Patent Publication Number: US-7899241-B2

Title: Method and system for progressive mesh storage and reconstruction using wavelet-encoded height fields

Description:
RELATED APPLICATIONS 
     This application is a divisional patent application of U.S. patent application Ser. No. 11/124,793, filed May 9, 2005, now U.S. Pat. No. 7,680,350, which claims the benefit of priority to U.S. Provisional Patent Application No. 60/569,332, filed 7 May 2004, both of which are incorporated herein by reference. 
    
    
     U.S. GOVERNMENT RIGHTS 
     This invention was made with Government support under contracts NAS5-01196 and NNL04AC32P awarded by NASA. The Government has certain rights in this invention. 
    
    
     BACKGROUND 
     The following patents provide useful background information and are incorporated herein by reference: U.S. Pat. No. 6,426,750; U.S. Pat. No. 6,208,997; U.S. Pat. No. 5,929,860; and U.S. Pat. No. 5,831,625. 
     Other useful background information includes the following articles: “Fast Terrain Rendering Using Geometrical MipMapping” by de Boer, W. H. (2000); “Compression of Digital Elevation Maps Using Nonlinear Wavelets” by Creusere, C. D. (2000); “Efficient Triangular Surface Approximations Using Wavelets and Quadtree Data Structures” by Gross, M. H., Staadt, O. G., and Gatti, R. (1996); “Adaptive Surface Meshing and Multi-Resolution Terrain Depiction for SVS” by Wiesemann, T., Schiefele, J., Kubbat, W., Proceedings SPIE Vol. 4363 Enhanced and Synthetic Vision (August 2001); “Multi-Resolution Terrain Depiction and Airport Navigation Function on an Embedded SVS” by Wiesemann, T., Schiefele, J., Bader, J., Proceedings SPIE Vol. 4713 Enhanced and Synthetic Vision (July 2002); “Wavelet Analysis for a New Multiresolution Model for Large-Scale Textured Terrains” by Abasolo, M. J., Perales, F. J., Journal of WSCG, (2003); “Multiresolution Surface and Volume Representations” by Staadt, O. G., Geometric modeling for Scientific Visualization, Springer-Verlag, Heidelberg, Germany, (2003); “Generation of Hierarchical Multiresolution terrain Databases Using Wavelet Filtering” by McArthur, D. E., Fuentes, R. W., Devarajan, V., Photogrammetric Engineering &amp; Remote Sensing (2000); “Compression Methods for Visualization” by Gross, M. H., Lippert, L., Staadt, O. G., Future Generation Computer Systems, Vol. 15, No. 1 (1999); “Multiresolution Compression and Reconstruction”, by Staadt, O. G., Gross, M. H., Weber, R., Proceedings of IEEE Visualization &#39;97 (1997); “Fast Multiresolution Surface Meshing” by Gross, M. H., Gatti, R., Staadt, O. G., 6th IEEE Visualization Conference (1995). 
     SUMMARY 
     A method and system are provided for progressive mesh storage and reconstruction using wavelet-encoded height fields. A system so constructed may provide for full-mesh storage of terrain elevation height field datasets, such as Digital Terrain Elevation Data (“DTED”), using wavelet-encoded terrain height fields. The system may then retrieve, prepare and render spatially-filtered, smoothly-continuous, level-of-detail 3D terrain geometry. 
     In one embodiment, a method for progressive mesh storage includes reading raster height field data, and processing the raster height field data with a discrete wavelet transform to generate wavelet-encoded height fields. Processing may include processing the raster height field data into a quadtree structure, and/or may include utilizing a wavelet subband filter that may be one of the integer biorthogonal 5/3 Daubechies form and the biorthogonal 9/7 Daubechies form. 
     In another embodiment, a method for progressive mesh storage includes reading texture map data, and processing the texture map data with a discrete wavelet transform to generate wavelet-encoded texture map fields. Processing may include processing the texture map data into a quadtree structure, and/or may include utilizing a wavelet subband filter that may be one of the integer biorthogonal 5/3 Daubechies form and the biorthogonal 9/7 Daubechies form. 
     In another embodiment, a method for reconstructing a progressive mesh from wavelet-encoded height field data includes determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint. Triangle strip constructs are generated from vertices of the terrain blocks, and an image is rendered utilizing the triangle strip constructs. Determining terrain blocks and/or the level of detail required may include (a) evaluating distance of the terrain blocks from the viewpoint, and/or (b) evaluating orientation of the viewpoint with respect to the terrain blocks. The method may include redetermining terrain blocks, and a level of detail required for each terrain block, based upon a change of the viewpoint. The method may include determining and unloading one or more unnecessary terrain blocks, based upon a change of the viewpoint. The method may include evaluating a distance parameter α for each terrain block; and performing a geomorph, utilizing distance parameter α, on each terrain block. The method may include determining texture map blocks and a level of detail for each texture map block, wherein the step of rendering comprises utilizing the texture map blocks. The method may include performing an edge-join operation to eliminate T-junctions where terrain blocks of differing levels of detail meet. The image may include ancillary scene data. Each terrain block may be divided into a field region and a trim region, so that vertices of the field region may be transmitted as one triangle strip construct and vertices of the trim region may be transmitted as one or more additional triangle strip constructs. Original height field minima and maxima may be preserved in the wavelet-encoded height fields and the rendered image at all levels of detail. 
     In another embodiment, a software product includes instructions for progressive mesh storage, including instructions for (a) reading one of raster height field data and texture map data as input data, and for (b) processing the input data with a discrete wavelet transform to generate wavelet-encoded data. 
     In another embodiment, a software product includes instructions for reconstructing a progressive mesh from wavelet-encoded height field data, including instructions for (a) determining terrain blocks, and a level of detail required for each terrain block, based upon a viewpoint; for (b) generating one or more triangle strip constructs from vertices of the terrain blocks; and for (c) rendering an image utilizing the triangle strip constructs. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1A  shows one exemplary system for progressive mesh storage that processes raster height field data into wavelet-encoded height fields. 
         FIG. 1B  shows one exemplary system for reconstruction using wavelet-encoded height fields. 
         FIG. 2A  shows a flowchart illustrating an exemplary process that creates wavelet-encoded height field data from raster height field data, and an exemplary run-time process that uses wavelet-encoded height field data and location/orientation/field-of-view data to produce output. 
         FIG. 2B  shows a flowchart illustrating one exemplary process suitable for use as a step of the process of  FIG. 2A , for processing terrain blocks and location/orientation/field-of-view data to produce output. 
         FIG. 2C  shows a flowchart illustrating one exemplary process that uses wavelet-encoded height field data, wavelet encoded texture map data, ancillary scene data and location/orientation/field-of-view data to produce output 
         FIG. 3  shows one flight-based 3D terrain rendering software system, illustrating functional software blocks suitable for progressive mesh storage and reconstruction using wavelet-encoded height fields. 
         FIG. 4A  and  FIG. 4B  illustrate relationships among wavelet-encoded terrain blocks at various levels of detail (“LOD”). 
         FIG. 5A  and  FIG. 5B  illustrate view frustum focused determination of wavelet-encoded terrain blocks containing height data of an area for rendering a scene. 
         FIG. 6  illustrates omni-directional determination of wavelet-encoded terrain blocks containing height data of an area for rendering a scene. 
         FIG. 7A  illustrates a data preparation process for reconstruction using terrain height fields. 
         FIG. 7B  illustrates a geomorphing process for reconstruction using terrain height fields. 
         FIG. 8  illustrates the steps performed in the processes of  FIG. 7A  and  FIG. 7B  from a terrain block data perspective. 
         FIG. 9A  illustrates generation of triangle strips from a terrain block. 
         FIG. 9B  illustrates initiation of a triangle strip from a portion of the terrain block of  FIG. 9A . 
         FIG. 10A  illustrates a process of joining terrain blocks that have differing LOD. 
         FIG. 10B  illustrates a composite terrain block that forms when the terrain blocks of  FIG. 10A  are joined. 
     
