Modeling Terrains and Subsurface Geology M. Natali, E. Lidal, J. - PowerPoint PPT Presentation

Modeling Terrains and Subsurface Geology M. Natali, E. Lidal, J. Parulek, I. Viola, D. Patel Vienna University of Technology, Austria University of Bergen, Norway Christian Michelsen Research, Norway

Presentations and Presenters ● Part 1: Introduction and Taxonomy (I. Viola 20 min) ● Part 2: Surface Creation and Representation (M. Natali 40 min) ● Part 3: Solid models (D. Patel 40 min) 2

Introduction and Taxonomy Part 1 Ivan Viola

Modeling of Terrains and Subsurface ● Rapid modeling in computer graphics ● Procedural modeling: fractals, erosion ● Sketch-based modeling directing procedure ● Surface modeling predominantly ● Domain: Film and gaming industry ● User group: artists, content creators Ebert et al.: Texturing and Modeling: A Procedural Approach ● Geosciences ● Developed their own methods (Kriging ~ RBF) ● Time-consuming modeling of complex structures (e.g. GoCAD) ● Dedicated interpolation methods of sparse data ● Users: Geoscientists, geologists Mallet: Geomodeling ● Rapid modeling in geoscience is needed! ● Intellectual crosspollination of CG and Geo 4

Geological Background ● Uniformitarianism ● Layer-cake model ● Sedimentation, horizons, faulting, folding, igneous processes, erosion ● Relevant for Oil&Gas ● Structural model (geo-bodies) ● Reservoir model (hydrocarbon flow) ● Complex geological model ● Mineralogy and metal 5

Modeling Complexity ● Man-made objects ● Architecture (orthogonal, regular) ● CAD (simple shapes, identical instances) ● Natural objects ● Vegetation, Animals, Terrain (complex shapes, individual instances, clear boundaries) ● Subsurface (unclear boundaries, unfamiliar shapes, complex 3D arrangement) Turner: Challenges and trends for geological modelling and visualisation 6

Geological Interpretation ● Measurements ● Boreholes ● Remote sensing ● Seismic slices ● Vertical outcrop analysis ● Simulations ● Forward simulation ● Inversion ● Palaeoclimate and Palaeogeography ● Uncertainty 7

Taxonomy According to Origin 8

Taxonomy According to Workflow 9

Surface Creation and Representation Part 2 M. Natali

Workflow T axonomy 2

Fractal and Erosion  Synthetic terrains from: ● Fractal landscape modelling ● Physical erosion simulation (Thermal or Hydraulic) ● Images or terrain patches [Belhadj et al. 2007] [Stava et al. 2008] 3

Fractal Example I  Stachniak and Stuerzlinger, An algorithm for automated fractal terrain deformation, 2005  More user control than previous techniques  Constraints to the created model according to user  Fractal approximation of terrain + function defining user constraints 4

Fractal Example II  Schneider et al., Realtime editing, synthesis, and rendering of infinite landscapes on GPUs, 2006  Reduction of parameter setting  Interactive fractal landscape synthesizer 5

Erosion Example I  Benes and Forsbach, Visual simulation of hydraulic erosion, 2002  Physically-based approach with high level control  Fast and stable 6

Erosion Example II  Benes et al., Hydraulic erosion, 2006  Fully based on fluid mechanics (Navier-Stokes)  Voxel grid representation 7

Erosion Example III Stava et al., Interactive terrain modeling using hydraulic erosion, 2008  Interactive physically-based erosion  Implemented on GPU  Subdivision in tiles (height-maps) 8

Erosion Example IV  Kristof et al., Hydraulic Erosion Using Smoothed Particle Hydrodynamics, 2009  Smoothed Particle Hydrodynamics (SPH) employed  Works on large terrains 9

Erosion Example V  Hnaidi et al., Feature based terrain generation using diffusion equation, 2010  Constrained modelling process  Curves with properties (elevation, slope angle, ...) 10

Erosion Example VI  Hudak and Durikovic, Terrain Models for Mass Movement Erosion, 2011  Long time period erosion  Particle system adopted  Discrete Element Method  SPH for water simulation 11

Sketching T errains  Rapid modelling  Expressive  Intuitive  No need to set parameters [Gain et al. 2009] 12

Sketching T errains - Example I  Watanabe and Igarashi, A sketching interface for terrain modeling, 2004  Noise after surface deformation  Local minima and maxima for area of influence 13

