I've found many people new to 3D printing don't understand where the process went sideways. It's difficult to determine where the round tire on the PC monitor turned into a 12 sided blob off the printer.
I'll try to lend some personal experience and things to look out for. Obviously encourage others with experience to throw something below.
On the Computer
There are 2 important things to understand at the beginning.
Most graphics programs (from google draw to high end CAD programs) have a display tolerance - actually tolerance in general is like the 3rd thing to keep in mind (all the time). If you picture a circle on a piece of paper (2D) - and you zoom in on it - sooner or later that circle turns into a bunch of straight lines (after all - what is a circle but a bunch of straight lines..Yes - wrap your head around that if you haven't heard it before... ) Anyway - The higher the display tolerance, the more you can zoom in on it - and it still looks round..... The display can be refreshed OR the program will auto refresh and the jagged lines turn back into what looks like a circle again..... Keep this in mind for a minute.
The meat of the solid model is how it was constructed and the method of the program you are using - to construct surfaces. I like doughnuts so I'll use an illustration I found on the net to describe this picture:
Polygon surfaces are the most important to keep in mind because most 3D printers work off of something close to this. A polygon surface has 3 or more edges - and the surface (or "sheet") between the edges is flat. Looking at the doughnut - if you tripled the number of sheets to make the doughnut - it would start to look round... And if you keep going you could eventually get something that "looked" round. But you are creating thousands of edges and surfaces now. You get into trouble with a CAD system when the model looks complete round and it's a polygon - because the file size would be extremely hefty and you will tax the computer to the point of crashing. The program has to do a calculation every time to model is moved - so eventually you run out of graphics power or disk cache...
NURBS (Non Uniform Rational B-Splines) surface is a parametric surface built on a mathematical formula. This actually means they are extra smooth without making an attempt to kill your GPU for showing them on the screen. The surface will have a curvature class that can be controlled and for people that know the Auto Industry - A fender usually requires a Class A surface detail. Most CAD programs work this way. The high end CAD tools have extremely good surfacing capability - BUT - Most don't do the hybrid (Subdivided surfaces)
Subdivided surfaces Important to note here is that these types of surfaces can only be sustained (to my knowledge) if they stay in the program they were created in.... These models are usually used for high tolerance surface creation - and allow for a very fluid looking surface. They are very desirable in the Industrial design world etc..... Once your ID guy creates his "artistry" - and you bring it into the CAD world - It usually turns into one of the two above (and sometimes turns square!).... The ID guy gets mad his creation has been ruined - the CAD guy is mad because he was given junk and the project goes late while they try to sort it out.... Not a big deal in what we're talking about - but there it is...
So - now imagine putting those two things together (display and a surface type...). As you zoom in/out - be aware of what you're looking at and how those 2 factors impact what you're seeing. If your tire is a square blob when you zoom in/out and you think its round because you imported a file from grabCAD that was called "round tire"...... I can guarantee you it's not going to print round.
If you grab a model from a website and pull it into your program - usually - unless its the same exact program the solid was created in - you will end up with a polygon model. So what the surface tolerance was on that model (how much edge data) - and the display is going to combine into your end result.... If you see a bunch of hard edges on the CAD model - it will just get worse, and here's why....
