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Lesson 3-3
3D Coordinate system | Rotation in 3D
THE 3-D CO-ORDINATE SYSTEM
By now you should be very comfortable working your way around the X-Y coordinate
system. Anyway, here is a quick review. Looking from the plan (top) view, this is what you
see to figure out where is positive X and positive Y.
If you were to look at the same picture, but at a slight angle, you would see the third axis.
This new axis is called the Z-axis. Imagine that the positive Z-axis is coming towards you out
of the monitor.
The Z-axis has always been there, lurking in the background, waiting for you.
When you entered points previously, you would enter them in the format: X,Y. By doing this,
you let AutoCAD know that in these cases, Z was equal to zero. Entering 4,3 would be the
same as entering 4,3,0. Now if you drew a line from the origin (0,0,0) to a point at 4,3,2, you
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would get a line that goes 4 inches to the right, 3 inches up and 2 inches towards you. The
properties of this line would be this:
Notice that the line is actually 5.3852" long. If you were to look at it from the plan view, it
would look exactly like a line drawn from 0,0 to 4,3 Draw a line from 0,0 to 4,3 and then
compare the properties.
The diagrams below, show this line from 4 different views to illustrate how things can look
different in 3D. Look at each one carefully, and see if it makes sense to you.
This is the usual view you have
seen when using AutoCAD in 2D.
You are looking straight down the
Z axis (positive Z is pointing at
your). It looks like any other line
you have drawn, going from 0,0 to
4,3 - but there is a difference...
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If you were to look at the line from
the front, instead of the top (as
shown above) you would be able to
notice the elevation of 2 units in
the Z axis. This is the same line as
above, only viewed from a
different angle. In this view, you
are looking straight down the -Y
axis.
Just for fun, here is the same line
but viewed from the left. This
would be looking down the -X
axis.
Finally, here is the line as viewed
in 3D space from the Southeast
view. This is where viewing 3D
objects on a 2D monitor gets
tricky. You need to visualize the Z
Axis.
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What the above images show you is that you will have to get used to looking at a 3D world
on a 2D monitor. In each image, the black line looks flat, but you have to use your reference
points to determine where it truly is. If you don't understand this perfectly right now, don't
worry. It's just an exercise to expose you to 3D viewing. As the lessons progress, you will get
much more familiar to this.
Why is this important to look at before entering the world of 3-D? If you were to only
look at a 3-D model from the plan (top) view, you would not be able to see any difference
between the two lines. (Draw them and see for yourself) On a 3-D model, you can easily have
many points over top of each other. This would be very difficult to work with. You may think
you're snapping to a particular endpoint, but the reality of it could be very different (think of
how the top of the wall looks the same as the bottom of the wall if you're looking straight
down it). Fortunately, AutoCAD provides different viewing options for 3-D drafting. This
will be discussed in a later lesson, but for now, if you want to see your 2 lines in a view
similar the Z-Axis image above, go to your menu called View > 3D Views > SW Isometric.
You'll see the lines that look identical in the top view, look very different when viewed from
an angle.
3D Rotation
Now for the confusing part. You already know how to rotate 2D objects, but you also have to
know how AutoCAD measures angles of rotation in 3-D. There is a somewhat simple rule for
this called "The Right Hand Rule". To figure out which is the positive rotation angle, imagine
that you are wrapping your right hand around the axis with your thumb pointing towards the
positive end. The direction that your fingers are wrapped is the positive direction. This
applies to all three axes.
DIRECTION OF POSITIVE ROTATION
The main point of this lesson is to tell you that objects can trick you in 3D space. Shortcuts
don't always work, you have to be careful with Osnaps and your drawing can turn into a
mess very quickly if you're not paying attention. Trust me, I've seen enough students take
the easy route and have to start over. If you want to learn 3D, review each lesson before
progressing. Make sure you know the concepts inside and out. This is just an introduction to
the concepts, you will learn more in the following lessons. You may still want to refer back to
this tutorial, though.