    
    
     DETAILED DESCRIPTION 
     In certain of the progressive mesh storage and processing systems and methods disclosed herein, particularly in connection with reconstruction using wavelet-encoded height fields for three-dimensional (3D) computer graphics and 3D terrain rendering, two general constructs may be employed. First, regular x, y-matrix terrain height fields and texture data may be processed and stored in wavelet-encoded forms (i.e., a terrain height field matrix and/or texture map data may be processed using a discrete wavelet transform (“DWT”) and the resulting data may be retained as source data for a 3D terrain renderer). Second, a terrain block-based 3D terrain renderer (1) manages scene level-of-detail data requirements depending on point of view, (2) reconstructs output from the wavelet-encoded source data, scene requirements and regions of interest (current and/or projected), and optionally (3) processes ancillary scene data to perform a complete 3D rendering of the resulting scene. 
     For example,  FIG. 1A  shows one exemplary system  10  for progressive mesh storage that processes raster height field data into wavelet-encoded height fields, in accord with an embodiment. System  10  includes a computer  12  that, for example, has a memory  14 , a storage device  16  and a processor  18 . Storage device  16  is for example a hard disk drive, and can store data encoder software  20 , raster height field data  22  and wavelet-encoded height field data  24 , as shown. Processor  18  operates to load data encoder software  20  into memory  14 , as illustrated by dashed lines of loaded data encoder software  20 ′. Processor  18  then executes loaded data encoder software  20 ′ to process raster height field data  22 , to produce wavelet-encoded height field data  24 . A working set  26  that may include part or all of raster height field data  22  may be created in memory  14  during the processing of raster height field data  22 . Wavelet-encoded height field data  24  includes terrain blocks at multiple levels of detail (“LOD”) that may also be indexed by spatial location (see  FIG. 4 ). For example,  FIG. 1A  shows wavelet-encoded height field data  24  including an LOD  0  terrain block  25 ( 1 ), LOD  1  terrain blocks  25 ( 2 )- 25 ( 4 ), LOD  2  terrain blocks  25 ( 5 )- 25 ( 7 ), and other terrain blocks denoted by ellipsis. 
     Raster height field data  22  may include multiple files which may cover different geographic areas and which may map different (adjacent or overlapping) areas with differing data densities (i.e., may have different numbers of data points per unit area). For example, areas around airports may be mapped with higher data density than other areas. Data encoder software  20  may process raster height field data  22  that has high data density into wavelet-encoded height field data  24  that has more levels of detail, and raster height field data  22  that has low data density into wavelet-encoded height field data  24  that has fewer levels of detail. Wavelet-encoded height field data  24  at a highest level of detail may include information enabling an exact reconstruction of vertices of raster height field data  22 . 
     Processing of raster height field data  22  into wavelet-encoded height field data  24  may also compress the data. A lossless compression mode, such as provided by the reversible integer biorthogonal 5/3 Daubechies form, typically creates wavelet-encoded height field data that is compressed by about 2:1 to 4:1 as compared to raster height field data. Lossy compression, such as provided by the irreversible biorthogonal 9/7 Daubechies form, may create wavelet-encoded height field data that is compressed by about 10:1 to 50:1 as compared to raster height field data. A compression mode used for a particular application may be chosen by evaluating tradeoffs such as memory size, speed of reconstruction, and tolerance in the application for visual errors that may result from reconstruction of data compressed with a lossy compression mode. 
