Partition of Unity Parametrics (PUP) is a new framework for modeling parametric curves and surfaces. As an extension of NURBS, PUPs are defined by replacing the weighted basis functions of NURBS with arbitrary functions. PUPs are affine invariant and preserve many properties of NURBS like strong convex hull property. They yield a comprehensive geometric modeling framework, accounting for a variety of beneficial properties such as local-support, specified smoothness, special type of features (like sharp features), interpolation and approximation. Since it is possible to use arbitrary functions, PUP provides a meta-modeling framework. This means that a super-user can design special types of functions for different purposes. This feature makes PUP beneficial for many industrial related applications.

#### Team

- Faramarz F. Samavati, Research lead
- Adam Runions, PhD
- Amirhessam Moltaji, MSc student

#### Related papers

- Adam Runions and Faramarz F. Samavati. 2011. Partition of unity parametrics: a framework for meta-modeling. The Visual Computer. 27, 6-8 (June 2011), 495-505.

#### Research Keywords

Geometric Modeling, Parametric Modeling, Sketch-Based Modeling, Curve and Surface Modeling, Interactive Modeling, Meta-Modeling Framework, Subdivision, Linear and Non-Linear Projection, B-Spline, NURBS.