| Orthogonal Shear-Warp Factorization | ||
|
The orthogonal Shear-Warp Algorithm produces an image
that shows the orthogonal projection of the volume
in its current position.
In the implementation for vuVolume first of all the viewing matrix had to be computed. This was neccessary because vuVolume only hands over the view-, up- and right-vectors that define the position of the eye relative to the volume (the distance between volume and eye was not given because this is not relevant for orthogonal viewing). The viewing matrix is computed as the matrix, that rotates the view vector first into the direction of the axis that encloses the minimal angle with this coordinate axis. For the rotation the cross product of view-vector and the main viewing axis is used as the rotation-axis. Then the up- and right-vectors are rotated into the right position. This time the main viewing direction is used as the axis of the rotation. The matrix that represents the above transformations is not the complete viewing matrix. What is missing, is the permutation of the coordinates. However in [2] exactly this viewing matrix without permutation (referred to as Mview') is used.
|
||
Factorization of the orthogonal viewing matrix
|
||
| The factors and values needed for shearing can directly be determined from Mview'. This is described in detail in [2]. |
|
back
main
