Terrain Decimation through Quadtree Morphing

We present a new terrain decimation technique called a Quadtree Morph, or Q-morph. The new approach eliminates the usual popping artifacts associated with polygon reduction, replacing them with less objectionable smooth morphing. We show that Q-morphing is fast enough to create a view-dependent terrain model for each frame in an interactive environment. In contrast to most Geomorph algorithms, Q-morphing does not use a time step to interpolate between geometric configurations. Instead, the geometry motion in a Q-morph is based solely on the position of the viewer. 1 Terrain Decimation A digital elevation model, or DEM, is a rectangular array of height samples taken from terrain data or some other scalar-valued 2D function. One common way to view a DEM is to render a set of triangles that approximates the terrain surface. Unfortunately, the obvious triangulation yields triangles, where and are the dimensions of the height grid. For large DEMs, this can run into millions of polygons, too many to be rendered in real time even by specialized graphics hardware. Terrain Decimation addresses the issue of rendering efficiency by producing a terrain model with significantly fewer triangles that is visually similar to the full resolution model. While terrain decimation is a widely studied topic, the majority of decimation algorithms in use today suffer from the so called ”popping” artifact. Popping occurs in an animation when successive frames show different approximate models that are visually discontinuous. Decimation algorithms that allow geometric discontinuities between successive approximations are referred to as discrete level-of-detail algorithms. Q-morphing avoids popping artifacts by using a continuous level-of-detail algorithm instead of a discrete level-of-detail algorithm. Continuous level-of-detail algorithms are able to produce a near infinite number of approximations, such that the visual difference between successive models approaches zero. 2 Previous Work in Terrain Decimation Several approaches to surface simplification in the setting of terrain models have been proposed. In this section we will discuss four of these, namely, the application of general polygon decimation algorithms to terrains, TIN methods, voxelized terrains, and algorithms that use semi-regular subdivision. 2.1 General Polygon Decimation Methods Although not intended specifically to work on terrain models, methods designed for general polygon decimation can be applied to triangulated DEMs. General methods have the advantage that [email protected], http://orca.cs.byu.edu/ cline [email protected] they can be used for any polygonal objects in the scene, not just terrains. On the other hand, these methods cannot exploit the regular structure of the DEM. Terrain models have several display characteristics that make some types of decimation algorithms more attractive than others. First, terrain models often consume a large amount of memory. Thus, decimation algorithms that allow progressive transmission of geometry can avert long startup times. Additionally, terrain models are often viewed at close range so that only a small portion of the DEM is visible in any particular view. Thus, algorithms that perform view-dependent simplification are of particular interest in terrain settings. Luebke and Erikson [15] describe one general method that simplifies complex polygonal environments in a view-dependent fashion. The system works by grouping vertices into hierarchical clusters, and then collapsing clusters into single vertices during animation. Another method that addresses the need for incremental transmission is the progressive mesh [9]. Progressive Meshes, introduced by Hoppe, represent polygonal objects as a small base mesh plus vertex-split transformations. Since the vertex splits can be added incrementally to the model, a progressive representation results. Hoppe later showed how Progressive Meshes can be used for view-dependent simplification, and how they can eliminate popping artifacts by using Geomorphs [10]. 2.2 TIN Methods Methods that produce TINs, or Triangulated Irregular Networks, form a large class of terrain decimation algorithms. In general, TIN methods attempt to create a mesh which contains the fewest possible triangles that satisfies some error criteria. Examples of basic TIN methods are found in [5], [21] and [20]. TIN algorithms can produce near optimal results in terms of the number of triangles needed to satisfy a particular error threshold, but most do not operate in real-time. Since the end goal is often to create a model that will be viewed interactively, TINs can be built off line and stored as triangle meshes. The stored meshes can then be rendered in real-time as long as they contain few enough triangles. One simple approach to detail management in terrains is to use a set of TINs with differing error thresholds as discrete level-of-detail models. Two drawbacks to this approach are that popping can occur when model levels switch, and view-dependent simplification of the terrain is not possible in the individual TINs because the viewpoint is not known at TIN creation time. Some researchers have suggested extensions to the basic TIN idea that make TINs more suitable for real-time display. Taylor and Barrett [22] address the problem of popping by defining a ”TIN morph” that interpolates between TIN models. Their approach does not address the need for view-dependent model refinement, however. Consequently, the transformations to the terrain geometry must be done on a global scale; local simplification is not possible. Without the ability to simplify local regions in the terrain, the models become too complex for real-time display as the viewer approaches the terrain. DeBerg and Dobrindt [4], and Cohen-Or et al. [3] extend the basic concept of TIN morphing to allow local refinement to the detail level. Both of these algorithms work by creating hierarchical versions of a Delaunay triangulation. A new tessellation is made for each viewpoint that allows different levels of the hierarchy to coexist on the same model. Another TIN algorithm that uses a hierarchical Delaunay triangulation is discussed by Rabinovich et al. [19]. Besides being able to produce a viewdependent simplification, this algorithm allows piece-wise terrain updates during scene interaction. In more recent work, Hoppe [11] describes a terrain decimation approach that produces terrain models based on a hierarchy of pre-decimated terrain blocks. The system uses run-time geomorphs to eliminate popping artifacts.