       FIG. 1B  shows one exemplary system  50  for reconstruction using wavelet-encoded height fields, in accord with an embodiment. System  50  includes a computer  52  and an output device  65 ; location/orientation/field-of-view data  70  is shown being input to computer  52 . Computer  52  is additionally shown to include memory  54 , a storage device  56 , a processor  58  and a display processor  60 . Storage device  56  is, for example, a hard disk drive. Storage device  56  is shown with 3D run-time terrain renderer software  62  and wavelet-encoded height field data  24  (which may be created by system  10 ,  FIG. 1A , for example). Wavelet-encoded height field data  24  includes terrain blocks  25 . Processor  58  operates to load 3D run-time terrain renderer software  62  into memory  54 , as illustrated by dashed lines of loaded 3D run-time terrain renderer software  62 ′. 3D run-time terrain renderer software  62  contains a scene manager  64  that loads into memory  54  as loaded scene manager  64 ′. Processor  58  then executes loaded 3D run-time terrain renderer software  62 ′ to process location/orientation/field-of-view data  70 , load selected terrain blocks  25  as loaded terrain blocks  25 ′ in a working set  66 , and process loaded terrain blocks  25 ′ to produce an output display signal  68  via display processor  60  (where terrain blocks  25  and  25 ′ denote general cases of terrain blocks  25 ( 1 ),  25 ( 2 ), . . . and  25 ( 1 )′,  25 ( 2 )′, . . . , respectively, as shown in  FIG. 1B ). Not every terrain block  25  of wavelet-encoded height field data  24  typically loads into working set  66  (e.g.,  FIG. 1B  shows terrain blocks  25 ( 1 )′,  25 ( 2 )′,  25 ( 4 )′,  25 ( 6 )′,  25 ( 10 )′, and others denoted by ellipsis, but not terrain blocks  25 ( 3 )′,  25 ( 5 )′ or  25 ( 7 )′- 25 ( 9 )′, for example). Working set  66  may also contain other kinds of data (see  FIG. 2C ). Display processor  60  may be, for example, a Graphics Processing Unit (“GPU”). Output  68  may be utilized by an output device  65  that may be, for example, a visual display, a printer, a plotter or a Web client. Location/orientation/field-of-view data  70  may be, for example, (1) received from an aircraft navigation computer, (2) received from a Web client, defining a view desired on output device  65 , or (3) received from an input device or devices. 
       FIG. 2A  shows a flowchart illustrating (1) an exemplary process  100  that creates wavelet-encoded height field data  24  from raster height field data  22  and (2) an exemplary process  106  that uses wavelet-encoded height field data  24  and location/orientation/field-of-view data  70  to produce output  68 , in accord with an embodiment. 
     Discrete wavelet transform  104  of process  100  converts raster height field data  22  (which is, for example, raw terrain elevation data) into wavelet encoded height field data  24 , utilizing sub-band decomposition. Process  100  is, for example, a pre-processing step to produce data  24 , and may occur only once. 
     Process  106  is for example performed by computer  52  under the control of loaded 3D run-time terrain renderer software  62 ′,  FIG. 1B . In step  108 , loaded scene manager  64 ′ directs computer  52  utilizing location/orientation/field-of-view data  70  to identify, within wavelet-encoded height field data  24 , terrain blocks  25  utilized at each LOD to produce output  68 . In step  110 , process  106  loads identified terrain blocks  25  from wavelet-encoded height field data  24  as loaded terrain blocks  25 ′ of working set  66 ,  FIG. 1B . In step  112 , process  106  renders output  68  utilizing loaded terrain blocks  25 ′ and location/orientation/field-of-view data  70 , as directed by loaded scene manager  64 ′. 
       FIG. 2B  shows a flowchart illustrating one exemplary process  150  suitable for use as step  112  of process  106 ,  FIG. 2A , for processing terrain blocks (e.g., loaded terrain blocks  25 ′) and location/orientation/field-of-view data  70  to produce output  68 . Process  150  may be performed by computer  52  under control of loaded 3D run-time terrain renderer software  62 ′, for example. Wavelet-encoded height field data  24 , step  110  of process  106 , and display output  68  are shown with dashed lines to illustrate processing context of process  150 . 
