Here is a taxonomy I have been developing for medieval tents. For brevity there are some default assumptions, so only differences from the default need to be mentioned.
1) Floor plan:
Round or Regular Polygon, Oval, Rectangular, Other. Medieval terminology distinguished between pavilions and tents, and where it's possible to tell, every reference to pavilions that I have read referred to tents with a single pole and a round or regular polygon floor plan.
2) Roof and shoulders:
The default assumption is that the roof spreads to a shoulder and the walls drop more steeply from that point. Shoulderless tents can go from the peak straight to the ground, like a modern pup tent, and some tents had a second shoulder. The default assumption is that the slope of the roof is straight or slightly concave, but a few tents had a convex or dome shaped roof.
The shoulder was typically a bit over six feet high, but a few were high enough that a man at arms could mount his horse within the pavilion and then ride out. Another fairly uncommon type of round tent had a very high shoulder of modest diameter. For the same height and footprint this type would have had less useable internal volume than a conventional tent, but internal structure to spread the shoulder could have been small enough to transport without disassembly.
The default assumption is that tent walls will have significant slope. Some had vertical walls, and it was not uncommon for rectangular tents to have shoulderless vertical walls at the short end.
4) Primary support:
The default assumption is that round and polygonal tents have a single central pole, and that oval and rectangular plans have two upright poles. Two pole tents are assumed to have poles close enough to the center of the tent that the roofs of the short ends have significant slope. I believe that most if not all two pole tents had a ridgepole. Some rectangular tents had posts at the ends so the short ends were vertical. Others were supported by A frames.
Some pavilions had their pole sunk into the ground to keep it upright.
5) Secondary support:
Although some tents look like they got their shape from the poles, rope and fabric alone, others had additional structure. We have documentary evidence of hoops and wall battens. We have visual evidence of rigid frames at the shoulders of rectangular tents, and some oval tents probably had them as well. The collapsing rectangular tents from Henry VIII's camp during the Boulogne campaign look very much like they have an internal rigid A frame in addition to a frame at the eaves and ridgepole.
Tents with convex domed roofs must have had some sort of internal structure, probably radial ribs like a parasol or yurt.
6) Primary ropes:
Some tents are shown with ropes that continue the direction of the roofline and could spread the canopy without additional structure. I call these spreading ropes. Others have ropes that descend much more steeply than the roofline. I call them stabilizing ropes. Some show no ropes at all or only storm guys.
A related detail is where the roops attach to the tent. Rope that meet the tent at the shoulder can spread the canopy at that point. Ropes that meet the tent below the shoulder or beneath a vertical valence are strong evidence that some internal structure is giving the shoulder its shape.
The slope of the ceiling and walls can be either a straight line or a catenary arc.
Valences are typical and the default assumption, but some tents had none and some had an internal valence as well.
Some tents are shown with the inside of the wall a different color, and the Carlos V tent is lined.
An inverted V formed by pulling the walls back on both sides from a vertical closure without detaching them from the roof is typical. Alternatives include:
Detaching a section of the walls from the roof and pulling them back on both sides to create a flat-topped opening;
A panel of the wall that can be rolled up to the bottom of the roof to create a rectangular opening, and;
A rectangular or arched doorway in the wall that can be closed by an internal flap.