I am soooooooo confused by vector functions... Any one have any good
recourses for learning about these elusive features... vrotate,
vnormalize, vaxis_rotate ',

If this is out of place forgive and redirect me please... =]
here is a pic to hold my place in bin img... =]

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Are you joking?

Well.. Fortunately I don't have problems with vnormalize and vaxis_rotate,
but with other vector operations.. I'm just too afraid to ask..

Hugo

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If I can help let me know.
What about collecting your questions?
Then I (or anyone else) can and post a document answering all these
questions (as far as I am able to). Possibly in an other group (e.g.
newuser)?

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I think he did ask the questions.  He wants to know what the
aforementioned functions do and how to control them.

Juergen Scharfy wrote:

> If I can help let me know.
> What about collecting your questions?
> Then I (or anyone else) can and post a document answering all these
> questions (as far as I am able to). Possibly in an other group (e.g.
> newuser)?

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> I think he did ask the questions.  He wants to know what the
> aforementioned functions do and how to control them.

Yep. But maybe he wants to know more than just the few functions implemented
POVRay. Maybe some more on vector algebra?
I think it is more important to understand the vector algebra first before
looking at the implementation.

But anyway, the functions are at least a base for a discussion. Let's see if
I can write a short AND understandable explanation..... but for now I have
to do something else. It's on the list ;-)

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> Yep. But maybe he wants to know more than just the few functions
implemented
> POVRay. Maybe some more on vector algebra?
> I think it is more important to understand the vector algebra first before
> looking at the implementation.
>
> But anyway, the functions are at least a base for a discussion. Let's see
if
> I can write a short AND understandable explanation

Could you please tell about vector cross & dot products too, then?  :o)
I've read the Pov docs, and 2 webpages explaining their use in Pov, and I've
searched on math pages, but still don't understand.. I don't have a higher
mathematical education and until recently I didn't know how important the
origin <0,0,0> is regarding to vector functions.. Now I do know that
everything involves origin, but I still can't SEE in my mind the picture of
cross & dots.. The examples in Pov with 3 cylinders pointing in each their
way, doesn't help.. I tried animating them too but..

You could argue that I should take a further education, but I don't have
time for this (I have work, and would have to change my life drastically)
and I'd prefer to learn in my sparetime.. Any clear and throughfull
explanation in simple english will be appriciated!  :o)  When you have
time..


Regards,
Hugo

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"Hugo" <hua### [at] post3teledk> wrote :
>
> Could you please tell about vector cross & dot products too, then?  :o)

    I finally got what dot products were about a year ago. I don't know how
ignorant of them you are, but I had no clue. Here's what I finally figured
out.

    If you have a vector #declare v = <1,2,3>;
    Then v.x = 1, v.y = 2, v.z = 3.

    That was enough for me to move on with, but I'm still not sure what all
that cross stuff is about.

    HTH

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> Could you please tell about vector cross & dot products too, then?  :o)

The dot product is an scalar binary vector space inner product operator.
Don't get scared, that only means that it is a function that takes TWO
VECTORS and gives a NUMBER as a result.

The dot product is very important because it lets you find the angle between
two vectors, see if they are orthogonal (perpendicular), etc.
It is also very important because it lets you project a vector into a
plane... something like finding the "shadow" of a vector in a plane. It lets
you do many things!

If we have two 3d vectors: A=(a1,a2,a3), B=(b1,b2,b3), you can compute it's
dot product in two alternative but equivalent ways:

1) A dot B = a1*b1 + a2*b2 + a3*b3
2) A dot B = |A|*|B|*cos(theta)

where theta is the angle (in radians!) between A and B. And |A| is the
euclidean norm (length) of A defined by

|A|=sqrt(a1^2 + a2^2 + a3^2)

So, if A and B are orthogonal (perpendicular), then cos(theta)=0 and then
the dot product is equal to zero.

Now, the cross product, is a function that takes TWO VECTORS and gives a
VECTOR as a result. The most important characteristic from the cross product
is that the resulting vector is orthogonal to the other two original
vectors. And that's very useful for finding normal vectors, and other
things.

The computation is more cumbersome (although there is a trick to memorize it
using a determinant, but I won't state it):

if A cross B = C = [c1,c2,c3] then

c1 = a2*b3 - a3*b2
c2 = a3*b1 - a1*b3
c3 = a1*b2 - a2*b1

As you can prove easily, the resulting vector C is orthogonal to A and B
(using dot product and a little of algebra)

Well, I hope I made myself clear and help you out of this,

Fernando.

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Wasn't it Bill DeWitt who wrote:
>
>"Hugo" <hua### [at] post3teledk> wrote :
>>
>> Could you please tell about vector cross & dot products too, then?  :o)
>
>    I finally got what dot products were about a year ago. I don't know how
>ignorant of them you are, but I had no clue. Here's what I finally figured
>out.
>
>    If you have a vector #declare v = <1,2,3>;
>    Then v.x = 1, v.y = 2, v.z = 3.

I guess that's a joke, but just in case your serious, the POV dot
operator (which is what you have there) is a completely different thing
from the vector dot product (which you can calculate with the "vdot()"
vector function).

-- 
Mike Williams
Gentleman of Leisure

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This is basically what i am looking for... Thank you... =]
I'm glad that someone mentioned the rest of the functions for i am only just
beginning to understand the vrotate and they are all equally as confusing as
the next...



> > Could you please tell about vector cross & dot products too, then?  :o)
>
> The dot product is an scalar binary vector space inner product operator.
> Don't get scared, that only means that it is a function that takes TWO
> VECTORS and gives a NUMBER as a result.
>
> The dot product is very important because it lets you find the angle between
> two vectors, see if they are orthogonal (perpendicular), etc.
> It is also very important because it lets you project a vector into a
> plane... something like finding the "shadow" of a vector in a plane. It lets
> you do many things!
>
> If we have two 3d vectors: A=(a1,a2,a3), B=(b1,b2,b3), you can compute it's
> dot product in two alternative but equivalent ways:
>
> 1) A dot B = a1*b1 + a2*b2 + a3*b3
> 2) A dot B = |A|*|B|*cos(theta)
>
> where theta is the angle (in radians!) between A and B. And |A| is the
> euclidean norm (length) of A defined by
>
> |A|=sqrt(a1^2 + a2^2 + a3^2)
>
> So, if A and B are orthogonal (perpendicular), then cos(theta)=0 and then
> the dot product is equal to zero.
>
> Now, the cross product, is a function that takes TWO VECTORS and gives a
> VECTOR as a result. The most important characteristic from the cross product
> is that the resulting vector is orthogonal to the other two original
> vectors. And that's very useful for finding normal vectors, and other
> things.
>
> The computation is more cumbersome (although there is a trick to memorize it
> using a determinant, but I won't state it):
>
> if A cross B = C = [c1,c2,c3] then
>
> c1 = a2*b3 - a3*b2
> c2 = a3*b1 - a1*b3
> c3 = a1*b2 - a2*b1
>
> As you can prove easily, the resulting vector C is orthogonal to A and B
> (using dot product and a little of algebra)
>
> Well, I hope I made myself clear and help you out of this,
>
> Fernando.

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