     In step  156 , process  150  performs a geomorph on terrain-blocks loaded in step  108  of process  106 . The geomorph eliminates vertex ‘popping’ artifacts on display output  68  by smoothly interpolating geometries of terrain-blocks loaded in step  108  (see also  FIG. 7A ,  FIG. 7B  and  FIG. 8 ). In step  158 , process  150  performs an edge-join operation to correct anomalies where terrain blocks of differing LOD join. In step  160 , process  150  organizes working set  26  into a triangle strip construct for rendering. In step  162 , process  150  outputs the triangle strip construct to display processor  20 ,  FIG. 1 . In step  164 , display processor  20  utilizes the triangle strip construct to render a 3D image, to produce output  68 . It will be appreciated that certain steps of process  150  may be performed in a different order than the order listed; for example, step  160  may precede step  158 , or steps  160  and steps  162  may be performed concurrently, in certain applications. 
       FIG. 2C  shows a flowchart illustrating one exemplary process  206  that uses wavelet-encoded height field data  24 , wavelet encoded texture map data  170 , ancillary scene data  174  and location/orientation/field-of-view data  70  to produce output  68 , in accord with an embodiment. Like process  106 , process  206  is for example performed by computer  52  under the control of loaded 3D run-time terrain renderer software  62 ′,  FIG. 1B . While process  106  renders a 3D terrain height image, process  206  adds texture information and ancillary scene data for increased realism and usefulness of output  68 . Raw texture map data is analogous to raster height field data  22 ,  FIG. 1A ; a process that produces wavelet encoded texture map data  170  is analogous to process  100 ,  FIG. 2A ; wavelet-encoded texture map data  170  is analogous to wavelet-encoded height field data  24 ,  FIG. 1B . Ancillary scene data may include flight-aid graphical elements and/or icons that may provide additional flight situational awareness when depicted within a rendered scene context in output  68  (see also  FIG. 3 ). 
     In step  208 , loaded scene manager  64 ′ directs computer  52  utilizing location/orientation/field-of-view data  70  to identify (a) specific terrain blocks  25  within wavelet-encoded height field data  24  and (b) texture blocks within wavelet encoded texture map data  170 , that are required at each LOD to produce output  68 . In step  210 , process  206  loads identified terrain blocks  25  and identified terrain blocks into working set  66 ,  FIG. 1B . In step  212 , process  206  renders output  68  utilizing loaded terrain blocks  25 ′, loaded texture blocks, ancillary scene data  174 , and location/orientation/field-of-view data  70 , as directed by loaded scene manager  64 ′. 
     Wavelet-Encoded, Multiple-Level-of-Detail Terrain Data Storage 
     Typically, raster height field data  22 ,  FIG. 1A , originates as a raster-ordered, regular matrix of values where each value represents the height of terrain at a particular x, y location; it is thus a parametric surface whereby height is a function of the x and y coordinates. Height values are typically formatted as a signed 16-bit integer, although, alternatively, larger integer or floating point formats may be used as required by a particular application. In one embodiment, system  10  processes raster height field data  22  into a wavelet-encoded form using a DWT yielding a resulting dataset (e.g., wavelet-encoded height field data  24 ) as source data for loaded 3D run-time terrain renderer software  62 ′. Texture map data typically originates as a raster-ordered regular matrix of pixels (e.g., an image). Each pixel of the texture map image may be, for example, composed of an 8-bit red value, an 8-bit green value, and an 8-bit blue value (i.e., a 24-bit Red-Green Blue “RGB” color pixel). Texture map data typically originates as raster image data at a higher level of detail than terrain data  22 , but it may originate at the same, or a lower, level of detail than terrain data  22 . In one embodiment, system  10  processes raster texture map data into a wavelet-encoded form using a DWT yielding a resulting dataset (e.g., wavelet-encoded texture map data  170 ) as source data for loaded 3D run-time terrain renderer software  62 ′. Ancillary scene data  174  may be stored as an arbitrary list of numeric geometric object descriptions that may include x, y, z vertices, may be associated with x, y, z object points, areas, or volumes in space, and may represent general cartographic features and fixed items (e.g., towers, buildings, runways), movable items (e.g., vehicles, aircraft) or flight-path or vehicle passage corridor representations (e.g., indications of the intended paths of aircraft and/or land vehicles). Loaded scene manager  64 ′ may determine when a specific item of ancillary scene data  174  should be included in output  68 . 
