By Traina A.J.M.
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Extra resources for 3D Reconstruction of Tomographic Images Applied to Largely Spaced Slices
Thorne et al.  demonstrate motion doodles, a sketching interface for generating character motion. A continuous sequence of lines, arcs, and loops are parsed and mapped to a parameterized set of output motions that reflect the location and timing of the input character sketch (see Fig. 3). The system supports different types of motions in 2D and a subset of them in 3D. It is useful for fast creation and quick experimentation with various kinds of character motion. However, it cannot resolve ambiguities introduced by 3D mapping, and it is not suitable for animations that require unique or detailed motions.
If we augment this relationship by associating the zero vector with the identity rotation, the relationship is continuous and is known as the exponential map (see Appendix B for more details on the exponential map). The exponential map is used as it does not require repeated normalization (like quaternions) to stay in a meaningful subspace, and it results in smaller dimension state vectors, which leads to faster performance. It is simple to compute the Jacobian at a node in a transformation hierarchy with respect to all the end-effectors below it in the hierarchy.
The full projective camera is computed using the Normalized Direct Linear Transformation Algorithm and the affine camera is computed using the Gold Standard Algorithm (for further details see Appendix A and ). These are numerically robust techniques and work well with 40 3 View-Dependent Animation from Sketches (a) A sketch withrigidjoints marked (b) The corresponding joints marked on the skeleton Fig. 8. Marking of joint correspondences. hand-clicked correspondences. The weak perspective and orthographic cameras are recovered using techniques similar to those used for affine cameras.