jd = julday(mon, day, yea, 12.0, fGreg) + rRound;
#endif
return (long)RFloor(jd);
#else
return 0; // Shouldn't ever be reached.
#endif // EPHEM
}
// Like above but return a fractional Julian time given the extra info.
real MdytszToJulian(int mon, int day, int yea, real tim, real dst, real zon)
{
if (dst == dstAuto)
dst = (real)is.fDst;
return (real)MdyToJulian(mon, day, yea) + (tim + zon - dst) / 24.0;
}
// Take a Julian day value, and convert it back into the corresponding month,
// day, and year.
void JulianToMdy(real JD, int *mon, int *day, int *yea)
{
#ifdef EPHEM
double tim;
#endif
#ifdef MATRIX
if (!us.fEphemFiles) {
MatrixJulianToMdy(JD, mon, day, yea);
return;
}
#endif
#ifdef SWISS
if (!us.fPlacalcPla) {
SwissRevJul(JD, JD >= 2299171.0 /* Oct 15, 1582 */, mon, day, yea, &tim);
return;
}
#endif
#ifdef PLACALC
if (us.fPlacalcPla) {
revjul(JD, JD >= 2299171.0 /* Oct 15, 1582 */, mon, day, yea, &tim);
return;
}
#endif
*mon = mJan; *day = 1; *yea = 2021;
}
/*
******************************************************************************
** House Cusp Calculations.
******************************************************************************
*/
// Compute 3D houses for 3D Campanus or the default case where houses are 12
// equal sized wedges covering the celestial sphere. Basically the same as
// doing local horizon, giving coordinates relative to prime vertical.
real RHousePlaceIn3DCore(real rLon, real rLat)
{
real lonM, latM, lon, lat;
lonM = Tropical(is.MC); latM = 0.0;
EclToEqu(&lonM, &latM);
lon = Tropical(rLon); lat = rLat;
EclToEqu(&lon, &lat);
lon = Mod(lonM - lon + rDegQuad);
EquToLocal(&lon, &lat, -Lat);
lon = rDegMax - lon;
return Mod(lon + rSmall);
}
// Compute 3D houses, or the house postion of a 3D location. Given a zodiac
// position and latitude, return the house position as a decimal number, which
// includes how far through the house the coordinates are.
real RHousePlaceIn3D(real rLon, real rLat)
{
real deg, rRet;
int i;
// Campanus houses are equal sized in 3D, and so a simple case to handle.
deg = RHousePlaceIn3DCore(rLon, rLat);
if (us.nHouseSystem == hsCampanus)
return deg;
// Determine which 3D house the prime vertical degree falls within.
i = 0;
do {
i++;
} while (!(i >= cSign ||
(deg >= chouse3[i] && deg < chouse3[Mod12(i + 1)]) ||
(chouse3[i] > chouse3[Mod12(i + 1)] &&
(deg >= chouse3[i] || deg < chouse3[Mod12(i + 1)]))));
rRet = Mod(ZFromS(i) + MinDistance(chouse3[i], deg) /
MinDistance(chouse3[i], chouse3[Mod12(i + 1)]) * 30.0);
return rRet;
}
// 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 NHousePlaceIn(real rLon, real rLat)
{
int i, di;
// Special processing for 3D houses.
if (us.fHouse3D && rLat != 0.0)
return SFromZ(RHousePlaceIn3D(rLon, rLat));
// This loop also works when house positions decrease through the zodiac.
rLon = Mod(rLon + rSmall);
di = MinDifference(chouse[1], chouse[2]) >= 0.0 ? 1 : -1;
i = 0;
do {
i++;
} while (!(i >= cSign ||
(rLon >= chouse[i] && rLon < chouse[Mod12(i + di)]) ||
(chouse[i] > chouse[Mod12(i + di)] &&
(rLon >= chouse[i] || rLon < chouse[Mod12(i + di)]))));
if (di < 0)
i = Mod12(i - 1);
return i;
}
// For each object in the chart, determine what house it belongs in.
void ComputeInHouses(void)
{
int i;
// First determine 3D house cusp offsets.
