zydgyy

12-10-2011, 03:50 AM

what is difference between these two terms??Or,they may be the same concept??Is there anybody can describe them?!Thanks~~~

View Full Version : Direction and orientation

zydgyy

12-10-2011, 03:50 AM

what is difference between these two terms??Or,they may be the same concept??Is there anybody can describe them?!Thanks~~~

BionicBytes

12-10-2011, 03:40 PM

I think the difference between them is really how they are used.

A direction applies to a vector when it is normalised.

If that direction vector is encoded into a matrix then that matrix could be used to orientate a model.

A direction applies to a vector when it is normalised.

If that direction vector is encoded into a matrix then that matrix could be used to orientate a model.

thokra

12-11-2011, 12:23 AM

Wait a second. In general, a specific orientation is the result of a rotation of some kind. If you turn your screen upside down you change its orientation. However, not every matrix is a rotation matrix.

A direction, either normalized or not, is just an interpretation of a vector, depending on the space that the vector is defined in. In R^3, you can interpret a vector either as position or direction. It's only when you use them in a certain context that the meaning is agreed upon. For instance, the difference of two positions is usually interpreted as a direction. You can also get different points by translating with the exact same direction. For instance

P' + D = P'

P2 + D = P2'

from which follows that

P != P2 -> P' != P2'

A position is also seen as the translation of the origin by a position vector. Still, the above are only geometric intrepretations of a vector. There is much more to vectors depending on the mathematical depth you're willing to endure.

A direction, either normalized or not, is just an interpretation of a vector, depending on the space that the vector is defined in. In R^3, you can interpret a vector either as position or direction. It's only when you use them in a certain context that the meaning is agreed upon. For instance, the difference of two positions is usually interpreted as a direction. You can also get different points by translating with the exact same direction. For instance

P' + D = P'

P2 + D = P2'

from which follows that

P != P2 -> P' != P2'

A position is also seen as the translation of the origin by a position vector. Still, the above are only geometric intrepretations of a vector. There is much more to vectors depending on the mathematical depth you're willing to endure.

tksuoran

12-11-2011, 12:43 AM

Orientation has more information than direction.

Direction can be specified with two spherical coordinates. Orientation can be specified with three euler angles.

Or using more common parametrizations: Direction can be represented with a vector, and orientation with axis vector plus rotation angle around that vector.

Most notably a direction vector alone does not define orientation.

Direction can be specified with two spherical coordinates. Orientation can be specified with three euler angles.

Or using more common parametrizations: Direction can be represented with a vector, and orientation with axis vector plus rotation angle around that vector.

Most notably a direction vector alone does not define orientation.

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