Unformatted Attachment Preview

Lesson 3-3 3D Coordinate system | Rotation in 3D THE 3-D CO-ORDINATE SYSTEM By now you should be very comfortable working your way around the X-Y coordinate system. Anyway, here is a quick review. Looking from the plan (top) view, this is what you see to figure out where is positive X and positive Y. If you were to look at the same picture, but at a slight angle, you would see the third axis. This new axis is called the Z-axis. Imagine that the positive Z-axis is coming towards you out of the monitor. The Z-axis has always been there, lurking in the background, waiting for you. When you entered points previously, you would enter them in the format: X,Y. By doing this, you let AutoCAD know that in these cases, Z was equal to zero. Entering 4,3 would be the same as entering 4,3,0. Now if you drew a line from the origin (0,0,0) to a point at 4,3,2, you would get a line that goes 4 inches to the right, 3 inches up and 2 inches towards you. The properties of this line would be this: Notice that the line is actually 5.3852" long. If you were to look at it from the plan view, it would look exactly like a line drawn from 0,0 to 4,3 Draw a line from 0,0 to 4,3 and then compare the properties. The diagrams below, show this line from 4 different views to illustrate how things can look different in 3D. Look at each one carefully, and see if it makes sense to you. This is the usual view you have seen when using AutoCAD in 2D. You are looking straight down the Z axis (positive Z is pointing at your). It looks like any other line you have drawn, going from 0,0 to 4,3 - but there is a difference... If you were to look at the line from the front, instead of the top (as shown above) you would be able to notice the elevation of 2 units in the Z axis. This is the same line as above, only viewed from a different angle. In this view, you are looking straight down the -Y axis. Just for fun, here is the same line but viewed from the left. This would be looking down the -X axis. Finally, here is the line as viewed in 3D space from the Southeast view. This is where viewing 3D objects on a 2D monitor gets tricky. You need to visualize the Z Axis. What the above images show you is that you will have to get used to looking at a 3D world on a 2D monitor. In each image, the black line looks flat, but you have to use your reference points to determine where it truly is. If you don't understand this perfectly right now, don't worry. It's just an exercise to expose you to 3D viewing. As the lessons progress, you will get much more familiar to this. Why is this important to look at before entering the world of 3-D? If you were to only look at a 3-D model from the plan (top) view, you would not be able to see any difference between the two lines. (Draw them and see for yourself) On a 3-D model, you can easily have many points over top of each other. This would be very difficult to work with. You may think you're snapping to a particular endpoint, but the reality of it could be very different (think of how the top of the wall looks the same as the bottom of the wall if you're looking straight down it). Fortunately, AutoCAD provides different viewing options for 3-D drafting. This will be discussed in a later lesson, but for now, if you want to see your 2 lines in a view similar the Z-Axis image above, go to your menu called View > 3D Views > SW Isometric. You'll see the lines that look identical in the top view, look very different when viewed from an angle. 3D Rotation Now for the confusing part. You already know how to rotate 2D objects, but you also have to know how AutoCAD measures angles of rotation in 3-D. There is a somewhat simple rule for this called "The Right Hand Rule". To figure out which is the positive rotation angle, imagine that you are wrapping your right hand around the axis with your thumb pointing towards the positive end. The direction that your fingers are wrapped is the positive direction. This applies to all three axes. DIRECTION OF POSITIVE ROTATION The main point of this lesson is to tell you that objects can trick you in 3D space. Shortcuts don't always work, you have to be careful with Osnaps and your drawing can turn into a mess very quickly if you're not paying attention. Trust me, I've seen enough students take the easy route and have to start over. If you want to learn 3D, review each lesson before progressing. Make sure you know the concepts inside and out. This is just an introduction to the concepts, you will learn more in the following lessons. You may still want to refer back to this tutorial, though. Name: Description: ...
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