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

Constructing Trivariate B-splines with Positive Jacobian by Pillow Operation and Geometric Iterative Fitting