ok ill try to explain some:

We know this:

A = (0,0,-50)
B = (-175,300,-25)

Direction of A (calling it V):
V = (0,0,1)

You want to make V point from point A to point B, that mean that it should point in the same direction as this vector (W):

W = B - A = (-175 - 0, 300 - 0, -25 - (-50)) = (-175, 300, 25)

normalizing W :

sqrt((-175)^2 + 300^2 + 25^2) = 348.2097 ..the current lenght

dividing by its lenght to normalize it:

W /= 348.2097 (divide the x/y/z values by 348.2097)

now:

W = (-0.5025, 0.8615, 0.0717)

W is now normalized and pointing from object a towards object B

if you want to rotate V towards W gradually you need to rotate it about an axis that is orthogonal to both V and W (two vectors beeing orthogonal mean that the angle between them on 90degs (or PI/2))

To get this vector you simply cross V and W

U = V x W

then get the angle between V and W by acos''ing their dot product

angl = acos(V dot W)

to rotate it smoothly you can rotate it (about the axis U) by steps of about angl/10 each frame (during ten frames)

Hope this makes sense, ask if you think something is unclear

ok here is a function I made once that rotates a vector about an axis:

1)

    void rotVector( Vector3D &vect,  // In vector, will be modified                Vector3D axis,   // Axis of rotation                float    angle   // angle, how many radians will the vector be rotated              ){   float tx = vect.x;   float ty = vect.y;   float tz = vect.z;   float cosa = cos(angle);   float sina = sin(angle);   float cosb = 1.0 - cosa;	   float a, b, c;   float nmlz = sqrt((axis.x*axis.x)+(axis.y*axis.y)+(axis.z*axis.z));   if(nmlz > 0)   {      a = axis.x / nmlz;      b = axis.y / nmlz;      c = axis.z / nmlz;   }   else return;    vect.x = (tx*((a*a*cosb) + (  cosa))) + (ty*((a*b*cosb) - (c*sina))) + (tz*((a*c*cosb) + (b*sina)));   vect.y = (tx*((a*b*cosb) + (c*sina))) + (ty*((b*b*cosb) + (  cosa))) + (tz*((b*c*cosb) - (a*sina)));   vect.z = (tx*((a*c*cosb) - (b*sina))) + (ty*((b*c*cosb) + (a*sina))) + (tz*((c*c*cosb) + (  cosa)));}    

the Vector3D is just a struct or a class that contains x, y, z as float values

basically what youll do is to call the function ten times like this:

void rotVector( V, U, angl );

Some optimisations is probably possible, like saving the sin/cos values since they are the same all the ten times when the angle is the same

And the function normalizes the U vector, this wouldnt really have to be done more than once either.

2)

Ah yes, I should have mentioned that, in this special case it isnt just a vector that is orthogonal to both V and W, its an entire plane (this will only happen in rare cases btw since you are using float values).

So what to do then.. hmm I'm not sure if this is the best possible way but its all I could think of at the mo:

Create a new vector (P) that is

P = V + (0.6, 0.6, 0.04) (this will work unless V is exactly (0.6, 0.6, 0.04))

Then cross it with V into U

U = P x V

Then U is orthogonal to V, and thus also to W since the angle between V and W is PI

If it turns out htat V is exactly (0.6, 0.6, 0.04) then you can use for example (0.6, 0.04, 0.6)

hope that works hehe




Edited by - Jesper T on March 6, 2002 3:57:24 PM

np at all