if (us.nHouseSystem != hsCampanus) {
for (i = 1; i <= cSign; i++)
chouse3[i] = RHousePlaceIn3DCore(chouse[i], 0.0);
} else {
// 3D Campanus cusps are always equally sized and distributed.
for (i = 1; i <= cSign; i++)
chouse3[i] = ZFromS(i);
}
// Loop over each object and place it.
for (i = 0; i <= is.nObj; i++)
inhouse[i] = NHousePlaceIn(planet[i], planetalt[i]);
if (us.fHouse3D) {
// 3D Campanus cusps should always be in the corresponding house.
if (us.nHouseSystem == hsCampanus) {
for (i = cuspLo; i <= cuspHi; i++)
inhouse[i] = i - cuspLo + 1;
// 3D angles should always be in the corresponding house.
} else if (us.fHouseAngle) {
for (i = cuspLo; i <= cuspHi; i += 3)
inhouse[i] = i - cuspLo + 1;
}
}
}
// Generic function to compute any of the various Equal house systems, in
// which all houses are an equal 30 degrees in size.
void HouseEqualGeneric(real rOffset)
{
int i;
for (i = 1; i <= cSign; i++)
chouse[i] = Mod(ZFromS(i) + rOffset);
}
// Compute the cusp positions using the Porphyry house system.
void HousePorphyry(void)
{
int i;
real rQuad, rSeg;
rQuad = MinDistance(is.MC, is.Asc);
rSeg = rQuad / 3.0;
for (i = 0; i < 3; i++)
chouse[sCap + i] = Mod(is.MC + rSeg*(real)i);
rSeg = (rDegHalf - rQuad) / 3.0;
for (i = 0; i < 3; i++)
chouse[sLib + i] = Mod(is.Asc + rSeg*(real)i + rDegHalf);
for (i = 1; i <= 6; i++)
chouse[i] = Mod(chouse[6 + i] + rDegHalf);
}
// The Sripati house system is like the Porphyry system except each house
// starts in the middle of the previous house as defined by Porphyry.
void HouseSripati(void)
{
int i;
real rgr[cSign+1];
HousePorphyry();
for (i = 1; i <= cSign; i++)
rgr[i] = chouse[i];
for (i = 1; i <= cSign; i++)
chouse[i] = Midpoint(rgr[i], rgr[Mod12(i-1)]);
}
// Compute the cusp positions using the Alcabitius house system.
void HouseAlcabitius(void)
{
real rDecl, rSda, rSna, r, rLon;
int i;
rDecl = RAsin(RSinD(is.OB) * RSinD(is.Asc));
r = -RTanD(AA) * RTan(rDecl);
rSda = DFromR(RAcos(r));
rSna = rDegHalf - rSda;
chouse[sLib] = is.RA - rSna;
chouse[sSco] = is.RA - rSna*2.0/3.0;
chouse[sSag] = is.RA - rSna/3.0;
chouse[sCap] = is.RA;
chouse[sAqu] = is.RA + rSda/3.0;
chouse[sPis] = is.RA + rSda*2.0/3.0;
for (i = sLib; i <= sPis; i++) {
r = RFromD(Mod(chouse[i]));
// The transformation below is also done in CuspMidheaven().
rLon = RAtn(RTan(r)/RCosD(is.OB));
if (rLon < 0.0)
rLon += rPi;
if (r > rPi)
rLon += rPi;
chouse[i] = Mod(DFromR(rLon)+is.rSid);
}
for (i = sAri; i <= sVir; i++)
chouse[i] = Mod(chouse[i+6]+rDegHalf);
}
// This is a newer house system similar in philosophy to Porphyry houses, and
// therefore (at least in the past) has also been called Neo-Porphyry. Instead
// of just trisecting the difference in each quadrant, do a smooth sinusoidal
// distribution of the difference around all the cusps. Note that middle
// houses become 0 sized if a quadrant is <= 30 degrees.
void HousePullenSinusoidalDelta(void)
{
real rQuad, rDelta;
int iHouse;
// Solve equations: x+n + x + x+n = q, x+3n + x+4n + x+3n = 180-q.
