What are the proper terms for these concepts?

[Daniel Pitts]

I have a few concepts in a program I'm writing, but I'm not sure if
there are "canonical" terms for them, and would like to use those terms
if possible. All these terms are for 2 dimensional shapes, but if there
is a more general term for n dimensional I'd be interested in that as
well, just for knowledge sake.

In my codebase, it makes sense to distinguish between an absolute angle
and a relative angle. Absolute angles are really relative to the fixed
"east" vector, and Relative angles are clockwise or counter-clockwise
rotations. You can scale relative angles, but not absolute angles. You
can add relative angles to each other or to absolute angles, but
absolute angles can't be added to each other. You can find a relative
angle between two absolute angles. Is there a more formal concept of this?

One thing I'm calling an "angle bracket", which is basically two angles,
the absolute angle "clockwise-bound" and the relative angle "width".
This can include a zero width bracket (basically just a ray), or an all
inclusive bracket.

If I add a radius to that (to make it a pie slice), the term I found is
"sector". Is a full circle also a "sector"? How about if the angle is zero?

Thanks in advance,
Daniel.

 

[Lew]

I have a few concepts in a program I'm writing, but I'm not sure if
there are "canonical" terms for them, and would like to use those terms
if possible. All these terms are for 2 dimensional shapes, but if there
is a more general term for n dimensional I'd be interested in that as
well, just for knowledge sake.

In my codebase, it makes sense to distinguish between an absolute angle
and a relative angle. Absolute angles are really relative to the fixed
"east" vector, and Relative angles are clockwise or counter-clockwise
rotations. You can scale relative angles, but not absolute angles. You
can add relative angles to each other or to absolute angles, but
absolute angles can't be added to each other. You can find a relative
angle between two absolute angles. Is there a more formal concept of this?

One thing I'm calling an "angle bracket", which is basically two angles,
the absolute angle "clockwise-bound" and the relative angle "width".
This can include a zero width bracket (basically just a ray), or an all
inclusive bracket.

If I add a radius to that (to make it a pie slice), the term I found is
"sector". Is a full circle also a "sector"? How about if the angle is zero?

The term "bearing" comes to mind, and I recall "absolute" vs. "relative" - let me double check.
http://en.wikipedia.org/wiki/Bearing_(navigation)
http://en.wikipedia.org/wiki/Relative_bearing
http://en.wikipedia.org/wiki/Absolute_bearing

The term "bearing" matches what you want as the augend. The addend you want is "angle".

So you add an angle to a bearing to get a new bearing.

 

[Lew]

If I add a radius to that (to make it a pie slice), the term I found is
"sector". Is a full circle also a "sector"? How about if the angle is zero?

http://en.wikipedia.org/wiki/Circular_sector
Seems to say yes.

 

[Daniel Pitts]

The term "bearing" comes to mind, and I recall "absolute" vs. "relative" - let me double check.
http://en.wikipedia.org/wiki/Bearing_(navigation)
http://en.wikipedia.org/wiki/Relative_bearing
http://en.wikipedia.org/wiki/Absolute_bearing

The term "bearing" matches what you want as the augend. The addend you want is "angle".

So you add an angle to a bearing to get a new bearing.

Ah, that actually makes a lot of sense, and generally that matches the
use of the value. It is use for things such as the heading of a robot,
missile, or other simulated item.

 

[Lew]

Ah, that actually makes a lot of sense, and generally that matches the
use of the value. It is use for things such as the heading of a robot,
missile, or other simulated item.

There's some code to model in Robocode:
<http://robocode.sourceforge.net/>

 

[Alex]

Seems to me that "polar angle" might be the mathematical term for an
absolute angle. It works in 3 dimensions as well (aka Zenith angle in
that context).

http://mathworld.wolfram.com/PolarAngle.html

Alex

 

[John B. Matthews]

On 3/13/12 11:25 AM, Lew wrote: [...]

The term "bearing" comes to mind, and I recall "absolute" vs. "relative" -
let me double check.
http://en.wikipedia.org/wiki/Bearing_(navigation)
http://en.wikipedia.org/wiki/Relative_bearing
http://en.wikipedia.org/wiki/Absolute_bearing

The term "bearing" matches what you want as the augend. The addend
you want is "angle".

So you add an angle to a bearing to get a new bearing.

Ah, that actually makes a lot of sense, and generally that matches
the use of the value. It is use for things such as the heading of a
robot, missile, or other simulated item.

