“Direction of rotation” isn’t a well defined concept. Imagine a spinning jack (a.k.a. knucklebone). At the moment that one of the arms is pointing north, that arm is tangentially moving east-west. At the same time, the next arm is pointing east and moving tangentially north-south, another arm is point south and moving west-east, and the last arm is pointing east and moving south-north.
The closest thing to describing the “direction” of a rotation is the axis vector, similar to the way we use the normal vector to define a plane. gray From: [email protected] [mailto:[email protected]] On Behalf Of Rob Chapman Sent: Tuesday, March 05, 2013 01:48 PM To: [email protected] Subject: Re: Orientation and vectors, foundations ah I see where your going with this Andy, so how can I get a particles rotation into a current direction of rotation vector? say its spinning or 'tumbling' how to get the vector to rotate with it. I was thinking an 'up vector' but particles dont have them On 5 March 2013 19:33, Grahame Fuller <[email protected]<mailto:[email protected]>> wrote: A particle's orientation is its offset in rotation relative to the point cloud's local reference frame. If as is typical, you leave the point cloud untransformed, then this is the same as its offset in rotation relative to the scene's global reference frame. The orientation is expressed as a rotation in axis and angle form, i.e., [X, Y, Z] coordinates that define a vector relative to the point cloud, and an angle of rotation around that vector. Axis and angle is just one of several ways to represent a rotation. The other ways that are available in ICE are Euler angles, quaternions, and matrices (but be aware that in general 3x3 matrices represent both rotation and scaling, and 4x4 matrices represent rotation, scaling, and translation, so be careful when using them in case you inadvertently apply more than just rotation). Each of these formats has advantages and disadvantages in different situations. There are nodes that can convert between them as required. Axis and angle was chosen to represent orientation and other rotations after some discussion on the Ariane beta list. It was felt to be fairly intuitive for artists, and is fairly easy to use in computations (or at least, easy to convert under the hood to a format that is useful for computations). As with transforms in general, rotations can be used to manipulate vectors and positions, or to convert between reference frames, among other things. It depends on the problem you are trying to solve and how it is framed. gray From: [email protected]<mailto:[email protected]> [mailto:[email protected]<mailto:[email protected]>] On Behalf Of Andy Moorer Sent: Tuesday, March 05, 2013 12:58 PM To: [email protected]<mailto:[email protected]> Subject: Orientation and vectors, foundations Hi all, As I was working today I realized that despite doing operations on ice "orientations" regularly I don't have a firm grasp on what they really are. Orientation relative to what? And what form is this orientation in? Trying to phrase it differently... How is a particle's "orientation" different from a 3x3 matrix describing the difference in rotation between it's local coordinate space and the global frame of reference? Both are clearly descriptions of the same thing. I know this is kind of an abstract subject, and (being tired at the moment) my question may not even be clear, but being self-taught and lacking adequate formal math education I'd be very interested in your answers and any discussion in general on how you all visualize rotations and orientation, For some people I talk to about rotations (I'm the life of any party) it seems to be all about manipulating vectors, others seem more comfortable thinking about rotations as transformations between reference frames... and I see a similar wide range of how people go about some of this stuff when looking into various compounds.
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