An example "chart sphere" animation.
The concept of three dimensional houses or "3D houses" refers to any method of placing planets in one of the 12 astrological houses that requires considering the planet's latitude in addition to its zodiac position longitude. All the various classic systems of house division (e.g. Placidus) attempt to define a single zodiac position for each house cusp. That model is simple and easy to work with, however it's limited because it doesn't take into account the third dimension, or a planet's ecliptic latitude. "3D houses" is not a standard system of house division like others, because it goes beyond the old model of picking a single zodiac position for each house cusp.
Visualize the nature of a house to begin with. The sky or celestial sphere is divided into 12 equally sized wedges (like pieces of an orange) with respect to the local horizon, with houses 1-6 below the horizon, and houses 7-12 above it. Similarly, houses 10-3 are to the east of the meridian, and houses 4-9 are to the west of the meridian. The signs of the zodiac are also a set of 12 equally sized "orange wedges", however they're oriented to a different coordinate system, or more specifically are rotated to be aligned with the ecliptic. The fact that houses consider the local horizon, and zodiac positions consider the ecliptic, and standard house systems attempt to use ecliptic coordinates to fully define houses, can be considered a distorted model and therefore less accurate astrology. Perhaps the reason why there's so much debate about which house system is correct, is that they're all wrong! ;-) In other words, perhaps each standard house system only seems to work in certain circumstances when the planetary latitudes happen to place them in the correct 3D house.
For a visual example, see the image below for a local horizon display of my chart in Astrolog. There are two charts side by side, which are identical except the left is using classic 2D houses, and the right 3D houses. In both charts, the middle horizontal line is the horizon, the middle vertical line is the south meridian, the vertical lines on either side of it are the prime vertical passing through the east and west points, and the far edges are the north meridian. The 12 houses are marked by the green dotted lines (and labeled with green numbers). The ecliptic and the signs of the zodiac are marked by purple dotted lines (and labeled with purple glyphs). Planets are plotted near the ecliptic, and the Ascendant, MC, and house cusps are plotted where they intersect the ecliptic. Notice how the star Sirius (labeled "Sir") is clearly in the 5th house well below the horizon, however with a zodiac position slightly later than the Descendant, all classic house systems will place it in the 7th house, making one think it's above the horizon! Similarly, the star Polaris (labeled "Pol") is high in the sky on the meridian and therefore correctly on the 10th cusp, however classic house systems will place it way down in the 6th house.
A standard wheel chart display doesn't work well to show 3D houses. That's because house cusps don't have single zodiac longitude positions anymore. In effect there needs to be something equivalent to a "chart sphere" instead of a "chart wheel"! With 3D houses, each planet is still unambiguously in a single house. That means it's still possible to have a simple table listing each planet's zodiac position and house placement. However, it is important to realize that two planets at the same zodiac position may be in different houses, because their latitudes differ. 3D houses doesn't have "house cusps" in the traditional sense that can be defined by a single zodiac position, because planetary latitude can change 3D house placement.
To compute 3D houses or determine which house a planet truly lies within, convert the planet's zodiac longitude and ecliptic latitude to local horizon coordinates centered on the prime vertical. That means the azimuth or 0-360 degrees (representing house positions 1-12) follows the prime vertical from the horizon east point through the west point via the nadir. Similarly, the altitude or -90 to +90 degrees ranges from the north to south points on the local horizon.
Some house systems have problems when computed in polar zones, or above the Arctic and Antarctic circles. 3D houses doesn't suffer from any polar zone issues. All 3D houses cover an equal percentage of space of the local horizon, or 1/12 the space of the celestial sphere, and this is true no matter where on the world you're positioned.
Campanus is the standard house system most similar to 3D houses. Campanus houses are defined by the intersection of the ecliptic with 12 equal sized 3D house wedges. That means Campanus houses and 3D houses give the same house placements for planets exactly on the ecliptic. Since most planets are near the ecliptic, and it's only things like Pluto, asteroids, and especially fixed stars that are located any significant distance from it, Campanus houses can be used as a rough approximation for 3D houses.
