difficult vector problem

Just make f the zero vector It will be orthogonal to b and |v+f|=|v|=|n| will be true.

v, b, f are calculated every frame and vary.
You cannot change them to get the solution to my problem.
However b is perpendicular f and don''t forget the component parallel to b must be the same for v and n.

Any answers guys

-CProgrammer

quote:

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Original post by CProgrammer
n = v+f;
|n| = |v|

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n = v+f;

lenV = v.length();
lenN = n.length();

n *= lenV/lenN;

if this vector n doesn''t fulfill your other requests, you can''t solve all your requests anyway...

Sorry thats not it either cause n doesnt have the same projection onto b as v does in your answer.
I think one must find a vector x which when added to the parallel komponent of n equals n(scaled). In addition one finds multiple equations and then uses these to specifie x;
But I can''t figure it out.

quote:

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if this vector n doesn''t fulfill your other requests, you can''t solve all your requests anyway...

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OmniBrain:Well I think theres a soulution but i have no garanty on that.

-CProgrammer
My Website

Youre right scaling was a bad therm.
I just want n to be modifed in such a way that the requests are met. In what way doesn''t matter.

You have an infinite number of solutions.
n.b = v.b constrains n to lie in the same plane as v with b as its normal. The constraint n = v + f with f orthogonal to b is automatically satisfied since n and v already lie in a plane perpendicular to b. The constraint |n| = |v| means n and v lie in a circle. Thus n = v is a solution, and so is n = 2(b.v/b.b)b - v. In 2d, these are the only solutions, otherwise you have the whole circle.
Do you have any more constraints, or more information about the problem?

"Math is hard" -Barbie

I''m confused as to why OmniBrain''s answer isn''t right. |n*|v|/|n||=|v|. So if n=|v|*(v+f)/|(v+f) then |n|=|v|. If n=v+f and you want |n|=|v|, but don''t want to change n, v or f then it is either true or it isn''t. It will only be true if (f/2).(v-f/2)=0. Then |f| is the base of an isoceles trangle, |v-f/2| is its height and the angle between them is 90 degrees.

You have |n | = |v | = |v + f |

Another way of writing this is

v .v = (v + f ).(v + f )

or v .f = 0.5 * |f |²

Is this satisfied for your given f and v ?

If so, then n = (v .b ) b / |b | - (v .f ) f / |f | should do it.

Edit: oops, this is what LilBudyWizer said

[edited by - sQuid on February 28, 2003 11:00:44 PM]

LilBudyWizer: The reason why OmniBrains and your solution are not what im looking for is the following:

First of i am talking of 3d-Vectors here i guess i wasn''t to clear on that my apologizes.
Secondly the equation:
n=|v|*(v+f)/|(v+f)
meets |n|=|v|
however not my second request:
the komponent of the vector v parallel to b must have the same Length as that of n parallel to b.
In other words:
|proj_b_v| = |proj_b_n|
|v.b|/|b|=|n.b|/|b|

I think this part was misunderstood:
n = v+f;

After assigning n this value n must be MODFIED to meet the requests. Being |n| = |v| it should then NOT be |n| = |v+f|
this should no longer be true due to the modification.
|n| = |v| and |proj_b_v| = |proj_b_n| should be true for the modified n. The reason i want n modified to the givin requests is cause the more similar n is to v+f with the requests the better.

Thanks for all the replies
Hope its clearer now

-CProgrammer

My first answer was just a joke and a mistaken conclusion from the problem statement. I also mistakenly assumed the last part of an observation to assist in solving the problem rather than a condition of the solution and ignored it.

I think you are going to need to restate the problem to get a solution. It might help to explain it in terms of what you are trying to accomplish rather than mathematical properties of the solution. You are doing a simulation and how does this fit in. Is v your velocity, f a force, b your binormal and n your normal? If so then f seems to point the wrong direction. n should point to the outside of the curve while f points to the inside.

The simulation shows the movement of an electron in the field of two point like magnets.
v is the velocity
f is the Lorenz force
b is the vector specifieng strength of magnet and direction in the given frame.
n is the new velocity vector after all effects have taken place.

Calculating this problem with physical standards does not work. The resulting vector using the standard proceadure of physiks is n.
n = v+f/m*deltaT;
where m is the mass of an elektron.
To simplify i made m and deltaT 1 so
n = v+f;
f, b are calculated every frame and are therefore given.

all i want now is that n be changed to meet the demands, for through only doing v+f n will increase in length every frame. If i only scale it to v''s length it slows down in the parallel direction to b.
Therefore n must be changed to meet the two requests.

Hope its clear now.

-CProgrammer

The problem is inherent to your usage of Euler integration, which doesn't take into accout the effects of the force field on the path between two frames.

V = (vx, 0, vz)
B = (0, 0, 1 )
q = 1
m = 1

Thus F = q V*B = (0, vx, 0)
Apply the force over a duration t.

V' = (vx, vx*t, vz)

Scaling V' back to V will unfortunately affect vz too.

The only real solution is to use a better numeric integration method. Fourth-order Runge-Kutta is typically used in such cases. Look it up in any good numerical methods textbook.

However, a ugly hack, which will only work in this very specific case exists : work with the projection of V onto the plance normal to B.

V_b = B*(V.B)/|B|^2
V₁ = V - Vb
V₂ = V₁ + F
V₃ = V₂ * |V₁|/|V₂|
V' = V₃ + Vb

It will break pathetically (or rather, produce completely wrong results) if your magnetic field is non-uniform. (And don't forget to take into account the field produced by the moving particle itself ... aaaaah the joys of electrodynamics )

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[edited by - Fruny on March 1, 2003 11:23:25 PM]

[edited by - Fruny on March 1, 2003 11:29:06 PM]

Thanks Fruny.
The magnetic field is non-uniform.
Thanks for the tip i''ll look up
Fourth-order Runge-Kutta
and i''ll try to figure it out with that.

-CProgrammer

Oh by the way. In case anybody has a good website on runge kutta or a good example source code similar to my problem please tell me.

-CProgrammer