rQuad = MinDistance(is.MC, is.Asc);
rDelta = (rQuad - rDegQuad)/4.0;
chouse[sLib] = Mod(is.Asc+rDegHalf); chouse[sCap] = is.MC;
if (rQuad >= 30.0) {
chouse[sAqu] = Mod(chouse[sCap] + 30.0 + rDelta);
chouse[sPis] = Mod(chouse[sAqu] + 30.0 + rDelta*2.0);
} else
chouse[sAqu] = chouse[sPis] = Midpoint(chouse[sCap], is.Asc);
if (rQuad <= 150.0) {
chouse[sSag] = Mod(chouse[sCap] - 30.0 + rDelta);
chouse[sSco] = Mod(chouse[sSag] - 30.0 + rDelta*2.0);
} else
chouse[sSag] = chouse[sSco] = Midpoint(chouse[sCap], chouse[sLib]);
for (iHouse = sAri; iHouse < sLib; iHouse++)
chouse[iHouse] = Mod(chouse[iHouse+6] + rDegHalf);
}
// This is a new house system very similar to Sinusoidal Delta. Instead of
// adding a sine wave offset, multiply a sine wave ratio.
void HousePullenSinusoidalRatio(void)
{
real qSmall, rRatio, rRatio3, rRatio4, xHouse, rLo, rHi;
int iHouse, dir;
// Start by determining the quadrant sizes.
qSmall = MinDistance(is.MC, is.Asc);
dir = qSmall <= rDegQuad ? 1 : -1;
if (dir < 0)
qSmall = rDegHalf - qSmall;
#if TRUE
// Solve equations: rx + x + rx = q, xr^3 + xr^4 + xr^3 = 180-q. Solve
// quartic for r, then compute x given 1st equation: x = q / (2r + 1).
if (qSmall > 0.0) {
rLo = (2.0*pow(qSmall*qSmall - 270.0*qSmall + 16200.0, 1.0/3.0)) /
pow(qSmall, 2.0/3.0);
rHi = RSqr(rLo + 1.0);
rRatio = 0.5*rHi +
0.5*RSqr(-6.0*(qSmall-120.0)/(qSmall*rHi) - rLo + 2.0) - 0.5;
} else
rRatio = 0.0;
rRatio3 = rRatio * rRatio * rRatio; rRatio4 = rRatio3 * rRatio;
xHouse = qSmall / (2.0 * rRatio + 1.0);
#else
// Can also solve equations empirically. Given candidate for r, compute x
// given 1st equation: x = q / (2r + 1), then compare both against 2nd:
// 2xr^3 + xr^4 = 180-q, to see whether current r is too large or small.
// Before binary searching, first keep doubling rHi until too large.
real qLarge = rDegHalf - qSmall;
flag fBinarySearch = fFalse;
rLo = rRatio = 1.0;
loop {
rRatio = fBinarySearch ? (rLo + rHi) / 2.0 : rRatio * 2.0;
rRatio3 = rRatio * rRatio * rRatio; rRatio4 = rRatio3 * rRatio;
xHouse = qSmall / (2.0 * rRatio + 1.0);
if ((fBinarySearch && (rRatio <= rLo || rRatio >= rHi)) || xHouse <= 0.0)
break;
if (2.0 * xHouse * rRatio3 + xHouse * rRatio4 >= qLarge) {
rHi = rRatio;
fBinarySearch = fTrue;
} else if (fBinarySearch)
rLo = rRatio;
}
#endif
// xHouse and rRatio have been calculated. Fill in the house cusps.
if (dir < 0)
neg(xHouse);
chouse[sAri] = is.Asc; chouse[sCap] = is.MC;
chouse[sLib] = Mod(is.Asc+rDegHalf);
chouse[sCap + dir] = Mod(chouse[sCap] + xHouse * rRatio);
chouse[sCap + dir*2] = Mod(chouse[Mod12(sCap + dir*3)] - xHouse * rRatio);
chouse[sCap - dir] = Mod(chouse[sCap] - xHouse * rRatio3);
chouse[sCap - dir*2] = Mod(chouse[Mod12(sCap - dir*3)] + xHouse * rRatio3);
for (iHouse = sTau; iHouse < sLib; iHouse++)
chouse[iHouse] = Mod(chouse[iHouse+6] + rDegHalf);
}
// Compute the cusp positions using the Equal (Ascendant) house system.