The page http://www.quadibloc.com/other/as01.htm shows a graphical depiction of Campanus houses. However, remember that only 3D houses fully uses the 3D "orange wedge" model of space to determine house placement. If a planet is anywhere within the 12th house wedge on the local horizon, then 3D houses places it in the 12th house. Campanus houses starts with the orange wedge model to determine where the ecliptic intersects each house, however once determined then Campanus becomes a standard house system like any other, in which a planet changing its ecliptic latitude will never change its house placement. In other words, Campanus and all standard house systems still use and define house cusps as positions along the ecliptic, and disregard planetary latitude when determining house placement. As the linked to page says, "To keep things simple for astrologers, tables of houses, instead of recording the entire path of the line between houses, give the boundary of each house as a single angular position." That's the essence of 3D houses: We no longer need to "keep things simple" as we did in the 19th century, and computers can properly see and work with the entire accurate path of the line between houses.
There are actually multiple systems of 3D houses. Everything described above is really 3D Campanus, in which each 3D house is an equal sized 30 degree slice of the celestial sphere. (For that reason, 3D Campanus can also be called "3D Equal houses", because the houses sizes are equal when looked at in 3D.) However, every standard house system has a corresponding 3D house system, defined by great circles drawn from the due South point to the due North point on the local horizon, passing through each 2D cusp where it intersects the ecliptic. This transformation changes the pole where all 12 houses meet from the ecliptic poles to the local horizon, but won't ever change the house of planets that are exactly on the ecliptic. For example, see http://www.astrolog.org/astrolog/pic/placidus.gif for "3D Placidus" houses, in contrast to http://www.astrolog.org/astrolog/pic/campanus.gif for "3D Campanus".
All standard house systems suffer from issues such as having planets or stars below the horizon being placed in houses 7-12, or planets east of the meridian being placed in houses 4-9. When using 3D houses (and only when using 3D houses) for all planets at all times the following statements are true. No classic system of house division can make all the below statements true, because they don't take into account planetary latitude:
Note that 3D houses have some similarities to Gauquelin sectors, as researched by Michael Gauquelin. Gauquelin sectors are computed based on the rising and setting times of planets, which is similar to 3D houses which are also based on the local horizon. When a planet is above the horizon, it's always in Gauquelin sectors 1-18, and when a planet is below the horizon it's in sectors 19-36. That's similar to how when a planet is above the horizon, it's always in the 7th through 12th 3D houses, and when a planet is below the horizon it's always in the 1st through 6th 3D houses. When a planet rises, it moves from Gauquelin sector 36 to sector 1, which is similar to how a planet rising always moves from the 1st 3D house to the 12th 3D house. When a planet sets, it moves from Gauquelin sector 18 to sector 19, which is similar to how a planet setting always moves from the 7th 3D house to the 6th 3D house.
Note that 3D houses also have some similarities to astrocartography. Standard astrocartography maps include Midheaven and Nadir lines, along with Ascendant and Descendant lines. The Midheaven lines trace where on the Earth a planet is straight up or along the meridian at the time, which traces the start of the boundary of the 10th 3D house. The Ascendant lines (at least when calculating the standard "in mundo" type) trace where on the Earth a planet is rising along the Eastern horizon at the time, which traces the start of the 1st 3D house.
In the article http://www.skyscript.co.uk/houprob_print.html#6back by Deborah Houlding, she also considers 3D houses and chart spheres, or how a planet's latitude can change what house it is properly within. As the linked to page says, "Rudhyar also proposed that a future development of the houses could utilize Campanus as the basis of a three dimensional 'birth sphere', in which the effect of planetary latitude could be fully acknowledged; although to do so requires some alternative way of representing this information other than our two-dimensional chart forms which only show measurements along the ecliptic. Those who consider the three dimensional perspective important, argue that defining house positions by zodiacal degree alone can often prove inaccurate since it assumes that the cusps cut through the ecliptic in a straight line whereas in reality the lines are curved..."
