# Multi-level Partition of Unity Implicits

##### ACM TOG (Proc. SIGGRAPH 2003), 22(3):463-470, 2003.

#### Abstract

We present a shape representation, the multi-level partition of unity
implicit surface, that allows us to construct surface models from very large
sets of points. There are three key ingredients to our approach: 1) piecewise
quadratic functions that capture the local shape of the surface, 2) weighting
functions (the partitions of unity) that blend together these local shape
functions, and 3) an octree subdivision method that adapts to variations
in the complexity of the local shape. Our approach gives us considerable flexibility
in the choice of local shape functions, and in particular we can accurately
represent sharp features such as edges and corners by selecting appropriate
shape functions.

### Paper

PDF file [6.4 MBytes]
PS file [8.8 MBytes]

### Software

Very preliminary version of MPU (March,
2003)

Preliminary version of MPU (October, 2003)

The zipped file includes a Windows executable binary file and the
source code to be complied by Microsoft Visual C++ 6.0.

(This version can only perform a standard polygonization of MPU
implicits created from the input points. A later version will include boolean
operations, blending, mesh optimization for polygonized surfaces,
and visualization by ray-tracing.)

Please note that the reconstructed sharp edges and corners are usually
lost during the polygonization stage. In order to restore them we use
the approach described in

Y. Ohtake and A. Belyaev, "Dual/Primal
Mesh Optimization for Polygonized Implicit Surfaces", ACM Solid Modeling
2002, Saarbruecken, Germany, June 17 - 21, 2002, pp. 171-178.

Probably we will bind the programs together.

### Sample data

Examples of input point datasets
Examples of output meshes obtained as polygonized MPU implicits

### Talk slides

Talk slides at SIGGRAPH2003

Presentation of the MPU method at a local
MPI-AG4 meeting

Movies: