https://forum.unity.com/threads/voronoi-based-map-generator.520707/

# Terrain Modeling Using Voronoi Hierarchies

Terrain Modeling Using Voronoi Hierarchies

Martin Bertram1, Shirley E. Konkle2, Hans Hagen1, Bernd Hamann3, and Kenneth I. Joy3

- 1 University of Kaiserslautern, Department of Computer Science, P.O. Box 3049, D-67653 Kaiserslautern, Germany.
- 2 Pixar Animation Studios, 1200 Park Ave., Emeryville, CA 94608, U.S.A.
- 3 Center for Image Processing and Integrated Computing (CIPIC), Departmentof Computer Science, University of California, Davis, CA 95616-8562, U.S.A.

Abstract. We present a new algorithm for terrain modeling based on Voronoi di- agrams and Sibsonâs interpolant. Starting with a set of scattered sites in the plane with associated function values defining a height field, our algorithm constructs a top-down hierarchy of smooth approximations. We use the convex hull of the given sites as domain for our hierarchical representation. Sibsonâs interpolant is used to approximate the underlying height field based on the associated function values of selected subsets of the sites. Therefore, our algorithm constructs a hierarchy of Voronoi diagrams for nested subsets of the given sites. The quality of approx- imations obtained with our method compares favorably to results obtained from other multiresolution algorithms like wavelet transforms. For every level of reso- lution, our approximations are C1 continuous, except at the selected sites, where only C0 continuity is satisfied. Considering n sites, the expected time complexity of our algorithm is O(n log n). In addition to a hierarchy of smooth approximations, our method provides a cluster hierarchy based on convex cells and an importance ranking for sites.

https://web.cs.ucdavis.edu/~hamann/

**BERND HAMANN** Curriculum Vitae

**UC Davis Director, Los Alamos National Laboratory** - UC Davis Institute of Next-generation Visualization and Analysis (INGVA), Los Alamos National Laboratory, New Mexico, and University of California, Davis, October 2012 â September 2017.

https://www.stratovan.com/meet-the-team

**An Interactive Visual Exploration Tool for Northern Californiaâs Water Monitoring Network**

Jaya Sreevalsan-Nair

a

Erwin Van Nieuwenhuyse

b

Ingrid Hotz

c

Lars Linsen

d

Bernd Hamann

a a

Institute for Data Analysis and Visualization, University of California, Davis, CA 95616, U.S.A.

b

U.S.Bureau of Reclamation, 2800 Cottage Way, Sacramento, CA 95825, U.S.A.

c

Visualization & Data Analysis, Konrad-Zuse-Zentrum fÂšur Informationstechnik Berlin, Germany

d

Computational Science and Computer Science, International University of Bremen, Germany

**ABSTRACT**

The water monitoring network in Northern California provides us with an integrated ïŹow and water-qualitydataset of the Sacramento-San Joaquin Delta, the reservoirs, and the two main rivers feeding the Delta, namelythe Sacramento and the San Joaquin rivers. Understanding the dynamics and complex interactions among thecomponents of this large water supply system and how they aïŹect the water quality, and ecological conditions forïŹsh and wildlife requires the assimilation of large amounts of data. A multivariate, time series data visualizationtool which encompasses various components of the system, in a geographical context, is the most appropriatesolution to this challenge. We have developed an abstract representation of the water system, which usesvarious information visualization techniques, like focus+context techniques, graph representation, 3D glyphs,and colormapping, to visualize time series data of multiple parameters.

Keywords:

Information Visualization, Focus+context, Multivariate data, Time series data

**4.6. Volume Representation for Reservoirs**

*As explained in Section 3, cylinders are used to represent reservoirs. The reservoirs have only one parameter to be displayed, namely, the current volume of water. The ïŹuctuating height indicated by the opaqueness in the cylinder represents the current âïŹlling-inâ or âdraining-outâ behavior of the reservoir.*