Local refinement for analysis-suitable++ T-splines

We develop an optimized local refinement algorithm for analysis-suitable++ T-splines (AS++ T-splines) which produces less propagation of control points. We then demonstrate its use as an adaptive framework for isogeometric analysis. AS++ T-splines are a class of T-splines which include analysis-suitable T-spline as a special case, are linearly independent, form a weighted partition of unity and are optimal convergent. These properties, coupled with the local refinement algorithm, make the AS++ T-spline appealing as a better basis both for design and analysis.