#define HouseEqual() HouseEqualGeneric(is.Asc)
// This house system is just like the Equal system except that we start our 12
// equal segments from the Midheaven instead of the Ascendant.
#define HouseEqualMC() HouseEqualGeneric(is.MC + rDegQuad)
// 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.
#define HouseWhole() HouseEqualGeneric((real)((SFromZ(is.Asc)-1)*30))
// Like "Whole" houses but the 10th house starts at the sign of the MC.
#define HouseWholeMC() \
HouseEqualGeneric((real)((SFromZ(is.MC)-1)*30) + rDegQuad)
// The "Vedic" house system is like the Equal system except each house starts
// 15 degrees earlier. The Asc falls in the middle of the 1st house.
#define HouseVedic() HouseEqualGeneric(is.Asc - 15.0)
// Like "Vedic" houses bit the MC falls in the middle of the 10th house.
#define HouseVedicMC() HouseEqualGeneric(is.MC + rDegQuad - 15.0)
// Balanced Equal house systems split the difference between Asc and MC.
#define HouseEqualBalanced() HouseEqualGeneric(Midpoint(is.Asc, is.MC) + 45.0)
#define HouseWholeBalanced() HouseEqualGeneric((real)\
((SFromZ(Midpoint(is.Asc, is.MC) + 15.0)-1)*30 + 30.0))
#define HouseVedicBalanced() HouseEqualGeneric(Midpoint(is.Asc, is.MC) + 30.0)
// East Point Equal house systems are based around the East Point.
#define HouseEqualEP() HouseEqualGeneric(is.EP)
#define HouseWholeEP() HouseEqualGeneric((real)((SFromZ(is.EP)-1)*30))
#define HouseVedicEP() HouseEqualGeneric(is.EP - 15.0)
// Vertex Equal house systems are based around the Antivertex.
#define HouseEqualVertex() HouseEqualGeneric(is.Vtx + rDegHalf)
#define HouseWholeVertex() \
HouseEqualGeneric((real)((SFromZ(is.Vtx + rDegHalf)-1)*30))
#define HouseVedicVertex() HouseEqualGeneric(is.Vtx + rDegHalf - 15.0)
// In "Null" houses, the cusps are fixed to start at their corresponding sign,
// i.e. the 1st house is always at 0 degrees Aries, etc.
#define HouseNull() HouseEqualGeneric(0.0)
// Calculate the house cusp positions, using the specified system. Note this
// is only called when Swiss Ephemeris is NOT computing the houses.
void ComputeHouses(int housesystem)
{
char sz[cchSzDef];
// Don't allow polar latitudes if system not defined in polar zones.
if ((housesystem == hsPlacidus || housesystem == hsKoch) &&
RAbs(AA) >= rDegQuad - is.OB) {
sprintf(sz,
"The %s system of houses is not defined at extreme latitudes.",
szSystem[housesystem]);
PrintWarning(sz);
housesystem = hsPorphyry;
}
// Flip the Ascendant or MC if it falls in the wrong half of the zodiac.