Sketching T errains - Example II  Gain et al., Terrain Sketching, 2009  Sketch-based procedural generation  Elevation + area of influence  Noise where required 14

Sketching T errains - Example III  Vital Brazil et al., Sketching Variational Hermite-RBF Implicits, 2010  3D closed surfaces using implicit functions  General tool, adaptable to geology 15

Sketching T errains - Example IV  Zhou et al., Terrain synthesis from digital elevation models, 2007  Sketches combined with exemplar-based technique  Height-map sketching 16

By-example - Example I  Brosz et al., Terrain synthesis by-example, 2007  Realistic terrains from reference examples  Rough base + target (small-scale characteristics)  Brush operation or procedural synthesis 17

Surface Representations [de Carpentier and  Height maps Bidarra 2009]  Implicit surfaces [Brazil et al. 2010]  Meshes 18

Workflow T axonomy 19

Sparse- and Dense-data  Geological measured data as input:  Seismic 2D or 3D (reflection of sound waves)  Collection of well logs (material samples and measurements)  Outcrop scan (combination of laser and photography, LIDAR) University of Idaho 20

Sparse-/Dense-data Example I  Caumon et al., Terrain synthesis from digital elevation models, 2007  Geometric surfaces for each stratigraphic layer  No holes  Shared vertices for intersecting surfaces 21

Sparse-/Dense-data Example II  Caumon et al., Surface-Based 3D Modeling of Geological Structures, 2009  Orientable surfaces  Implicit surfaces imply validity conditions 22

Interpolation  B-spline  Inverse distance  Kriging  Discrete Smooth Interpolation (DSI)  Natural Neighbor Interpolation 23

Interpolation  B-spline  Inverse distance  Kriging  Discrete Smooth Interpolation (DSI)  Natural Neighbor Interpolation  A spline is a pw-defined smooth polynomial function  A B-spline is a linear combination of spline functions with minimal support wrt a given degree, smoothness, and domain partition  Given m+1 knots  n+1 control points P0 , … , Pn Weisstein, Eric W. "B-Spline." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/B-Spline.html 24

Interpolation  B-spline  B-spline  Inverse distance  Inverse distance  Kriging  Kriging  Discrete Smooth Interpolation (DSI)  Discrete Smooth Interpolation (DSI)  Natural Neighbor Interpolation  Natural Neighbor Interpolation  Data points closer to the grid points have more effect than those which are further away  Estimates the values of an attribute at unsampled points using a linear combination of values at sampled points Jin Li and Andrew D. Heap, A Review of Spatial Interpolation Methods for Environmental Scientists 25

Interpolation  B-spline  Inverse distance  Kriging  Discrete Smooth Interpolation (DSI)  Natural Neighbor Interpolation  Data points and their spatial variance are used to determine trends which are applied to the grid points Jin Li and Andrew D. Heap, A Review of Spatial Interpolation Methods for Environmental Scientists 26

Interpolation  B-spline  Inverse distance  Kriging  Discrete Smooth Interpolation (DSI)  Natural Neighbor Interpolation  Interpolation of a function f known at some data points (n dimensional)  Most classical methods find a function defined everywhere, DSI produces values only at grid points 27

Interpolation  B-spline  Inverse distance  Kriging  Discrete Smooth Interpolation (DSI)  Natural Neighbor Interpolation  The natural neighbors of any node are those in the neighboring Voronoi cells, or equivalently, those to which the node is connected by the sides of the Delaunay triangle 28 N. Sukumar, UCDAVIS

Surface Representations 29

Fractal and Noise-based  Realistic appearance of the surface  Self-similarity of fractals like in nature  (Height-maps) Do not allow discontinuities  Not intuitive, no local control  No multi-z values 30

Erosion  Weathering simulation  Natural appearance of top surface  No discontinuity  Hard to control  Low storage, high processing 31

Exemplar-based  Surface reconstruction (geometry and texture) through a collection of data from photography and laser  Computational expensive to create a terrain  Little control on the process  High storage requirements 32

Radial Basis Functions  Interpolation of a set of n points with their normal vector  Unordered points (unlike splines)  C n continuity  No gap in the surface  Overhangs feasible 33

Splines  From a set of control points with normal  No fault (continuity of surface)  Parametric form facilitates computation and visualization  Ordered list of points 34