Citations & Acknowledgments• Kazhdan, Michael, Matthew Bolitho, and Hugues

Hoppe. "Poisson surface reconstruction." Proceedings of the fourth Eurographics symposium on Geometry processing. 2006.

• Meshlab. Computer Software. Sourceforge. Vers. 1.3.2. CNR, VCL, ISTI.

• Mark S. Shephard, Cameron W. Smith, and Guðmundur Heimisson.“Construction of Models and Meshes for Large-Scale Earth Science Applications.” SIAM CSE. Boston MA. 2012.

The distance field

Earth surface topography (colored by curvature).

Poisson Surface Reconstruction

To reconstruct the surface :• Want to find 3D indicator function .• is zero except at the boundary.• Oriented point cloud approximates .• Want such that .• Must satisfy Poisson equation, .• Find approximate solution numerically,

using least squares approach.

Point Normal ComputingThe point normals are computed using a naïve algorithm. For each point :

• The closest neighbors of are found.• The normal of is found by fitting a

plane to and its neighbors.• Orientation (inside/outside) is arbitrarily

assigned to the first point, and propagated thereafter.

Trimming & Bounding Box Generation

Biscay Bay

Geological data is typically given in latitude (), longitude (), and depth () with respect to the WGS84 reference ellipsoid.It must be projected into Cartesian co-ordinates using the transformation:

Geometric Model Generation from Structured Point Data: An Approach to Construct Geometries for Earth Science Domains

Guðmundur Heimisson (heimig@rpi.edu), Cameron W. Smith (smithc11@rpi.edu), Mark S. Shephard (shephard@rpi.edu)

Scientific Computation Research Center, Rensselaer Polytechnic InstituteIntroduction Workflow

The goal is to develop a workflow for automated generation of multi-layer geometric models suitable for seismic wave propagation simulations.

An example of a mesh generated using the current process.*

Current method of generating models and meshes using Gambit is unsatisfactory:

• It requires many man-hours of manual editing.

• It is difficult to integrate multiple layers.

Problem

Researchers at the Ludwig-Maximilians-Universität München (LMU) are working to:

• Simulate dynamic earthquake rupture.• Study wave propagation through complex

media in complex fault system geometries.In order to:

• Address fundamental questions in earthquake dynamics.

• Generate realistic earthquake scenarios for hazard assessment.

Examples of multi-layer geometric data sets.*

Background

For each geometric model layer:• Project the source data.• Compute the point normals.• Perform surface reconstruction.• Trim the surface

Once all of the surfaces have been generated:• Generate a bounding box.• Remove interface intersection artifacts and

‘small’ features.• Generate the non-manifold geometric model.

Model Generation Workflow

Preliminary Results

Automated workflow demonstrated on Biscay Bay data set is significant improvement on Gambit based workflow.• Replaces hours of manual work with automated

script that executes in minutes on a laptop.• Uses a robust, scalable algorithm for surface

reconstruction.• Supports inclusion of multiple geometric layers.• Incorporates data from multiple data sets.• Extensible implementation using combination of

Python and MeshLab.Illustration of the WGS84

ellipsoid projection.

The surface is trimmed using a simple approach:• For each vertex in surface, compute

distance to nearest vertex in point cloud.• Delete any vertex with a distance above

some threshold.The bounding box is then generated using the WGS84 ellipsoid projection.

Ongoing WorkIdentify and remove unwanted features:

• Layer intersection artifacts caused by numerical errors.

• ‘Small’ features – a feature whose length scale is less than minimal wave length supported by the analysis.

Automate non-manifold model generation• Use Simmetrix C++ API to intersect layer

and bounding box surfaces.Pursue source of layer data sets

• Possibly generate higher fidelity layer representations

Data Projection

• Simulations provide an understanding of the effect of earthquakes for which no data exists.

• Simulating earthquakes accurately is of immediate concern to millions of people living in earthquake prone areas.

• An automated workflow for generating complex earth science geometries would represent a significant step forward for current research, and would enable further research into this important topic.

Closing Remarks

• Earth surface topography and ocean.• Sedimentary interface.• Upper and lower crust interfaces.• The Mohorovičić discontinuity.

Geometric Model Layers of Interest

Trimmed surface with bounding box

* Images courtesy of LMU.

Non-manifold Biscay Bay geometric model.

Biscay Bay geometric model: sediment to upper crust.

http://www.geod.nrcan.gc.ca/images/wgs84geoid_e.jpg

A reconstructed surface, with the underlying data set superimposed

(colored by curvature).