if (MinDifference(is.MC, is.Asc) < 0.0) {
if (us.fPolarAsc)
is.MC = Mod(is.MC + rDegHalf);
else
is.Asc = Mod(is.Asc + rDegHalf);
}
switch (housesystem) {
#ifdef MATRIX
case hsPlacidus: HousePlacidus(); break;
case hsKoch: HouseKoch(); break;
case hsCampanus: HouseCampanus(); break;
case hsMeridian: HouseMeridian(); break;
case hsRegiomontanus: HouseRegiomontanus(); break;
case hsMorinus: HouseMorinus(); break;
case hsTopocentric: HouseTopocentric(); break;
#endif
case hsEqual: HouseEqual(); break;
case hsPorphyry: HousePorphyry(); break;
case hsAlcabitius: HouseAlcabitius(); break;
case hsEqualMC: HouseEqualMC(); break;
case hsSinewaveRatio: HousePullenSinusoidalRatio(); break;
case hsSinewaveDelta: HousePullenSinusoidalDelta(); break;
case hsWhole: HouseWhole(); break;
case hsVedic: HouseVedic(); break;
case hsSripati: HouseSripati(); break;
// New experimental house systems follow:
case hsWholeMC: HouseWholeMC(); break;
case hsVedicMC: HouseVedicMC(); break;
case hsEqualBalanced: HouseEqualBalanced(); break;
case hsWholeBalanced: HouseWholeBalanced(); break;
case hsVedicBalanced: HouseVedicBalanced(); break;
case hsEqualEP: HouseEqualEP(); break;
case hsWholeEP: HouseWholeEP(); break;
case hsVedicEP: HouseVedicEP(); break;
case hsEqualVertex: HouseEqualVertex(); break;
case hsWholeVertex: HouseWholeVertex(); break;
case hsVedicVertex: HouseVedicVertex(); break;
default: HouseNull();
housesystem = hsNull;
}
is.nHouseSystem = housesystem;
}
/*
******************************************************************************
** Star Position Calculations.
******************************************************************************
*/
// This is used by the chart calculation routine to calculate the positions
// of the fixed stars. Since stars don't move much 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, have to add in
// the correct precession for the tropical zodiac.
void ComputeStars(real t, real Off)
{
#ifdef MATRIX
int i;
real x, y, z;
#endif
// Read in star positions.
#ifdef SWISS
if (FCmSwissStar())
SwissComputeStars(t, fFalse);
else
#endif
{
#ifdef MATRIX
for (i = 1; i <= cStar; i++) {
x = rStarData[i*6-6]; y = rStarData[i*6-5]; z = rStarData[i*6-4];
planet[oNorm+i] = x*rDegMax/24.0 + y*15.0/60.0 + z*0.25/60.0;
x = rStarData[i*6-3]; y = rStarData[i*6-2]; z = rStarData[i*6-1];
if (x < 0.0) {
neg(y); neg(z);
}
planetalt[oNorm+i] = 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(planet[oNorm+i] + rEpoch2000 + Off);
if (!us.fSidereal)
ret[oNorm+i] = !us.fVelocity ? rDegMax/25765.0/rDayInYear : 1.0;
SphToRec(rStarDist[i], planet[oNorm+i], planetalt[oNorm+i],
&space[oNorm+i].x, &space[oNorm+i].y, &space[oNorm+i].z);
}
#endif
}
}
// Given the list of computed planet positions, sort and compose the final
// index list based on what order the planets are supposed to be printed in.
void SortPlanets()
{
int i;
#ifdef EXPRESS
real rgrSort[oNorm1];
int j;
#endif
// By default, objects are displayed in object index order.
for (i = 0; i <= oNorm; i++)
rgobjList[i] = i;
#ifdef EXPRESS
// Adjust indexes used for display with AstroExpressions.
if (!FSzSet(us.szExpSort))
return;
for (i = 0; i <= oNorm; i++) {
ExpSetN(iLetterZ, i);
ParseExpression(us.szExpSort);
rgrSort[i] = RExpGet(iLetterZ);
}
// Sort adjusted list to determine final display ordering.
for (i = 1; i <= oNorm; i++) {
j = i-1;
while (j >= 0 && rgrSort[rgobjList[j]] > rgrSort[rgobjList[j+1]]) {
SwapN(rgobjList[j], rgobjList[j+1]);
j--;
}
}
#endif
}
// Given the list of computed star positions, sort and compose the final index
// list based on what order the stars are supposed to be printed in.
void SortStars()
{
int i, j;
// Sort the index list if one of the special -U subswitches is in effect.
if (us.nStar <= 1)
return;
for (i = starLo+1; i <= starHi; i++) {
j = i-1;
// Compare star names for -Un switch.
if (us.nStar == 'n') while (j >= starLo && NCompareSz(
szObjDisp[rgobjList[j]], szObjDisp[rgobjList[j+1]]) > 0) {
SwapN(rgobjList[j], rgobjList[j+1]);
j--;
// Compare star brightnesses for -Ub switch.