In addition to multiple systems of 3D houses (in which all classic house systems can presented in a 3D manner) there are also multiple models for 3D houses altogether. Everything above describes a model of 3D houses which measures house wedges along the prime vertical, instead of along the ecliptic. That nicely allows all parts of houses 7-12 to be above the horizon, and all parts of houses 1-6 to be below the horizon. However, houses can also be arranged along other planes in addition to the ecliptic and prime vertical. For example, houses can be measured along the local horizon, in which the house wedges meet at the local Zenith and Nadir points located straight up and straight down. (The classic system of Horizon houses is modeled this way, which means the 3D model of Horizon houses when aligned with the local horizon is another "3D equal" house system, since all wedges are always 30 degrees in size.) For another example, houses can also be measured along the celestial equator, in which the house wedges meet at the North and South celestial poles above Earth's North and South poles. (Meridian houses is modeled this way, which means the 3D model of Meridian houses when aligned with the celestial equator is another "3D equal" house system, since all wedges are 30 degrees in size.) All this means Campanus (when measured along the prime vertical), Horizon (measured along the local horizon), and Meridian (measured along the celestial equator) are the three "3D equal" systems, so these systems could be considered "better" or at least more mathematically balanced than other classic house systems. Of these three, only 3D Campanus along the prime vertical has all parts of houses 7-12 above the horizon, and all parts of houses 1-6 below the horizon. See http://www.astrolog.org/astrolog/pic/houses2.gif for an example of the 3D models of Equal, Campanus, Horizon, and Meridian houses, which are all "3D equal" systems modeled by 12 wedges covering the celestial sphere, with the only difference that they're aligned with different planes. For an example of Porphyry houses in all four models (2D along ecliptic, 3D along prime vertical, 3D along local horizon, and 3D along celestial equator), see: http://www.astrolog.org/astrolog/pic/sphere3d.gif
Atmospheric refraction is one more variable that can optionally be applied to influence 3D house position. 3D Campanus house boundaries are defined by covering the sky with 12 equal sized wedges aligned with the local horizon (such that planets that appear above the horizon are always in houses 7-12). That means 3D Campanus positions can be considered as defined in terms of actual local horizon positions (as opposed to just standard zodiacal positions coordinate transformed to align with the local horizon). Local horizon positions are influenced by atmospheric refraction, in which objects technically below the horizon may appear visible to the eye above it. To compute the effects of refraction, elevation above sea level as well as air temperature at the location need to be taken into account (to determine atmospheric pressure which affects refraction) which become additional variables to specify for a birth chart. Refraction isn't a major effect, and will never "move" a planet more than half a degree, but it can move planets near a 3D house boundary into a different 3D house.
In Astrolog, one can turn on 3D houses with the "-c3" command switch, or in the Windows version with the "3D Houses" checkbox in the Calculation Settings dialog. One can also select the "Setting / House Settings / 3D Houses" command, or just press the "a" key. The different models of 3D houses can be selected with an optional parameter to the -c3 switch, in which "-c3 1" is the default 3D model along the prime vertical, "-c3 2" is along the local horizon, and "-c3 3" is along the celestial equator (or in the Windows version with the "3D Houses Plane" button group in Calculation Settings). Atmospheric refraction can be enabled to influence 3D house placements with the -Yf switch, or in the Windows version with the "Local Horizon Positions Apply Atmospheric Refraction" setting in Calculation Settings.
A chart sphere is a 3D wheel chart. Instead of a flat 2D wheel that only positions planets based on their zodiac longitude, a 3D model of the celestial sphere is depicted which shows the 12 equal sized sign "orange wedges" and the separate set of of 12 house wedges, and how planets are positioned within them. Chart spheres are a good way to visualize and work with 3D houses.
A chart sphere is similar to a local horizon chart, such as seen above, just that it's displayed around a sphere instead of on a flat rectangle. The sphere is by default transparent, which means that both sides of the sphere are overlapping and can be seen at once. Because chart spheres are 3D displays, they are effective when animated (i.e. rotated) to get a better sense of their depth. There are various ways that display of chart spheres can be customized in Astrolog, such as one can select what things to display and what colors to use for them.
An example chart sphere is below. Sign wedges are in dark blue, and house wedges are in green. Aspect lines (turned off in this picture) are interesting because they're 3D lines passing through the interior of the sphere. Also, see the top of this page for an animated chart sphere. In the animated sphere above the ecliptic is a brighter purple, and you can also see the aspect lines crossing through the sphere.
In Astrolog, show a chart sphere for the current chart with the "-XX" command switch, or in the Windows version with the "Graphics / Show Chart Sphere" command, or just press the "X" key. For more information about doing chart spheres in Astrolog, see new feature #1 at the top of the Astrolog 6.30 release notes.