       FIG. 3  shows one flight-based 3D terrain rendering software system  300 , illustrating functional software blocks suitable for progressive mesh storage and reconstruction using wavelet-encoded height fields, in accord with an embodiment. System  300  includes a synthetic vision (“SV”) flight application  310  that may be, for example, software that directs a computer (e.g., computer  52 ,  FIG. 1B ) aboard an aircraft. Flight application  310  is in communication with a flight terrain renderer applications program interface (“API”)  320  that includes an LOD processor and wavelet quadtree data structure manager  350  and a scene manager  360 . API  320  also includes a viewpoint processor and data access predictor  330  that receives location/orientation/FOV data  70 , a wavelet terrain data LOD loader  340  that receives wavelet-encoded terrain data  24 , a wavelet texture map data LOD loader  344  that receives wavelet-encoded texture map  170 , and an ancillary scene data loader  348  that receives ancillary scene data  174 . Flight application  310  and API  320  are in communication with a Graphical User Interface (“GUI”)/Display layer API  370 . API  320  and API  370  generate output that is received by a Graphics Processor Unit (“GPU”)  390  via a graphics device driver  380 , such as an OpenGL driver, which processes the output into a format recognized by GPU  390 . GPU  390  processes data received from API  320  and API  370  via driver  380  to produce output (e.g., output  68 , not shown) that may be displayed, for example, on one or more monitors of an aircraft. 
     One advantage of using a wavelet-encoded form of terrain data may be to provide a compact, multiple-level-of-detail representation of the original data (see, e.g.,  FIG. 4 ). Wavelet encoding of raster height field data  22  to produce wavelet-encoded terrain height field data  24  generates a plurality of spatially-filtered levels of detail, similar to texture mipmapping. The DWT uses digital sub-band filters to decompose raster height field data  22  into groups of components, namely a low-frequency component and high-frequency components in the y-, x-, and xy-directions. 
       FIG. 4A  and  FIG. 4B  illustrate relationships among wavelet-encoded terrain blocks  25  at various LOD, in accord with an embodiment. The DWT process breaks the original data into powers-of-2-sized blocks containing spatial detail to a given LOD, where each block at a higher LOD contains high-frequency components to increase LOD of a reconstructed image, compared to blocks of lower LOD. In  FIG. 4A  and  FIG. 4B , a data set  300  includes only terrain block  25 ( 1 ) at LOD  0 . Data set  305  includes data set  300  and additional terrain blocks  25 ( 2 ),  25 ( 3 ) and  25 ( 4 ) that contain y-direction, x-direction, and xy-direction information, respectively, at LOD  1  for the terrain represented by terrain block  25 ( 1 ). Data set  310  includes data set  305  and additional terrain blocks  25 ( 5 ),  25 ( 6 ) and  25 ( 7 ) that contain y-direction, x-direction, and xy-direction information, respectively, at LOD  2  for the terrain represented by terrain block  25 ( 1 ). Data set  315  includes data set  310  and additional terrain blocks  25 ( 8 ),  25 ( 9 ) and  25 ( 10 ) at LOD  3 . 
     Only four LOD levels are shown in  FIG. 4A  and  FIG. 4B , for clarity of illustration; though additional possible LOD levels are suggested by ellipsis  316 . The number of levels used in a DWT process may be arbitrary, though they may depend upon source image size and a smallest reconstructable block size. Each level may create, for example, x-direction, y-direction, and xy-direction detail for a ½-size (in each axis) LOD+1 block of the preceding level (e.g., LODn is the full-size image, LODn−1 is ½ size, LODn−2 is ¼ size, and so on, down to LOD 0  that represents the lowest level of detail representation of the original source data). The number of levels used in wavelet decomposition may therefore be described as a function of source height field size and the smallest desired reconstructable terrain block size, as follows:
 