} else if (us.nStar == 'b') while (j >= starLo &&
rStarBright[rgobjList[j]-oNorm] > rStarBright[rgobjList[j+1]-oNorm]) {
SwapN(rgobjList[j], rgobjList[j+1]);
j--;
// Compare star zodiac locations for -Uz switch.
} else if (us.nStar == 'z') while (j >= starLo &&
planet[rgobjList[j]] > planet[rgobjList[j+1]]) {
SwapN(rgobjList[j], rgobjList[j+1]);
j--;
// Compare star latitudes for -Ul switch.
} else if (us.nStar == 'l') while (j >= starLo &&
planetalt[rgobjList[j]] < planetalt[rgobjList[j+1]]) {
SwapN(rgobjList[j], rgobjList[j+1]);
j--;
// Compare star distances for -Ud switch.
} else if (us.nStar == 'd') while (j >= starLo &&
rStarDist[rgobjList[j]-oNorm] > rStarDist[rgobjList[j+1]-oNorm]) {
SwapN(rgobjList[j], rgobjList[j+1]);
j--;
// Compare star velocities for -Uv switch.
} else if (us.nStar == 'v') while (j >= starLo &&
ret[rgobjList[j]] < ret[rgobjList[j+1]]) {
SwapN(rgobjList[j], rgobjList[j+1]);
j--;
}
}
}
/*
******************************************************************************
** Chart Calculation.
******************************************************************************
*/
// Given a zodiac degree, transform it into its Decan sign, in which 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(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;
}
// Given a zodiac degree, transform it into its Dwad sign, in which each
// sign is divided into twelfths, starting with its own sign. For example:
// 15 Aries -> 0 Libra, 10 Leo -> 0 Sagittarius, 20 Sagittarius -> 0 Leo.
real Dwad(real deg)
{
int sign;
real unit;
sign = SFromZ(deg);
unit = deg - ZFromS(sign);
sign = Mod12(sign + ((int)RFloor(unit/2.5)));
unit = (unit - RFloor(unit/2.5)*2.5)*12.0;
return ZFromS(sign)+unit;
}
// Given a zodiac degree, transform it into its Navamsa position, in which
// each sign is divided into ninths, which determines the number of signs
// after a base element sign to use. Degrees within signs are unaffected.
real Navamsa(real deg)
{
int sign, sign2;
real unit;
sign = SFromZ(deg);
unit = deg - ZFromS(sign);
sign2 = Mod12(((sign-1 & 3)^(2*FOdd(sign-1)))*3 + (int)(unit*0.3) + 1);
return ZFromS(sign2) + unit;
}
// Transform rectangular coordinates in x, y to polar coordinates.
void RecToPol(real x, real y, real *a, real *r)
{
*r = RLength2(x, y);
*a = RAngle(x, y);
}
// Transform spherical to rectangular coordinates in x, y, z.
void SphToRec(real r, real azi, real alt, real *rx, real *ry, real *rz)
{
real rT;
*rz = r *RSinD(alt);
rT = r *RCosD(alt);
*rx = rT*RCosD(azi);
*ry = rT*RSinD(azi);
}
// Convert 3D rectangular to spherical coordinates.
void RecToSph3(real rx, real ry, real rz, real *azi, real *alt)
{
real ang, rad;
RecToPol(rx, ry, &ang, &rad);
*azi = DFromR(ang);
ang = RAngleD(rad, rz);
// Ensure latitude is from -90 to +90 degrees.
