The Placidus house system divides the diurnal/nocturnal semi-arc of any point in the celestial sphere into three equal parts. They are identical to the thirds of the time interval between the rise/set and culmination of any given point.
Let's take a set of points ascending on the horizon. For each point, we put a green mark in the 1st third of its way from the ascension to the culmination. If we draw a line that connects all these marks, we will get an S-curve. The intersection of that curve with the ecliptic is the 12th house cusp.
If we do the same for the 2nd third of the path from ascension to culmination, we will get the S-curve for the 11th house. And so with the rest.
In the same way, we can draw an S-curve through any planet or a star. In the example below, the planet has traveled 20% of its ascending path. The same is true for each point on the curve.
We may call this line a curve of planet's position similar to a circle of position in the Regiomontanus system.
The intersection of the curve of position with the equator is called the mundane position of the planet in the Placidus system.
Problem of Placidus House
This system is very unstable at extreme latitudes. Let's cast a chart with the following coordinates: 10.10.2022, 44e46, 76n43, 20:10 UTC+4.
The figure above shows that the 11th house curve intersects the ecliptic in two points. So the Moon is now between the cusp of the 11th house and the cusp of the 11th house, which makes no astrological sense.
Moreover, the 12th house cusp has no common points with the ecliptic, which means we have no 12th house in the chart.
It means that anyone born beyond a Polar circle should have a very special fate, with no illnesses at all, since the 12th house matters cannot occur without the 12th houses. Or the Moon in such a horoscope cannot have a terrestrial state and determination by the house.
All these are controversial to practice.