It may also be important to distinguish between mathematical (counter-
clockwise from the positive x-axis) and navigational (clockwise from the
positive y-axis) conventions, as suggested in this example:

<http://stackoverflow.com/a/3467341/230513>

 

[Daniel Pitts]

On 3/13/12 11:25 AM, Lew wrote: [...]

The term "bearing" comes to mind, and I recall "absolute" vs. "relative" -
let me double check.
http://en.wikipedia.org/wiki/Bearing_(navigation)
http://en.wikipedia.org/wiki/Relative_bearing
http://en.wikipedia.org/wiki/Absolute_bearing

The term "bearing" matches what you want as the augend. The addend
you want is "angle".

So you add an angle to a bearing to get a new bearing.

Ah, that actually makes a lot of sense, and generally that matches
the use of the value. It is use for things such as the heading of a
robot, missile, or other simulated item.

It may also be important to distinguish between mathematical (counter-
clockwise from the positive x-axis) and navigational (clockwise from the
positive y-axis) conventions, as suggested in this example:

<http://stackoverflow.com/a/3467341/230513>

This is actually why I use the abstractions I do, there are no
constructors for AbsoluteAngle or RelativeAngle, only factory methods
clockwiseRadians, counterClockwiseRadians, etc...

The simulated robots do have a different convention (it may be somewhat
standard navigational). They don't use standard units though, they use a
single unsigned byte to represent angle: 0 is NORTH, 64 is EAST, 128 is
SOUTH, 192 is WEST. In my code, I call this "bygrees" (byte-degrees).

 

[Daniel Pitts]

There's some code to model in Robocode:
<http://robocode.sourceforge.net/>

There is also some code to model in my own project Lew
<https://sourceforge.net/projects/at-robots2-j/>

It's not quite release ready, but the simulation engine is complete, and
fairly modular. The UI requires some work, and is currently dependent on
IntelliJ IDEA to build. This is a rewrite, with permission, of an older
open-source game (written by Ed Toton III in Pascal).

I'm hoping to create a community around it, but its not quite ready for
that yet. My next goal is to create a tournament service so anyone can
submit a robot online to compete against the current champions.

Thanks,
Daniel.

 

[Roedy Green]

If I add a radius to that (to make it a pie slice), the term I found is
"sector". Is a full circle also a "sector"? How about if the angle is zero?

One place to look for terminology is Logo turtle graphics.

absolute angles might be called "headings"
relative angles might be called "rotations"

Other places to look for terminology:
aircraft navigation, naval navigation, GPS units, PostScript polygons.

I am big on a project glossary where the precise way you use such
terms is defined. So long as you are consistent, you could call them
peanuts and pickles and all would work out.

 

[Martin Gregorie]

Other places to look for terminology:
aircraft navigation,

Here the 'bearing' is the direction from the aircraft to an external
point. The bearing is expressed in degrees where 0=N, 90=E, 180=S and
270=W. If its undescribed or described as 'true', the reference line runs
through the geographic North Pole and if described as 'magnetic' the
reference line is through the magnetic North Pole.

'Heading' describes where the aircraft is pointing using the same units,
description and reference, so a heading of 90 means the aircraft is
pointing east.

'Track' or 'ground track' is similar to heading except that it refers to
the ground track of the aircraft and is not the same as the heading
unless the aircraft is flying parallel to the wind direction.

The wind direction is where the wind is coming from, so 45 is a north-
easterly and runways are named the same way except that the direction is
divided by 10 and rounded with a leading zero added if the result has
less then 2 digits, so a runway on which you take off to the NE is
referred to as 05.

naval navigation,

AFAIK this is the same as aviation usage except that what aircrew call
the 'track' is known as the 'course'.

 

[Lew]

Referenced by the links provided upthread.

Here the 'bearing' is the direction from the aircraft to an external
point. The bearing is expressed in degrees where 0=N, 90=E, 180=S and
270=W. If its undescribed or described as 'true', the reference line runs
through the geographic North Pole and if described as 'magnetic' the
reference line is through the magnetic North Pole.

Don't forget that that definition applies to absolute bearing. Relative bearing is taken from the craft's heading.

 

[Martin Gregorie]

Don't forget that that definition applies to absolute bearing. Relative
bearing is taken from the craft's heading.

Not necessarily. FLARM warnings show bearings that are always relative to
track because all it knows about the position and movement of the craft
its in derived from GPS: it knows its current 3D position and a movement
vector, i.e. ground track and ground speed. It makes no attempt to deduce
wind direction and so has no clue about the aircraft heading. I wouldn't
be surprised if other similar systems, e.g. TCAS, also report threat
bearings relative to track.