As I seek to understand how Rhino’s NURBS geometry works just a little bit more, as well as seeking information to help me understand continuity, edge joining, how tolerances affect downstream actions in production it brings me to a question about tolerances. I also particularily liked the recent video on tolerances with the tip of working in tolerance tighter than you NEED, then if there are naked edges, change tolerance to what you do NEED, hoping that the tolerance shift will be enough to join the naked edges then stay the same or go back to the tight tolerances. That tip makes so much sense to me, and really helped me understand the approximations made with certain commands.
 My question, is most tolerances are + or , and I really have not worked with many things requiring a tight tolerance such as cnc machining or 3d printing. I certainly understand the concept of the + or .
But, is Rhino’s tolerances somehow not + or ?
Example of my question: Absolute Tolerance set to .001, 1/1000th of a inch
Now with + or  a object (A, object being aligned/projected) can line up tangent to another object in any position radiating from the From object (B the exact positioned object).
So not like cutting a 2 x 4, where you either cut short () or long (+) 1/1000.
(with a highly precisioned caliper square with a real long jaw, some real high tech sanding jigs, a precision lever action sanding fixture with precision lathelike crossfeed, intense patience, this level of handcrafted 2x4 precision for your scrap 2x4 project may be possible)(that was a joke)

But I would assume Rhino’s tolerances do indeed extend out radially in all axes x,y,z from a given exact spot. Is Rhino’s tolerance in reference to all axes from a given known or already defined location? So, radially from a given location, the 1/1000 of a inch is rotated on all axes from known location?

Which leads to my original question, which this is a part of.
New example, the Absolute Tolerance is 1 inch.
Does Rhino use this full inch? Or does it account for, if This object were to be placed 1 inch away from the known location in 1 spot, then the distance between where it can be set 1 inch away on the other direction of the axes on a straight line would actually be 2 inches, and therefore cannot place 1 inch away. The max radius extending from the known location would be .5 inches.
Does this makes sense, and is this how rhino tolerances operate?
A clearer example.
 A line is 2 inches long
 The center/midpoint of the line is 1 inch
 The distance from end of line to other end of line =2
 The distance to the center of the line is 1
This line could be the tolerance I am referring to. But this line can extend in all axes of 3d space from the center of that line, making it spherical.
So, although it was listed above in another question, both sections here make my question more clear. Is rhino’s geometry tolerances spherical from a known position?
Does the tolerance account for how far it would be from the opposite point on the sphere thus making a 1inch tolerance actually have a maximum distance from known point .5?
FACTORS IN WHERE APPROXIMATE OPERATIONS ACTAULLY LAND
IN VARIOUS COMMANDS

Do, U and V directions of a known object + Known location affect where a approximate operation will be placed? quick example: right/left, top/bottom?

If you project a object onto a object, will rhino always place the object on top of the fixed object, with a gap between the outside geometry of the fixed shape, and the inside/bottom of the shape projected? Example thoughts: placing a banana on a sphere. Will rhino always have the gap between the outer parameters of the sphere and the banana? So that approximation operations never place a object overlapping? Or do approximate operations have the possibility of placing the banana inside the sphere’s geometry but within tolerances thus making it directly tangent? But when there are issues, and there is a naked edge, can it be on the inside?
I’d also like to gather a list of approximate operations to make a mindmap, so that I understand more as I am working about tolerances, and can make tolerance decisions as to what I am working on. I could be using a lot of approximation operations for random creativity, and I wanna know just what combinations of these operations are definitely leading to trouble, fixing them up to have less fitting issues etc…
So I’ll start with what I know, and anyone whom contributes would be be super awesome. I am making all kinds of mindmaps for nearly everything in Rhino to help me understand, and so far it has helped out a lot. Along with study software/quizzes, diagrams, databasing quizzes/types/options to search them in need with my own words/combinations of all sources, tasklist software, mindmaps to categorize things, I can learn Rhino. With plain notes, I have no shot!
So categorizing things such everything relating to input, constraints, mouse constraints, selection filters, coordinates and working them out visually in a mindmap, can aid in my progress. I could post em, and I could post some ones I already made but wouldn’t really be sure where to do so appropriately.
To cross categorize everything will help me a lot. I could update the post if people wanna contribute, and then eventually mindmap with pertinent information. It will also be including anything I can find about closed polysurfaces, joining naked edges, importing tolerance related, prepreparing for 3d printing/Cnc , etc…
Items ???, and list these items at the bottom of category lists
before will denote not sure and listed but not sure for correction
to help and fix the answer, copy/paste the whole lists and add === to the right of the command/type of command in question as well as feeling free to add information you know relating to:
(And subject to heavy review, please chime), question commands with ??? list at bottom of lists please
(Any plugin commands are also appreciated)
Related info such as:
 How the approximation works
 Related Issues regarding tolerances, and joining operations
List of Exact Operations
Points
Radius
Object Snaps
????? **Edges**
List of Approximate Operations
Smash
Offsets
Offset
OffsetcrvonSrf
OffsetMesh
OffsetNormal
ptOffsetEdges
ptOffsetPoints
ptOffsetBorder
VariableOffsetSrf
???ptOffsetgridbyheightfield
Projects
Project
ProjectToCplane
**Fillets**
**Sweeps**
**Trimming +
Trimming Related +
Commands Affected Downstream**
–Trim surface
TrimAtline
TrimAtSurface
MaqueTools
Trim curves inside/outside boundaries 1, 2, and 3. (3 diff commands, same name)
Osnaps
???projectOsnap
Deformation Tools
**???Twist**
**???Stretch**
**???Bend**
**???Taper**
**???Maelstrom**
**???FlowAlongSurface**
**???FlowAlongCurve**
**???Orient Tools**
???Orient
???Orient3Pt
???OrientOnSrf
???OrientOnCrv
???Orient perpendicular to curve
???Orient curve to edge
???RemapToCplane
???Curve Tools
???_Extend to boundaries, surface, by arc
anything involving from or to other curves,etc…
_connect
_Join
**Moving Tools**
Line Tools
anything involving tangent and perpendicular to or from curves
But the main part, is if I can understand how rhino approximates and tolerance, and directions, etc…it will help me tremendously as I continue to learn Rhino.