Chart spheres are a good way to visualize the difference between 3D houses and 2D houses. Below are two chart spheres side by side, which are identical except the left sphere is using 2D houses, and the right 3D houses. In the left sphere with 2D houses, planetary latitude is ignored when determining house position, which means the 12 house "orange wedges" share the same poles as the 12 equal sized sign wedges. Notice how all 12 houses have areas which are above and below the horizon, which is counterintuitive. In the right sphere with 3D houses, the 12 equal sized house wedges are aligned with the local horizon, and always have their poles at the north and south points on the horizon. In this model, all of houses 1-6 are always below the horizon, and all of houses 7-12 are above the horizon. Because the poles are different, planetary latitude needs to be taken into account to correctly determine house position.
The animation below shows how Campanus house cusps change over time. A standard 2D wheel chart is compared side-by-side to a 3D chart sphere, with both animating the same chart at the same times. Campanus houses are defined by dividing the local horizon into 12 equal sized wedges (with the horizon as their "equator"). That's similar to how signs of the zodiac divide the celestial sphere into 12 equal sized wedges (with the ecliptic as their equator). Where the ecliptic intersects these houses defines the 12 Campanus cusps. That means Campanus houses are effectively a 3D version of Equal houses, because house sizes are equal from a 3D standpoint. (That's one argument in favor of Campanus being the "best" house system.) A 2D chart wheel is basically a 2D cross-section of the 3D chart sphere, taken on the plane of the ecliptic. At high latitudes, Campanus can produce narrower houses (at least when looking at the 2D wheel). As can be seen on the 3D chart sphere, this happens at times when the ecliptic is nearly parallel to the horizon, which causes the ecliptic cross section to slice near the point on the horizon where all the houses meet, which means planets can enter and leave certain houses more quickly. Notice how the Sun and Pluto are tightly conjunct on the wheel chart, however they're actually a bit farther away from each other in space on the celestial sphere, because their ecliptic latitudes differ.
Compare this Campanus animation to the corresponding animation for Regiomontanus houses. Notice how with Campanus the 3D wedges on the celestial sphere are always the same size. They're always fixed 30 degree wedges (even though Campanus houses appear to vary in size in the 2D wheel cross section). Regiomontanus houses are fixed and unchanging wedges on the 3D sphere too, however unlike Campanus its houses are differently sized based on where you are in the world. This is why a more descriptive name for 3D Campanus houses is "3D Equal houses". Also compare the Campanus animation to the animation for Placidus houses. Placidus houses are different sizes not only based on where you are in the world, but also based on the time of day. You can see them changing and wobbling over time not only on the wheel, but also in the green colored house wedges on the 3D sphere.
Left: Campanus houses in classic 2D wheel.
Right: Campanus house boundaries on celestial sphere.
Chart spheres aren't just a 2D display that happens to looks 3D, but they can be actual 3D wireframe models. In 3D model form, one can move among a chart sphere or render it in perspective. The video below animates flying around and within a chart sphere, while the chart within the sphere is also animating forward through time. In the sphere, the 12 zodiac sign wedges can be seen in dark blue (moving around the local horizon as the things rise and set), the 12 house wedges can be seen in green (which are always fixed and don't move with respect to the local horizon), aspect lines can be seen appearing and disappearing over time passing through the interior of the sphere, and even constellations are added half way through in purple. This video can demonstrate the difference between the 12 equally sized signs used in astrology, and the various irregularly shaped constellations used in astronomy.
In Astrolog, create 3D wireframe files with the -X3 command switch, or in the Windows version with the “File / Save Wireframe” command.
Video of flying within and around an animating chart sphere
wireframe model.
Can a standard 2D wheel chart be better at taking into account planetary latitude? The answer is yes, if it is displayed in an alternative fashion.
Standard wheel charts are "sign focused", which means that a planet is plotted within the wheel based only on its sign position or zodiac longitude, and its latitude is ignored. Wheel charts can instead be "house focused", which means that the graphical position of where a planet is placed around the wheel will be its proportion through the 3D house. (In other words, the planet's proportion through the 3D house or percentage across the prime vertical on the local horizon, will be used to position the planet between the two appropriate house cusps on the wheel.) The result will cause planets to seem to move, or even seem to be in a different sign (however they will always be in the right 3D house). That's the reverse of a standard "sign focused" wheel which will always position planets in the right sign (however they may be in the wrong 3D house). If one wants a graphical display accurate for both zodiac sign positions and 3D house positions at the same time, then they should use a chart sphere.
