Beatpairing and Patterning
Fairly easy as an idea, this relates rather directly to the active and passive hitsounding mentioned above, basic concept being the following: If the song has a destinct group of alike-pressured or heightening beats of same or similar fashion, you will logically want accentuate all of these equally.
For reasons such as sheerly keeping it a bit more tame and able to more easily get a grasp of the idea of things, I won't be going into describing every sort of pattern individually – for more ideas in a less wordy fashion, feel free to browse the good old Mapping Techniques subforum (and think your part as to when the depicted techniques would make sense to apply).
Line-line combos / Beatpairings
Source: kors k – smooooch by Priti
While this would generally sound pretty simple, I am going to be an elitist about it anyways (as I generally am in this thread): What you see are three pairs of two circles each, played as combos of two, making this a switch of practically three "flowlines", if you would want to call it that – things like these emphasize the mini soundpatterns that two alike-sounding beats build and (depending on the song) can happen to occure more or less frequently.
Important to note is that in such scenarios where there is a destinct pairgrouping in the song, you will want to give your minicombos a destinct change in angle or direction between each pairing as to emphasize it is not just simply repeating over and to keep it fresh and shapy.
There are also cases where part of one or multiple pairings may be delayed or speeding up while keeping the same individual strength, so don't feel like it's all that static in the end – an example for this would be Lesjuh's Freestyler.
Oh, and obviously this isn't just limited to circles, though it can get a bit tricky to do properly when using sliders instead and only fit on very few occasions, i.e. when mapping a lot of wubs that happen to still fall into this category of musical pattern (please refer to the previous topic of hitobject gameplay and understanding for this).
Triangles
Source: Tomoya Ohtani - Rooftop Run (Classic) by Kyshiro
Source: DragonForce – Cry for Eternity by Lesjuh
Triangles feel a little weird to me, actually – in lower spacing, they feel extremely smooth while the further they are upscaled, they get a lot more individually pressured; this is probably due to the fact that triangles are awfully nice to use a slider in an blanket a previous note (as in the first example), resulting in a much more even-looking map and pattern and easing the player into the finishing slider, therefore subconsciously establishing a more circular and rounded motion before the actual smooth slider is even starting.
As for the spaced ones, it seems rather clear: They're far apart, so playing them in a circular motion just seems unnecessarily confusing and not indicated nor encouraged by anything – therefore, they are individually snapped to in most cases (more or less stuttering, anyways).
Square
Source: Hommarju feat. Latte – masterpiece by simplistiC
Say you have four beats that are the same pressure and each of them feels fairly impactful and individual, what would you come up with? - Most logically a square because it does exactly that: all of the angles are the same, it's a sharp geometrical shape and every note is played and snapped to individually; there's many examples for how awkwardly harsh squares can play, so this should be approached with caution, specifically if you are going to make it a tornado combo.
Pentagons / Star Shapes
Soure: REDALiCE - FLOWER REDALiCE Remix by me
Source: IOSYS – Poinsettia by Aakiha
The pentagon is the smoother variation of the five-beat (and equally accentuated) geometrical patterns we can do - unlike than the triangles before because the angles between the objects themselves have shrunk down to 72° from the previous overly sharp 120° and 90° (triangles and squares respectively); the pentagon is pretty much just a curved move through all of the objects after another. No big accentuation or anything on any individual notes, just one smooth circular motion – obviously that will get more choppy if you scale it up further and change the beatsnap and object density, but for the basic idea, this spaced stream will suffice (hue).
Stars are pretty much just that but.. well, with a little turn or two.. or three.. or four – snappy and more on a beat-per-beat basis rather than actual underlying rolls of five that the pentagon suits better.
Instead of the previously smooth circular motion you jump across the pattern between each note, covering a 144° angle rather than 72°, making this an even more snappy and individually accentuating pattern than a scaled square or a triangle.