if (ang > rDegHalf)
ang -= rDegMax;
*alt = ang;
}
// 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(real *azi, real *alt, real tilt)
{
real x, y, a1, l1;
real sinalt, cosalt, sinazi, sintilt, costilt;
*azi = RFromD(*azi); *alt = RFromD(*alt); tilt = RFromD(tilt);
sinalt = RSin(*alt); cosalt = RCos(*alt); sinazi = RSin(*azi);
sintilt = RSin(tilt); costilt = RCos(tilt);
x = cosalt * sinazi * costilt - sinalt * sintilt;
y = cosalt * RCos(*azi);
l1 = RAngle(y, x);
a1 = cosalt * sinazi * sintilt + sinalt * costilt;
a1 = RAsin(a1);
*azi = DFromR(l1); *alt = DFromR(a1);
}
// Fast version of CoorXForm() in which the slow trigonometry values have
// already been computed. Useful when doing many transforms in a row.
void CoorXformFast(real *azi, real *alt, real sinazi, real cosazi,
real sinalt, real cosalt, real sintilt, real costilt)
{
real x, y, a1, l1;
x = cosalt * sinazi * costilt - sinalt * sintilt;
y = cosalt * cosazi;
l1 = RAngle(y, x);
a1 = cosalt * sinazi * sintilt + sinalt * costilt;
a1 = RAsin(a1);
*azi = DFromR(l1); *alt = DFromR(a1);
}
// Another subprocedure of the ComputeEphem() routine. Convert the final
// rectangular coordinates of a planet to zodiac position and latitude.
void ProcessPlanet(int ind, real aber)
{
real ang, rad;
RecToPol(space[ind].x, space[ind].y, &ang, &rad);
planet[ind] = Mod(DFromR(ang) - aber + is.rSid);
RecToPol(rad, space[ind].z, &ang, &rad);
if (us.objCenter == oSun && ind == oSun)
ang = 0.0;
ang = DFromR(ang);
// Ensure latitude is from -90 to +90 degrees.
while (ang > rDegQuad)
ang -= rDegHalf;
while (ang < -rDegQuad)
ang += rDegHalf;
planetalt[ind] = ang;
}
#ifdef EPHEM
// Compute the positions of the planets at a certain time using the Swiss
// Ephemeris accurate formulas. This will supersede the Matrix routine values
// and is only called when 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 main place in
// Astrolog which calls the Swiss Ephemeris functions.)
void ComputeEphem(real t)
{
int objCentCalc, i, j;
real r1, r2, r3, r4, r5, r6, dist1, dist2;
flag fSwiss = !us.fPlacalcPla, fRet;
#ifdef SWISS
int objOrbit;
#endif
// Can compute the positions of Sun through Pluto, Chiron, the four
// asteroids, Lilith, North Node, and Uranians using ephemeris files.
objCentCalc = us.objCenter;
if (objCentCalc > oNorm || FNodal(objCentCalc) ||
(!fSwiss && objCentCalc != oEar))
objCentCalc = oSun;
for (i = oEar; i <= oNorm; i++) {
if ((ignore[i] && i > oMoo && (i != oNod || ignore[oSou])) ||
!FThing(i) ||
(i == objCentCalc &&
!(fSwiss && objCentCalc == oEar && us.fBarycenter)) ||
(!fSwiss && (i >= oFor ||
(us.fPlacalcAst && FBetween(i, oCer, oVes)))))
continue;
// Calculate planet using Swiss Ephemeris or Placalc
fRet = fFalse;
#ifdef SWISS
if (fSwiss) {
objOrbit = us.fMoonMove ? ObjOrbit(i) : -1;
if (objOrbit < 0 || objOrbit == oSun)
objOrbit = objCentCalc;
fRet = FSwissPlanet(i, JulianDayFromTime(t), objOrbit,
&r1, &r2, &r3, &r4, &r5, &r6);
}
#endif
#ifdef PLACALC
if (!fSwiss)
fRet = FPlacalcPlanet(i, JulianDayFromTime(t), objCentCalc != oEar,
&r1, &r2, &r3, &r4, &r5, &r6);
#endif
if (!fRet)
continue;
planet[i] = Mod(r1 + is.rSid);
planetalt[i] = r2;
ret[i] = r3;
retalt[i] = r5;
retlen[i] = r6;
if (us.fVelocity && i <= cThing) {
ret[i] /= (rDegMax / (rObjYear[i == oSun ||
(i == oMoo && objCentCalc != oEar) ? oEar : i] * rDayInYear));
if (i == oNod)
neg(ret[i]);
}
// Compute x,y,z coordinates from azimuth, altitude, and distance.
