# Isosurfaces Over Simplicial Partitions of Multiresolution Grids

This method calculates isosurfaces of functions with thin and sharp features sampled over an octree. The surfaces are guaranteed to be manifold and have no self-intersections. We also introduce a way to simplify the triangulation while preserving surface topology.

## BibTeX

@article{Manson:2010:ISP,
author    = {Josiah Manson and
Scott Schaefer},
title     = {Isosurfaces Over Simplicial Partitions of Multiresolution
Grids},
journal   = {Computer Graphics Forum (Proceedings of Eurographics)},
year      = {2010},
volume    = {29},
number    = {2},
pages     = {377--385},
}


## Abstract

We provide a simple method that extracts an isosurface that is manifold and intersection-free from a function over an arbitrary octree. Our method samples the function dual to minimal edges, faces, and cells, and we show how to position those samples to reconstruct sharp and thin features of the surface. Moreover, we describe an error metric designed to guide octree expansion such that flat regions of the function are tiled with fewer polygons than curved regions to create an adaptive polygonalization of the isosurface. We then show how to improve the quality of the triangulation by moving dual vertices to the isosurface and provide a topological test that guarantees we maintain the topology of the surface. While we describe our algorithm in terms of extracting surfaces from volumetric functions, we also show that our algorithm extends to generating manifold level sets of co-dimension 1 of functions of arbitrary dimension.

## Supplemental Materials

iso_simplicial.zip

Implementation of the method described in the paper.

eg_presentation.pptx

This is the set of slides that I used in my presentation of the paper at Eurographics 2010.