  The advent of isogeometric analysis has prompted a need for methods to
generate Trivariate B-spline Solids (TBS) with positive Jacobian. However, it
is difficult to guarantee a positive Jacobian of a TBS since the geometric
pre-condition for ensuring the positive Jacobian is very complicated. In this
paper, we propose a method for generating TBSs with guaranteed positive
Jacobian. For the study, we used a tetrahedral (tet) mesh model and segmented
it into sub-volumes using the pillow operation. Then, to reduce the difficulty
in ensuring a positive Jacobian, we separately fitted the boundary curves and
surfaces and the sub-volumes using a geometric iterative fitting algorithm.
Finally, the smoothness between adjacent TBSs is improved. The experimental
examples presented in this paper demonstrate the effectiveness and efficiency
of the developed algorithm.
