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### Is there a collective name for a vector and a point?

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I am not sure if this is entirely on-topic, but I figured such a thing
had to exist for computer graphics.

Is there a name for a vector and a point that it passes through?
Effectively, such an object would store both a position and a
direction.
 0
Reply raphfrk (53) 12/17/2011 11:31:07 AM

See related articles to this posting

On 2011-12-17, raphfrk@gmail.com <raphfrk@gmail.com> wrote:
> I am not sure if this is entirely on-topic, but I figured such a thing
> had to exist for computer graphics.
>
> Is there a name for a vector and a point that it passes through?
> Effectively, such an object would store both a position and a
> direction.

A ray ?

Btw a point is also represented by a vector. A vector isn't a direction,
it's an n-tuple which can be used to *represent* directions, or
cartesian points, or whatever.

--
John Tsiombikas
http://nuclear.mutantstargoat.com/
 0
Reply nuclear6 (34) 12/17/2011 11:47:01 AM

raphfrk@gmail.com wrote:

> I am not sure if this is entirely on-topic, but I figured such a thing
> had to exist for computer graphics.
>
> Is there a name for a vector and a point that it passes through?
> Effectively, such an object would store both a position and a
> direction.

If that line starts at the point and goes on forever in the direction of the
vector then I believe it is called ray or half-line.  Autocad uses the term
"ray" to refer to this sort of drawing object.

Rui Maciel
 0
Reply rui.maciel (1816) 12/17/2011 11:49:08 AM

Are you thinking of an "oriented point" -- a point with a normal?

--
Andy V
 0

Am 17 Dec 2011 11:47:01 GMT
schrieb John Tsiombikas <nuclear@member.fsf.org>:

> Btw a point is also represented by a vector. A vector isn't a
> direction, it's an n-tuple which can be used to *represent*
> directions, or cartesian points, or whatever.

A direction with length is one certain kind of vector, but there are
much more.

=46rom a purely mathematical point of view, a vector is simply an element
of a so called "vector space". A vector space is formed by a set of
linear independent bases (base vectors) which are compatible with the
calculation rules for vectors. In the most general case

Orthogonality: a . b =3D 0

Linear Independence: a, b linear independent if there is no lambda for
which lambda * a =3D b

Spatiality is turned into a vector space, by introducing base vectors
up, right, out (or any images of them mapped through a isomorphism, like
cyclical or cylindrical coordinates). In the case of a computer system
we have the up and right introduced by the signaling of the display
device. Out is a number in the depth buffer. Please take a minute and
think about it: The spatiality of a vector space arises, because we
first (axiomatically) introduce notions of spatial directions.

However there are as well vectors which are not spatial at all. For
example numbers itself are vectors (just think of the bits in a CPU
register, each bit being one element of the vector). Now think about
the definition of a vector space; we need a set of linear independent
base vectors. Certainly the powers of 2 are one set of base vectors,
but remember about dual spaces. Are the some fundamental base vectors
for numbers? Indeed there are: Prime numbers.

So what other vectors that are not spatial do we come across on a
regular base? Colors for sure. But also things like quantum states
apart from position and impulse, like spin. In engineering and physics
the spectrum of resonant modes and frequencies of a system.

Those are all vectors, but none of them is spatial.

Heck the elements and bases of a vector space don't need to be
ordinals, or even numerals at all. They may be things like furniture or
whatever.

So to answer the OPs question

| | Is there a name for a vector and a point that it passes through?

If we understand the term "vector" as "spatial direction", then in the
mathematical term it is either "a ray" or "a line":

p(tau) =3D r + v * tau

The distinction between ray and line lies in the range of tau

tau in [0, infinity] <-> ray
tau in [-infinity, infinity] <-> line
tau in [a, b] <-> line segment

Wolfgang

 0
Reply wdraxinger (438) 12/18/2011 12:35:46 AM

On Dec 17, 1:31=A0pm, "raph...@gmail.com" <raph...@gmail.com> wrote:
> I am not sure if this is entirely on-topic, but I figured such a thing
> had to exist for computer graphics.
>
> Is there a name for a vector and a point that it passes through?
> Effectively, such an object would store both a position and a
> direction.

