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the renderer. Therefore, we do not need to update the surface mesh each time we
update the volumetric mesh.
Storing ξ requires four floating-point values per surface-mesh vertex. If the
surface mesh is dense, a tetrahedron may have many associated vertices. In this
case, we can save memory by computing the transformation T ( p ) of a point p ,as
shown in Equation (10.19).
Therefore, each time we want to update the surface mesh, we compute T
once for each tetrahedron e and the new position T ( p ) of all the surface vertices
associated with e using Equation (10.19). It should be noticed that C e changes
in every iteration step and P e can be precomputed and stored. Now we have
to save 16 floating-point values per tetrahedron instead of four values per surface
Thanks to the nature of the operations used by the two processes described
above, we can dramatically speed-up our system if we perform all the operations
in the GPU. Due to space constraints, we are not going to describe the GPU algo-
rithm, but it can be obtained quite straightforwardly from the description made in
this section.
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