The concept of three dimensional houses or "3D houses" refers to a 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, could 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, each house system only seems to work in certain circumstances when the planetary latitudes happen to place them in the correct 3D house.
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.
For a visual example, see the image below for a local horizon display of my chart in Astrolog. 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 dark blue dotted lines (and labeled with blue 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 below the horizon, however with a zodiac position slightly later than the Descendant, all ordinary 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 ordinary 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.
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 the 12 house "orange 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 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 orange 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.
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, for all planets at all times, the following statements are true:
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.
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.
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 twelve sign and house "orange 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 quite a few 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.
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 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 if the house system is Campanus, than 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 Campanus houses and 3D houses have the same cusp points for objects on the ecliptic.
In Astrolog, if you turn on the "3D Houses" setting, then its 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, 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 will cause some aspects to disappear if they're pushed beyond the orb limit.
Parallel and contraparallel aspects are one classic astrology technique that takes into consideration the latitude of planets. However, they only look at latitude in isolation separately from zodiac position longitude. 3D aspects are similar to standard and parallel aspects combined into one.
In Astrolog, one can turn on 3D aspects with the "-A3" command switch, or in the Windows version with the "3D Aspects" checkbox in the Calculation Settings dialog.