A tuple.Don't use it. ;)
 0
Reply jukka (294) 12/18/2011 2:40:32 AM

hanukas wrote:

> On Dec 17, 1:31 pm, "raph...@gmail.com" <raph...@gmail.com> wrote:
>> I am not sure if this is entirely on-topic, but I figured such a thing
>> had to exist for computer graphics.
>>
>> Is there a name for a vector and a point that it passes through?
>> Effectively, such an object would store both a position and a
>> direction.
>
> A tuple.Don't use it. ;)

A vector is a bit more than a mere tuple.

Rui Maciel
 0
Reply rui.maciel (1816) 12/18/2011 12:37:55 PM

On Dec 17, 3:16=A0pm, Andy V <vesper.spamonly.and...@gmail.com> wrote:
> Are you thinking of an "oriented point" -- a point with a normal?
>
> --
> Andy V

Yes, the direction would be a unit vector.

I am thinking Ray sounds good actually.

Point -> 3d position
Ray -> Point + unit direction vector
? -> Point + unit direction + scaling factor (3d)

Next, I need a name for a Ray + 3d scaling.
 0
Reply raphfrk (53) 12/18/2011 2:15:36 PM

On 2011-12-18, raphfrk@gmail.com <raphfrk@gmail.com> wrote:
>
> I am thinking Ray sounds good actually.
>
> Point -> 3d position
> Ray -> Point + unit direction vector
> ? -> Point + unit direction + scaling factor (3d)
>
> Next, I need a name for a Ray + 3d scaling.

Wether you use unit direction vector with separate magnitude, or just a
direction vector with the particular magnitude is a matter of
convention. The only real difference being how you treat parametric
distances along the ray. I.e. in one case they would be values in the
interval [0, 1] while in the other case they would be values in the
interval [0, magnitude].

So my point is, they're both called rays.

--
John Tsiombikas
http://nuclear.mutantstargoat.com/
 0
Reply nuclear6 (34) 12/18/2011 2:57:23 PM

raphfrk@gmail.com wrote:

> Yes, the direction would be a unit vector.
>
> I am thinking Ray sounds good actually.
>
> Point -> 3d position
> Ray -> Point + unit direction vector
> ? -> Point + unit direction + scaling factor (3d)
>
> Next, I need a name for a Ray + 3d scaling.

If we take the parametric definition of a line as being:

l = p + k*v

with:
p: point
v: direction vector
k: real number

then the parametric definition of a ray is:

r = p + l*v

with:
p: point
v: direction vector
l: non-negative real number

Rui Maciel
 0
Reply rui.maciel (1816) 12/18/2011 5:23:28 PM

On Dec 18, 2:57=A0pm, John Tsiombikas <nucl...@member.fsf.org> wrote:
> Wether you use unit direction vector with separate magnitude, or just a
> direction vector with the particular magnitude is a matter of
> convention.

Sorry, it was a separate scaling parameter.  The object would have a
position, size and would be scaled in x, y and z.

I am thinking about ScaledRay ... but the ray isn't really scaled.
 0
Reply raphfrk (53) 12/18/2011 5:33:44 PM

On Dec 18, 2:37=A0pm, Rui Maciel <rui.mac...@gmail.com> wrote:
> hanukas wrote:
> > On Dec 17, 1:31 pm, "raph...@gmail.com" <raph...@gmail.com> wrote:
> >> I am not sure if this is entirely on-topic, but I figured such a thing
> >> had to exist for computer graphics.
>
> >> Is there a name for a vector and a point that it passes through?
> >> Effectively, such an object would store both a position and a
> >> direction.
>
> > A tuple.Don't use it. ;)
>
> A vector is a bit more than a mere tuple.
>
> Rui Maciel

Yeah, and points don't pass through vectors.. this thread is from the
twilight zone. From storage point of view my statement at least makes
a resemblance of sense. <insert a LOL here>

 0
Reply jukka (294) 12/19/2011 6:58:24 AM

On Dec 17, 1:31=A0pm, "raph...@gmail.com" <raph...@gmail.com> wrote:
> I am not sure if this is entirely on-topic, but I figured such a thing
> had to exist for computer graphics.
>
> Is there a name for a vector and a point that it passes through?
> Effectively, such an object would store both a position and a
> direction.