SphToRec(r4, planet[i], planetalt[i],
&space[i].x, &space[i].y, &space[i].z);
}
// If Sun is solar system barycenter, offset it by Earth's position.
if (us.fBarycenter && fSwiss && objCentCalc == oEar) {
PtNeg2(space[oSun], space[oEar]);
ProcessPlanet(oSun, 0.0);
}
// The central object should be opposite the Sun (or the Earth).
if (fSwiss && !FNodal(us.objCenter)) {
i = (objCentCalc != oSun ? oSun : oEar);
PtNeg2(space[objCentCalc], space[i]);
}
// South Node object is geocentrically opposite the North Node.
if (!ignore[oSou]) {
PtNeg2(space[oSou], space[oNod]);
planet[oSou] = Mod(planet[oNod] + rDegHalf);
ret[oSou] = ret[oNod];
}
// Nodes and Lilith are always generated geocentric, so make heliocentric.
if (objCentCalc != oEar)
for (i = oNod; i <= oLil; i++) if (!ignore[i]) {
PtAdd2(space[i], space[oEar]);
if (fSwiss && us.objCenter > oSun && !FNodal(us.objCenter)) {
PtSub2(space[i], space[oSun]);
}
ProcessPlanet(i, 0.0);
ret[i] = ret[oEar];
}
// If other planet centered, shift all positions by central planet.
if (us.objCenter > oSun) {
for (i = 0; i <= is.nObj; i++) {
// Don't shift if Swiss Ephemeris already shifted for us.
if (fSwiss && !FNodal(i) && !FNodal(us.objCenter) &&
us.objCenter <= oNorm)
continue;
// Don't shift if object restricted, or if it's central object.
if ((ignore[i] && i != oSun) || i == us.objCenter || !FThing(i))
continue;
if (us.fStarMagDist && FStar(i))
dist1 = RLength3(space[i].x, space[i].y, space[i].z);
PtSub2(space[i], space[us.objCenter]);
if (us.fStarMagDist && FStar(i)) {
dist2 = us.fStarMagAbs ? 10.0 * rPCToAU :
RLength3(space[i].x, space[i].y, space[i].z);
rStarBright[i-oNorm] =
RStarBright(rStarBrightDef[i-oNorm], dist1, dist2);
kObjA[i] = KStarA(rStarBright[i-oNorm]);
}
ProcessPlanet(i, us.fSidereal ? is.rSid : 0.0);
}
}
space[us.objCenter].x = space[us.objCenter].y = space[us.objCenter].z = 0.0;
// Potentially relocate objects so they orbit the central planet.
if (!us.fMoonMove || (fSwiss && us.objCenter <= oNorm))
return;
for (i = oMoo; i <= oNorm; i++) {
if (ignore[i])
continue;
j = ObjOrbit(i);
if (j < 0 || j == us.objCenter || (j == oSun && us.objCenter <= oNorm))
continue;
PtSub2(space[i], space[j]);
ProcessPlanet(i, us.objCenter > oSun && us.fSidereal ? is.rSid : 0.0);
}
}
#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(int nContext)
{
CI ciSav;
real housetemp[cSign+1], r, r2;
int i, k, k2;
is.nContext = nContext;
#ifdef EXPRESS
// Notify AstroExpression a chart is about to be cast.
if (!us.fExpOff && FSzSet(us.szExpCast1))
ParseExpression(us.szExpCast1);
#endif
// Hack: If month is negative, then know chart was read in through a -o0
// position file, so planet positions are already in the arrays.
if (FNoTimeOrSpace(ciCore)) {
is.MC = planet[oMC]; is.Asc = planet[oAsc];
ComputeInHouses();
return 0.0;
}
// 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