Visualization of 3D Geologic maps: an example using ... - CiteSeerX

Visualization of 3D Geologic maps: an example using volumetric clipping with hardware Guillaume Caumon, Eric A. de Kemp and Fabien Bosquet June 11, 2005

abstract

spread stencil buffer can be used to cap a 3D solid model with one or several planes. Originally defined The geological map is an essential means of convey- in the field of Constructive Solid Geometry, we show ing information about a geological domain. However, how this method can be adapted to interactively visuquantitative applications and precise depth mapping alize sealed subsurface models. The OpenGL-based call for a 3D representation of geological units. On code is available. such 3D maps, the 2D visualization of rock units along a section remains essential to understand and check the consistency of a 3D model. We propose a fast and simple tool to slice in real-time a sealed geological model by one or several arbitrary planes. Introduction The intersection polygon between a section plane and 1 the geological model is never explicitly computed in three-dimensions, but filled by graphics hardware in Maps have been the traditional way to represent geoscreen space using the stencil buffer. Edge deteclogical knowledge on an area. However, the depth of tion algorithms can be run on the section to draw the geological structures reliably described from a gesharp unit boundaries. The polygon is filled either ological map can be orders of magnitude smaller than by one single color corresponding to the legend, or the depth of domains of economic or scientific interby a two-dimensional texture image corresponding to est (hydrocarbon reservoir, ore deposit, crust slabs, the interpolation of a rock property inside the geologMOHO, etc.). ical unit. The method is applied to the imaging of a continuous velocity model in an oil reservoir without citer les Catalans (AAPG 04), De Kemp, ... generating a large velocity cube, and to the visualizaThinking about it, the geological map is nothing tion of complex Precambrian units in the Canadian but a particular cross-section of the 3D geological Shield. structures along the topographic surface. (Caumon et al., 2004; Aziz and Settari, 1979; Goovaerts, 1997; Chil`es and Delfiner, 1999; M¨antyl¨a, During the last few decades, the visualization of 1988; de Kemp, 2000; de Kemp and Sprague, 2003; subsurface structures has been much improved by the Courrioux et al., 2001; Cavalcanti et al., 1997; Weiler, advent of graphic cards. The rasterization capabili1988) ties have considerably increased to reach several milThe development of computer-aided 3D geological lions of fragments per second. modeling does not remove the need for a 2D. Subsurface structures The ever increasing graphic capabilities open new perspectives for 3D modeling. Thus, the widely 1

2

Clipping Method

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Visualizing Solid Models : solid slicing

R

As for any other object in a 3D modeling environment, it is important to have efficient and explicit visualization functions for a b-rep. In complement to the visualization of regions boundaries, we have developped a solid section tool that can slice a model along an arbitrary plane. For that purpose, two approaches have been considered : object-space and image-space.

3.1

P

0 2 2 1 1 1 1 3 3 3 3 0 0

0 0 0 1 1 1 1 1 1 1 1 0 0

Inter

Sten

Col

Figure 1: Drawing the intersection between a polyhedral region R and a slicing plane P. For each pixel, the odd numbers of intersections of the ray (inter ) are tracked in the stencil buffer (Sten). These values are then used as a mask when drawing the plane P to the color buffer (Col ).

Object-space approach

In a classical object-space method, a cross-section in a 3D b-rep is computed from the the intersections of the b-rep with the section plane. Currently in Gocad, this computation is performed by looking for all the intersected triangular facets of the b-rep. The extremities of the resulting segments are associated to the edges of the b-rep in a table. The intersection polygons are then retrieved from this information for each polyhedral region. As it is partly based on geometrical computations to compute the topology of the intersection polygons, this approach may not be the most robust. Therefore, we propose to use a tracking algorithm, that would get most of the topological information from the brep itself : For all the potentially intersected triangles :

a structure is actually not necessary if we consider the visualization problem in the image space.