DWT levels=log 2 (Height Field Edge Length)−log 2 (Terrain Block Edge Length)+1
 
     As wavelet decomposition stores data as the smallest size image (sometimes denoted herein as a “DC component”), with each ascending level&#39;s high-frequency information (sometimes denoted herein as “AC components”), the next-highest LOD may be generated. For instance, a 6-level wavelet decomposition has a ½ 5 , or 1/32 size image as its lowest LOD 0  form along with the successive high-frequency components for the 1/16, ⅛, ¼, ½, and full-size image LODs. See, e.g.,  FIG. 4A  and  FIG. 4B . The wavelet subband filters used are those of the reversible (lossless) integer biorthogonal 5/3 Daubechies form and the irreversible (lossy) biorthogonal 9/7 Daubechies form, although the use of other wavelet subband filters, such as those with minima- and maxima-preserving characteristics, is contemplated and may be more appropriate for some applications. The wavelet-transformed height field is partitioned and indexed into spatially-contiguous blocks providing for efficient access to arbitrary LODs and spatial regions of interest. 
     A further illustration showing a 3-level wavelet decomposition of a 16-bit terrain height field into three resolution levels may be seen in FIGS. 5, 6, 7 of U.S. Provisional Patent Application No. 60/569,332, which is incorporated herein by reference. 
     The wavelet-encoding process efficiently stores multi-LOD forms of an image, for example using the encoded “image” as the 16-bit-per-height raster height field. When levels at one LOD are each one-half the size in each axis of a next higher LOD, the data may form an LOD quadtree data structure; each height field block at one LOD corresponding with four height field blocks in the next highest LOD. 
     For an 8-level, wavelet-encoded height field with a 64×64 minimum terrain-block size, the following number of terrain-block grids and total height field size for the LOD may be given: 
     
