https://cg.informatik.uni-freiburg.de/intern/seminar/surfaceReconstruction_survey%20of%20marching%20cubes.pdf

A survey of the marching cubes algorithm

Presents a brute-force ray-tracing system for interactive volume visualization. The system runs on a conventional (distributed) shared-memory multiprocessor machine. For each pixel, we trace a ray through a volume to compute the color for that pixel. Although this method has a high intrinsic computational cost, its simplicity and scalability make it ideal for large data sets on current high-end parallel systems. To gain efficiency, several optimizations are used, including a volume bricking scheme and a shallow data hierarchy. These optimizations are used in three separate visualization algorithms: isosurfacing of rectilinear data, isosurfacing of unstructured data, and maximum-intensity projection on rectilinear data. The system runs interactively (i.e. at several frames per second) on an SGI Reality Monster. The graphics capabilities of the Reality Monster are used only for display of the final color image.

Interactive ray tracing for volume visualization

Interactive ray tracing for isosurface rendering

The term ray tracing is commonly associated with highly realistic images but certainly not with interactive graphics. However, with the increasing hardware resources of today, interactive ray tracing is becoming a reality and offers a number of benefits over the traditional rasterization pipeline. The goal of this report is to provide a better understanding of the potential and challenges of interactive ray tracing. We start with a review of the problems associated with rasterization based rendering and contrast this with the advantages offered by ray tracing. Next we discuss different approaches towards interactive ray tracing using techniques such as approximation, hybrid rendering, and direct optimization of the ray tracing algorithm itself. After a brief review of interactive ray tracing on supercomputers we describe implementations on standard PCs and clusters of networked PCs. This system improves ray tracing performance by more than an order of magnitude and outperforms even high-end graphics hardware for complex scenes up to tens of millions of polygons. Finally, we discuss recent research towards implementing ray tracing in hardware as an alternative to current graphics chips. This report ends with a discussion of the remaining challenges and and the future of ray tracing in interactive 3D graphics.

/pdf/state-of-the-art-in-interactive-ray-tracing-59cmp0fcdz.pdf

State of the Art in Interactive Ray Tracing

This paper presents several improvements to the marching triangles algorithm for general implicit surfaces. The original method generates equilateral triangles of constant size almost everywhere on the surface. We present several modifications to adapt the size of the triangles to the curvature of the surface. As cracks may arise in the resulting polygonization, we propose a specific crack-closing method invoked at the end of the mesh growing step. Eventually, we show that the marching triangles can be used as an incremental meshing technique in an interactive modeling environment. In contrast to existing incremental techniques based on spatial sudvision, no extra datastructure is needed to incrementally edit skeletal implicit surfaces, which saves both memory and computation time.

Adaptive Implicit Surface Polygonization Using Marching Triangles

We present a new approach, analytic isosurface rendering, for volume rendering. The isosurface of a cell can be modeled as an analytic function, and the intersection between a ray and the isosurface can be computed directly. An octree structure efficiently searches the cells containing isosurfaces. The octree is easy to implement and can be stored in a compact form. It needs extra memory space - at most 27/64 of the size of the original data volume. Front-to-back projection can easily be implemented under the octree structure. A union-find-based algorithm maintains the frame buffer efficiently. Experimental results show that a volume rendering program with our approach is very efficient and maintains the quality of the rendered images.

An efficient volume-rendering algorithm with an analytic approach

The marching cubes method (Lorensen 1987) is a popular technique for visualizing a set of volume data. This method uses 15 base cases to construct polygons for each cube to approximate the isosurfaces F(x, y, z)"t for various values of t. The advantages of the polygon-based approach make it easy to adopt the technique on hardware platforms and to execute it efficiently. Unfortunately, the method has an ambiguity problem that causes anomalies in the rendered images (Durst 1988). Several improved approaches have been proposed (Montani et al. 1994; Nielson et al. 1991; Pasco 1988; Wilhelms and Gelder 1990). These methods try to resolve ambiguous situations by preventing possible ‘‘holes’’ in the isosurfaces. However, these approaches could introduce the topological inconsistency problem (Natarajan 1994), which confuses our perception of the observed objects, especially when supersampling the original data is necessary. In 1994, Natarajan developed a technique that computes topologically consistent isosurfaces by examining the saddle values of a trilinear interpolant. This technique also improves the method proposed by Pasco in 1988, which investigated saddle values for the bilinear interpolant only. In this note, we analyze the trilinear interpolant. We show that the cost for computing the body saddle value can be reduced.

https://ir.nctu.edu.tw/bitstream/11536/825/1/A1997YA42800004.pdf

A note on computing the saddle values in isosurface polygonization

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An efficient volume-rendering algorithm with an analytic approach

A note on computing the saddle values in isosurface polygonization