Vertices in meshes commonly have a position and normal.
 0
Reply jukka (294) 12/19/2011 7:03:29 AM

hanukas wrote:

> Yeah, and points don't pass through vectors..

If you read the thread you will notice that you were the only one who
suggested that points pass through vectors.

<snip/>

Rui Maciel
 0
Reply rui.maciel (1816) 12/19/2011 12:15:06 PM

John Tsiombikas wrote:

> Wether you use unit direction vector with separate magnitude, or just a
> direction vector with the particular magnitude is a matter of
> convention. The only real difference being how you treat parametric
> distances along the ray. I.e. in one case they would be values in the
> interval [0, 1] while in the other case they would be values in the
> interval [0, magnitude].
>
> So my point is, they're both called rays.

If the parameter used in a parametric definition of a line is limited to an
interval, such as [0,1], then we aren't defining a ray, only a line segment.

Rui Maciel
 0
Reply rui.maciel (1816) 12/19/2011 12:19:20 PM

On 2011-12-19, Rui Maciel <rui.maciel@gmail.com> wrote:
> John Tsiombikas wrote:
>
>> Wether you use unit direction vector with separate magnitude, or just a
>> direction vector with the particular magnitude is a matter of
>> convention. The only real difference being how you treat parametric
>> distances along the ray. I.e. in one case they would be values in the
>> interval [0, 1] while in the other case they would be values in the
>> interval [0, magnitude].
>>
>> So my point is, they're both called rays.
>
> If the parameter used in a parametric definition of a line is limited to an
> interval, such as [0,1], then we aren't defining a ray, only a line segment.

Rays in graphics always tend to be line segments with a start and an
end. Otherwise if we were to use strictly mathematical terms we only
have "half-lines" and "line segments".

--
John Tsiombikas
http://nuclear.mutantstargoat.com/
 0
Reply nuclear6 (34) 12/19/2011 1:32:08 PM

John Tsiombikas wrote:

> Rays in graphics always tend to be line segments with a start and an
> end. Otherwise if we were to use strictly mathematical terms we only
> have "half-lines" and "line segments".

It depends on what you mean by "in graphics" and what you mean by "always
tend".  As I've mentioned before, in autocad the ray drawing object
represents a ray, not a line segment.

And the terms "ray" and "half-line" are synonyms.

Rui Maciel
 0
Reply rui.maciel (1816) 12/19/2011 2:20:26 PM

On 2011-12-19, Rui Maciel <rui.maciel@gmail.com> wrote:
> John Tsiombikas wrote:
>
>> Rays in graphics always tend to be line segments with a start and an
>> end. Otherwise if we were to use strictly mathematical terms we only
>> have "half-lines" and "line segments".
>
> It depends on what you mean by "in graphics"

In "graphics algorithms", for instance raytracing.

--
John Tsiombikas
http://nuclear.mutantstargoat.com/
 0
Reply nuclear6 (34) 12/19/2011 6:31:01 PM

Euhm,

How about dick and clit ?

A diclit ! ;) :)

Bye,
Skybuck =D

wrote in message

I am not sure if this is entirely on-topic, but I figured such a thing
had to exist for computer graphics.

Is there a name for a vector and a point that it passes through?
Effectively, such an object would store both a position and a
direction.

 0
Reply Windows7IsOK (506) 12/20/2011 11:00:30 AM

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