# Jana Vrablikova, Philipp Langgruber: Predavanji v okviru obiska avstrijskih kolegov

Ob obisku kolegov iz univerz Johannes Kepler Universität Linz in Carinthia University of Applied Sciences bosta na seminarju dve polurni predavanji.

**Jana Vrablikova: Arc spline approximation of planar swept volumes**

Given a planar object and a one parameter family of motions we define the swept volume to be the infinite union of the object transformed by each member of the family of motions. Sweeping has a wide variety of applications in the fields of motion planning, collision detection, CNC machining verification or geometric modeling.

In this talk, we focus on planar objects undergoing a rigid body motion. We approximate the motion by a piecewise rotational and translational motion and we show that such approximation converges quadratically. This approach simplifies the computation of the envelope of the swept volume and ensures that if the boundary of the moving object is an arc spline, then the envelope of the swept volume is also an arc spline.

Finally, we discuss some ideas on how to determine the envelope of a planar object undergoing a more general motion.

**Philipp Langgruber: C^1-smooth isogeometric splines on multipatch domains**

Isogeometric splines on multipatch domains are needed for the discretization of partial differential equations on general domains. However, achieving smoothness at extraordinary vertices (EVs) - while maintaining the approximation power - is a challenging problem. Several approaches for solving this problem have been explored in the rich literature on this topic.

We focus on a construction of Prautzsch, which is based on composing polynomial mappings with spline parameterizations. We show how to generate suitable basis functions in the vicinity of EVs and discuss the approximation power of the resulting spline space.