See below for an example of "sign focused" and "house focused" wheels displayed side by size. On the left is a standard "sign focused" wheel. The correct zodiac position of each planet is indicated by the planet's positioning within the surrounding ring of signs. Similarly, the standard house position of each planet is indicated by the planet's positioning within the surrounding ring of houses. However, since the wheel doesn't do anything with planetary latitude, the apparent house may not be the correct 3D house. On the right is a "house focused" wheel. The correct 3D house position of each planet is indicated by the planet's positioning within the surrounding ring of houses. However, the sign position of each planet isn't necessarily the positioning within the surrounding ring of signs. Notice how planets are positioned differently in the two wheels, usually subtly but sometimes significantly, especially for the fixed stars Sirius and Polaris.
Note that switching between "sign focused" and "house focused" for a wheel chart will result in objects like the Sun and lunar Nodes not moving at all. That's because those objects are on the ecliptic (i.e. at 0 latitude) and standard and 3D versions of a house always give the same house placements for objects exactly on the ecliptic.
In Astrolog, if you turn on the "3D Houses" setting, then its standard wheel chart will be displayed "house focused" instead of "sign focused".
"3D aspects" refers to aspect calculations that take planetary latitude into account. When calculating the angle and orb of aspects, in classic astrology only the zodiac position longitude of a planet is considered, and the planet's latitude is ignored. However, it's possible for aspect calculations to take the latitude of planets into account too. In other words, the aspect angle between two planets is determined by the 3D great circle distance between them on the celestial sphere, and not just the 2D difference between their zodiac position longitudes.
For example, during a New Moon the Sun and Moon may be as much as 5 degrees different in latitude. That means that even when a New Moon is exact, the 3D aspect orb between them may be up to 5 degrees. (If the Sun and Moon are conjunct in both zodiac position and latitude, then a solar eclipse is taking place.) For bodies with latitudes that can be widely different from the ecliptic, such as Pluto, asteroids, and especially fixed stars, the difference is more pronounced. For example, a body at 0Leo and -30 latitude will be Square a body at 0Leo and +60 latitude, because they're 90 degrees apart, even though they’re both at the same longitude and would be considered Conjunct normally.
3D aspects suggests that an exact time New Moon in which the Sun and Moon are different by 5 degrees in latitude, has the same orb or strength as a standard Sun/Moon conjunction different in zodiac position longitude by 5 degrees. If you use 3D aspects, then aspect orbs will increase by up to the latitude difference, which can cause some aspects to disappear if they're pushed beyond the orb limit.
"3D orbs" is a related concept to 3D aspects. 3D orbs means orb limits apply to latitude as well as zodiac position longitude. With 3D orbs active, a Conjunction with a 5 degree orb will be considered out of bounds (and therefore not a valid Conjunction) if the zodiac positions are different by more than 5 degrees, or if the latitudes are different by more than 5 degrees. 3D orbs can be considered a "lighter" version of 3D aspects or 3D aspects partially applied, because no aspects will change into other aspects, however some aspects will disappear if pushed beyond the vertical orb limit. For example, two bodies at 0Leo will potentially be considered Conjunct (and never any other aspect, no matter how much their latitudes differ) however they'll only be Conjunct if their latitudes are close enough to be within orb.
3D Aspects and 3D orbs are two separate settings independent of each other, and one can use either or both of them. This results in four possible combinations, or different ways to determine aspects. Assume there's one body at 0Leo and -30 latitude, and another body at 0Leo and +60 latitude. That results in the following aspects between them:
Parallel and contraparallel aspects are one classic astrology technique that takes into consideration the latitude of planets (or more specifically declination relative to Earth's equator). However, they only look at latitude in isolation separately from zodiac position longitude. 3D aspects are similar to standard and parallel aspects unified and combined into one.
Cazimi is another astrology term that considers planetary latitude. A planet is "cazimi" if it's exactly Conjunct the Sun within a 16 or 17 arc minute orb. However, in order to truly be cazimi the tight Conjunction must also be in effect "vertically" as well as horizontally, or in other words a 3D aspect. Cazimi is in effect an eclipse with the Sun (i.e. a transit over the Sun's disk, or an occultation behind the Sun's disk). The Sun is half a degree or 30 minutes across, so its radius is 15 minutes, which means a planet needs to get within about 16 minutes in order to actually start overlapping the Sun.
