### Alex Januszkiewicz's Article On AutoCad Accuracy

Many designers using CAD today don't fully realize the magnitude of accuracy provided by AutoCAD. Often in the past I could hear polemics, where Intergraph IGDS and Microstation users were "proving" that "their" software is better in all respects, one of them being accuracy. This was never the truth, as even in its infancy, in early eighties, AutoCAD was using double precision floating numbers to store and process DWG data, where IGDS was using 32 bit integer cube to define space positioning of its elements.

Read on, and once you are through, download SOLAR.DWG and go on your interplanetary trip to witness AutoCAD accuracy :)

How much more precise is double precision number than 32 bit integer?
Double precision number uses 64 bits (8 bytes) to represent single floating point number, twice as much as 32 bit integer. Of these 64 bits, one is used for sign, 11 are used for exponent and 52 are used to define mantissa

Graphical representation of such 64 bit number would be:

S EEEEEEEEEEE FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

where:-
S - sign bit, 1 means negative, 0 positive
E - each E means one bit of exponent. 11 bit number can represent values from -1022 to 1023
F - each F represents one bit of a mantissa. 52 bit mantissa can represent 4503599627370496 fractions.

32 bit integer cube can represent  4294967296 discrete points in each of three directions.

Below is a translation of what these numbers will mean to processing and storage of CAD entities.

If you try to do a drawing that extends 4 km in each direction, Microstation's 32 bit format will limit your accuracy to 0.001 mm. The same size AutoCAD drawing can be drawn with an accuracy of 0.000000001 mm, that is one million times more accurate.

One could say "a certain level of accuracy is high enough and more is overkill, so what?". But be aware that with almost EVERY geometrical operation performed on an entity, the accuracy is reduced. When entities are moved, rotated, scaled and stretched etc., complex mathematical transformations are being applied to their geometry. The results are stored back in the drawing database in AutoCAD with double precision floating point accuracy and in Microstation with 32 bit integer accuracy. Both math transformation and storage, are REDUCING accuracy of a drawing. Where an AutoCAD user can safely ignore 3 or 4 significant digit reduction in accuracy on the drawing that has been modified many times over the years (it still has 12 precise digits), the same cannot be said about Microstation that has maximum of 10 precise digits and loses 3 of them in complex processing.

To showcase the power of AutoCAD, Autodesk included in earlier releases of AutoCAD (up to R12 I think) the simple, yet very impressive, 2D drawing file SOLAR.DWG (drawn in 1983 by John Walker, co-founder of Autodesk). You can download this file below (when you finish reading ;).

I will always remember my first "interplanetary" DWG travel that I did in 1985, after learning how to zoom:

• after you open the drawing, you are looking at whole solar system from outer space, drawn to scale in kilometers as DWG units
• zooming into blob at the center reveals inner solar system with few orbits, 3-rd of them being Earth's, Sun in the center.
• On Earth orbit you can see small flickering dot. Zoom in on it, the larger circle is Moon's orbit around Earth, the dot in the middle is Earth.
• On Moon's orbit you can see flickering dot. Zoom in on it, it's Moon
• On Moon you can see flickering dot. Zoom in on it, you will see the crater
• Near the crater (200 meters from it) you can see small green item. Zoom on it, it's LEM, landing module that brought Neil Armstrong and his colleagues to the Moon.
• On the leg of LEM you can see 30cm plaque. Zoom in on it and you can read the message:
HERE MEN FROM THE PLANET EARTH FIRST SET FOOT UPON THE MOON etc. signed by the three astronauts and President Nixon.

One day, when I have some time I'll add solar.dwg screen shots to this web page.

Now download SOLAR.ZIP (4kb zipped which becomes SOLAR.DWG unzipped ..don't worry, it's just 10kB, in 1985 my computer had 20MB hard disk and "huge" CAD files where 200kB). So start your (CAD) engine up and take off on your interplanetary trip. Let me know how it went when you come back. (Sadly this is no longer possible. The Creator in his infinite wisdom has taken Jack to be by His side. -AJ)

For Microstation accuracy believers, with all their tools starting with "ACCU", for accurate ;) I propose the following form of treatment:
Try to replicate SOLAR.DWG (drawn on AutoCAD in 1983!!!), make it into SOLAR.DGN ;) with today's latest Microstation. The 20 year old, 64 bit double precision DWG, can have everything in Solar System positioned with accuracy of few millimeters (you can read 3.7mm text on a plaque). While with DGN, the smallest item that can be drawn in this drawing (showing orbit of Pluto,  11916840000 km diameter) is a 3 kilometers line, both endpoints being positioned with 3 kilometer "accuracy" in X,Y and Z direction.

Alex Januszkiewicz