3.2

Image-Space approach

Consider a closed region R of a b-rep. In most cases, it consists of an arbitrary closed polyhedron 1 . For any given line L in space, the number of intersections of L with R is always even. Therefore, when drawing all the faces of a closed region to a computer screen without considering their depth, each pixel of the resulting polygon is processed an even number of times. This remark is at the core of the hardware-based Constructive Solid Geometry approaches. When a polyhedral region R is clipped by a plane P, the pixels corresponding to the projection of R ∩ P onto the screen are processed an odd number of times. Using OpenGL’s stencil buffer (Neider et al., 1993, Chapter 10), it is possible to keep track of this parity (Fig. 1). For that purpose, one needs to disactivate depth and color buffer, activate clipping with P, and activate the stencil buffer with :

1. Get current triangle t, and mark it as visited; 2. If t is intersected by the slicing plane, track the intersection to one of its neighbors, as in Caumon. This tracking has to be oriented, and propagate across non-manifold contacts between surfaces.

This paper being witten, this algorithm is not yet fully implemented, making performance and robust- glClear(GL_STENCIL_BUFFER_BIT); ness comparisons difficult. Whatever the computa1 geological models, this is not always true, as a polyhetion method, this object-space approach uses a 2D dral In region may have internal free boundaries corresponding to b-rep data structure, capable of representing non- dying fault. For our purpose, we just propose to ignore such manifold polygons with internal boundaries. Such boundaries. 2

glStencilMask(1); Cavalcanti, P. R., Carvalho, P. C. P., Martha, L. F., glEnable(GL_STENCIL_TEST); 1997. Non-manifold modelling: an approach based glStencilFunc(GL_ALWAYS, 0, 0x1); on spatial subdivision. Computer-Aided Design, 29 glStencilOp(GL_INVERT, GL_INVERT, GL_INVERT); (3),209–220. After this, the image of R ∩ P is marked in the Chil`es, J.-P. Delfiner, P., 1999. Geostatistics: Modeling Spatial Uncertainty. Series in Probability stencil buffer simply by passing the faces of R to and Statistics. John Wiley and Sons. ISBN 0-471OpenGL’s rendering pipeline. 08315-1. 696 p. These values can be used later on to mask the drawing of the plane P to the color buffer : Courrioux, G., Nullans, S., Guillen, A., Boissonnat, J.-D., Repusseau, P., Renaud, X., Thibaut, M., glStencilFunc(GL_EQUAL, 1, 1); 2001. 3d volumetric modelling of Cadomian terglStencilOp(GL_KEEP, GL_KEEP, GL_KEEP); ranes (Northern Brittany, France): an automatic In summary, this image-space method is very atmethod using Voronoi diagrams. Tectonophysics, tractive. Indeed, a single pass for each model re331,181–196. gion is needed to render all the intersection polygons. The integration of this method with the slicer tool is de Kemp, E. A., 2000. 3-d visualization of structural field data: examples from the Archean shown on Figure ??. We are currently investigating Caopatina Formation, Abitibi greenstone belt, an extension of this approach to visualize the analytQu´ebec, Canada. Computers and Geosciences, 26 ical property model defined in a b-rep using texture (5),509–530. mapping.

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Texturing properties

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Conclusion

de Kemp, E. A. Sprague, K. B., 2003. Interpretive tools for 3D structural geological modeling parti: B´ezier-based curves, ribbons and grip frames. GeoInformatica, 7(1),55–71. Goovaerts, P., 1997. Geostatistics for natural resources evaluation. Applied Geostatistics. Oxford University Press, New York, NY. ISBN 0-19511538-4. 483 p.

Acknowledgements

Part of this work was performed in the frame of the Gocad Research Consortium, and at Earth Decision Sciences, SA. The authors want to thank the sponsors M¨antyl¨a, M., 1988. An Introduction to Solid Modeling. Computer Science Press, Rockville, MD. 401 of the consortium for their financial support. p.

Neider, J., Davis, T., Woo, M., 1993. OpenGL Programming Guide. Addison-Wesley.

References Aziz, K. Settari, A., 1979. Petroleum Reservoir Simulation. 497p.

Weiler, K., 1988. The Radial Edge structure: a topological representation for non-manifold geometric boundary modeling. In: Wozny, M., McLaughlin, Caumon, G. Interactive manipulations of geologiH., Encarna¸c˜ao, J. (Eds.), Geometric Modeling for cal models through cross-sections. in 21st Gocad CAD applications, pp. 3–36. Elsevier Science PubMeeting Report, Nancy, June 2001. lishers, Amsterdam. Caumon, G., Sword, C. H., Mallet, J.-L., 2004. Building and editing a Sealed Geological Model. Mathematical Geology, 36(4),405–424. 3