In Astrolog, turn on 3D aspects with the "-A3" command switch, or in the Windows version with the "3D Aspects" checkbox in the Calculation Settings dialog. Also, turn on 3D orbs with the "-Ap" command switch, or in the Windows version with the "3D Orbs" checkbox in the Calculation settings dialog.
"3D midpoints" refers to midpoint calculations that take planetary latitude into account. When calculating the midpoint of two planets, in classic astrology only the zodiac position longitude of the planet is considered, and the planet's latitude is ignored. However, it's possible for midpoint calculations to take the latitude of planets into account too. In other words, the midpoint between two planets is determined by the middle point along the 3D great circle arc between them on the celestial sphere, and not just the midpoint between their zodiac position longitudes. For example, the classic midpoint of a planet at 0Ari and 0 latitude, and another planet at 0Leo and +89 latitude, will just be 0Gem, however the 3D midpoint will be close to 0Ari and +45 latitude.
In Astrolog, if its "3D houses" setting is on, then midpoints will be calculated as 3D midpoints. This will affect Astrolog's midpoint chart, midpoints in the aspect/midpoint grid chart, and the time space midpoint relationship chart. Also, if the "parallel aspects" setting is on, then the midpoint chart will display the latitude of the midpoint too (whether 2D or 3D). The latitude of a midpoint will simply be the average of the two latitudes considered separately for 2D midpoints, but will be the latitude of the 3D great circle arc for 3D midpoints.
"3D astrocartography" refers to astrocartography positions that take planetary latitude into account. The most common form of astrocartography (such as that popularized by Jim Lewis when astrocartography techniques were first being developed) is "in mundo", in which the lines mark where on the world planets are actually rising or setting on the local horizon, or culminating or anticulminating on the meridian. This standard form of astrocartography is already 3D, because accurately determining when a planet rises and sets requires knowing its actual location in space, which means considering its latitude. Line crossings with in mundo astrocartography will indicate "parans", or where two rising/setting/culminating events are taking place at the same time and place.
An alternative form of astrocartography is "zodiacal", which effectively ignores planetary latitude and assumes that all planets are located within the 2D plane of the ecliptic. In this form of astrocartography, lines don't correspond to the local horizon, but rather to where on Earth a planet will be Conjunct with the degree of the Ascendant, Midheaven, Descendant, or Nadir. Lines for bodies located significantly above or below the ecliptic, such as Pluto, many asteroids, and especially fixed stars, will move significantly between in mundo and zodiacal. Note that zodiacal astrocartography will never have two lines of the same type cross, such as an Ascendant line cross a different body's Ascendant line.
Both types of astrocartography are illustrated in the picture above. In both types, Midheaven and Nadir lines are always straight lines of longitude, and they all intersect at Earth's North and South poles. Ascendant and Descendant lines are angled with respect to the poles, and will appear curved on a flat world map. In zodiacal, all these Ascendant and Descendant lines will intersect at exactly the same points on the Arctic and Antarctic Circles. However, in mundo has these lines cross at many different points in roughly the same area. This can be used to distinguish between in mundo and zodiacal astrocartography charts: Look at the Ascendant and Descendant lines, and if they all intersect at the exact same spot then it's zodiacal, otherwise if the lines are more distributed it's in mundo.
"3D astrocartography" can also refer to the presentation of the astrocartography itself. Most astrocartography charts are drawn as a flat 2D map of the world, with longitude on the horizontal axis and latitude on the vertical. However, it's also possible to draw astrocartography as a 3D globe, or even as 3D models which can be animated and rendered in perspective. Either way, regardless of 2D versus 3D presentation, the lines are still at the same locations on the world (unless one switches between in mundo and zodiacal).
Astrolog does standard 3D "in mundo" astrocartography by default. To do "zodiacal" astrocartography, use the command line "-~O '=x 0'" (not including the surrounding double quotes), which can be typed or copy/pasted into the "Enter Command Line" dialog in the Windows version. Astrolog will show a flat 2D astrocartography map with the -L switch or the "Chart / Astro-Graph" menu command, and will show a 3D globe astrocartography chart with the -XG switch or the "Graphics / Draw Globe" command.
