Rotating A Vector Around Another Vector

[hessiess]

Say I have a 2D vector 'C' which is located at (0,0), and a second 2D vector 'O' which should 'orbit' around 'C' at angle 'A' and at a distance of 'D'.

How would this be implemented? Preferably without using matrices, as they go strait over my head .

Thanks.

 

[fiveseven]

In 2D, a parametric equation somewhere along the lines of:

y=a + m*sin(T)
x=b + n*cos(T)

(a, b ) should be the coordinates of C, m and n being the distances (allows for elliptical orbits).

There are similar formulae for 3D, but I can't remember them off the top of my head.

EDIT: stopped b ) becoming a smiley face

 

[hessiess]

Thanks.

 

[bzar]

For all your coordinate system transformation needs:
http://en.wikipedia.org/wiki/List_of_canon...transformations

 

[sinoth]

Phew... I saw the thread title and thought I was gonna have to explain quaternions, but thankfully you wanted 2D. 3D rotation around an arbitrary axis is much more of a pain :/

 

[hessiess]

Phew... I saw the thread title and thought I was gonna have to explain quaternions, but thankfully you wanted 2D. 3D rotation around an arbitrary axis is much more of a pain :/

That's why im sticking to 2D for now, 3D maths is just so much more complicated. Im only just starting to understand 2D vector maths...

 

[.Gogeta§§J4BR.]

For all your coordinate system transformation needs:
http://en.wikipedia.org/wiki/List_of_canon...transformations


awwww I remember having to look at that same wikipedia page... I just don't remember what subject I was looking at that for (linear algebra, physics, calculus... many areas use them)
anyway, don't feel scared of 3D just because of that. your game idea is 2D, so no problem of doing it like that good luck

 

[hessiess]

Im having some issues with my rotation code:

CODE
bool dirswitch = false;
for(int vert = 0; vert < 4; vert ++)
{
// calculate the distance between the vert and the
// center of the quad
vector2d_f vert_offs;
vert_offs.X = 0 - data .vertices[vert].X;
vert_offs.Y = 0 - data .vertices[vert].Y;

// calculate rotated vertex location
vertex new_vert;

// fix problem with the veracities at opposite corners rotating in opposite directions
if(dirswitch == false)
{
dirswitch = true;
new_vert.X = vert_offs.X * cos(rotation *
(3.142/180));
new_vert.Y = vert_offs.Y * sin(rotation *
(3.142/180));
}
else
{
dirswitch = false;
new_vert.X = vert_offs.X * sin(rotation *
(3.142/180));
new_vert.Y = vert_offs.Y * cos(rotation *
(3.142/180));
}
// apply
data .vertices[vert] = new_vert;
}



If this is applied to a square, it works correctilly, however if it is applied to a rectangle

rotating by 45 degrees gives this, which is obviously wrong.

Thanks.

 

[multiplex]

I don't think that's right. For rotating a point around the origin, try something like:
CODE
vector2d_f rotate_point(vector2d_f old_point, float rotation)
{
vector2d_f new_point;
new_point.X = old_point.X * cos(rotation) - old_point.Y * sin(rotation);
new_point.Y = old_point.X * sin(rotation) + old_point.Y * cos(rotation);
return new_point;
}

(from http://en.wikipedia.org/wiki/Rotation_(mathematics) )

 

[Svartalf]

Phew... I saw the thread title and thought I was gonna have to explain quaternions, but thankfully you wanted 2D. 3D rotation around an arbitrary axis is much more of a pain :/

Yeah, I did the same sort of double-take. "Evil" doesn't even begin to describe that sort of computational task...

 

[fiveseven]

Actually, I believe there is a formula I learnt last year that makes orbits in 3D a lot simpler (although I never tried using it when programming ). When I can get to them, I'll have a dig through my old notes and see if I can find it.

 

[hessiess]

I don't think that's right. For rotating a point around the origin, try something like:
CODE
vector2d_f rotate_point(vector2d_f old_point, float rotation)
{
vector2d_f new_point;
new_point.X = old_point.X * cos(rotation) - old_point.Y * sin(rotation);
new_point.Y = old_point.X * sin(rotation) + old_point.Y * cos(rotation);
return new_point;
}

(from http://en.wikipedia.org/wiki/Rotation_(mathematics) )


Thanks allot, workers perfectly, and in vastly fewer lines of code. Though exactly how i managed to miss that wiki page while looking for a fix I honestly don't know.

QUOTE
Actually, I believe there is a formula I learnt last year that makes orbits in 3D a lot simpler (although I never tried using it when programming ). When I can get to them, I'll have a dig through my old notes and see if I can find it.


Sounds interesting, 3D that isn't dreadfully complicated

Is there any way to mark this topic as solved?