       
         
           
               
               
               
             
               
                   
               
               
                 LOD level 
                 Grid of 64 × 64 terrain blocks 
                 Total LOD height field size 
               
               
                   
               
             
            
               
                 LOD0 
                 1 × 1 
                 64 × 64 
               
               
                 LOD1 
                 2 × 2 
                 128 × 128 
               
               
                 LOD2 
                 4 × 4 
                 256 × 256 
               
               
                 LOD3 
                 8 × 8 
                 512 × 512 
               
               
                 LOD4 
                 16 × 16 
                 1024 × 1024 
               
               
                 LOD5 
                 32 × 32 
                 2048 × 2048 
               
               
                 LOD6 
                 64 × 64 
                 4096 × 4096 
               
               
                 LOD7 
                 128 × 128 
                 8092 × 8092 
               
               
                   
               
            
           
         
       
     
     Although the resulting wavelet-encoded data may include only height values, the sequence of the height values within the wavelet-encoded data allows for efficient reconstruction of a complete 3D x, y, z height vertex representation, eliminating the need to store full x, y, and z coordinates for each height value. 
     3D Terrain Block Renderer 
     In one embodiment, terrain rendering by system  50 ,  FIG. 1B , processes terrain data primarily as blocks of data, rather than as individual terrain vertices. The wavelet-encoded format of terrain data (e.g., wavelet-encoded height field data  24  as discussed in the preceding section) provides needed terrain blocks at needed LOD at run time. Under the control of loaded scene manager  64 ′, system  50  sets up a scene and determines which terrain blocks are necessary to provide detail at various depths in the scene relative to a viewpoint. For instance, foreground terrain may be rendered using high-LOD blocks, whereas background terrain may utilize low-LOD blocks of terrain data. Regardless of LOD, all blocks may have the same number of vertices; because of the quadtree data structure of the wavelet-encoded terrain data, the spatial dimensions of a block may be one-half (in each axis) the size of a block at a lower LOD. Thus, a number of vertices in a scene is moderated block by block rather than vertex by vertex, conserving considerable central processor unit (CPU) effort. Certain processing may be performed vertex by vertex, such as geomorphing and generation of triangle strips, as discussed below. 
       FIG. 5A  illustrates view frustum focused determination of wavelet-encoded terrain blocks  25  containing height data of an area  400  for rendering a scene, in accord with an embodiment. A desired viewpoint  410  is provided as part of location/orientation/FOV data  70 ; loaded scene manager  64 ′ uses data  70  to generate a view frustum  420 , in this example, to identify terrain blocks  25  with varying LOD based on distance of each terrain block from viewpoint  410 . Only some terrain blocks  25  are labeled within  FIG. 5  for clarity of illustration. Terrain blocks  25 ( 20 ) at a distance from viewpoint  410 , or significantly outside view frustum  420 , are at a low LOD (here denoted LOD n). Terrain blocks  25 ( 21 ) that are closer to viewpoint  410  (e.g., closer to viewpoint  410  than about line  422 ) are at LOD n+1. Terrain blocks  25 ( 22 ) that are still closer to viewpoint  410 , and terrain blocks  25 ( 23 ) that are still closer to viewpoint  410  are not labeled within  FIG. 5B  for clarity of illustration; a region labeled  5 B is shown in  FIG. 5B , showing terrain blocks  25 ( 22 ) and  25 ( 23 ). The use of four LODs in  FIG. 5A  is illustrative only; more or fewer LODs may be used, with the distances utilized to determine loading of each LOD demarked by a correspondingly larger set of lines (e.g., like lines  422 ,  424  and  426 ). It should be apparent that the number of LODs may be arbitrarily large, limited only by a density of the raster data that is processed to form wavelet encoded terrain blocks  25 . At a highest level of detail, wavelet-encoded height field data  24  may include information that enables exact reconstruction of a scene to the level of detail stored in raster height field data  22 . 
       FIG. 5B  is an enlarged illustration of region  5 B of  FIG. 5A . Terrain blocks  25 ( 22 ) that are closer to viewpoint  410  than about line  424  are at LOD n+2 (compared to the LOD of blocks  25 ( 20 ) and  25 ( 21 ) of  FIG. 5A ); Terrain blocks  25 ( 23 ) that are closer to viewpoint  410  than about line  426  are at LOD n+3. 
     The example shown in  FIG. 5A  and  FIG. 5B  illustrates only one way that terrain blocks of specific spatial areas and LOD may be identified. In  FIG. 5A  and  FIG. 5B  blocks in or near view frustum  420  are preferentially loaded, or loaded at higher LOD, as compared to blocks that are significantly outside view frustum  420 . Other embodiments may utilize different methods of loading terrain blocks corresponding with specific spatial areas and LOD. 
       FIG. 6  illustrates omni-directional determination of wavelet-encoded terrain blocks  25  containing height data of an area  450  for rendering a scene, in accord with an embodiment. The example of  FIG. 6  loads an omni-directional (“bomb blast”) pattern of blocks  25  based on a location of a viewpoint  460 . The “bomb blast” pattern utilizes only distance from viewpoint  460  to determine an LOD at which a given terrain block  25  is loaded. For example, in  FIG. 6 , terrain blocks  25  that correspond to locations within about a small distance from viewpoint  460  (indicated by a line  476 ) are loaded at LOD n+2 as terrain blocks  25 ( 22 ). Terrain blocks  25  that correspond to locations within about a larger distance from viewpoint  460  (indicated by an area between line  476  and line  474 ) are loaded at LOD n+1 as terrain blocks  25 ( 21 ). Terrain blocks  25  that correspond with locations within about a still larger distance from viewpoint  460  (indicated by an area between line  474  and line  472 ) are loaded at LOD n as terrain blocks  25 ( 20 ). 
     While the pattern illustrated in  FIG. 5  loads spatial areas within or near view frustum  410  at higher LOD than areas that are not within or near view frustum  410 , the “bomb blast” pattern illustrated in  FIG. 6  may load data at a given LOD in all directions from viewpoint  460 . Loading at least some data, or loading data at a higher LOD, in directions that are not within a current view frustum may facilitate transitions wherein the view frustum moves (e.g., because an aircraft changes course, or because a user looks in a different direction). Other schemes for identifying terrain blocks at specific spatial locations and/or LOD for loading may be used. One such scheme identifies terrain blocks based on recent aircraft movements; for example, if an aircraft has been turning right, terrain blocks to the right of the center of the current view frustum may be loaded at higher LOD. In another example, a scheme identifies terrain blocks based on a predetermined flight plan. 
     In one embodiment, system  50  accesses terrain blocks at varied levels of detail from wavelet-encoded source data, depending on viewpoint location and/or orientation; but it does not cull out individual vertices based on the viewpoint. Reconstructed terrain blocks are LOD-filtered and scaled by the wavelet decomposition process to eliminate further vertex-by-vertex processing. Such terrain rendering may therefore represent a hybrid between a View Independent Progressive Mesh (VIPM) and a View Dependent Progressive Mesh (VDPM) methodology; except run-time processing performance of a VDPM approach (minimized triangle count at run-time based on viewpoint) is achieved without the vertex-by-vertex CPU processing overhead required by other VDPM approaches. 
     System  50  of  FIG. 1B  may for example utilize wavelet-encoded height field data  24  that forms a quadtree structure to facilitate tracking of terrain block levels of detail and to determine, based on viewpoint distance to each block, for example, a required terrain block LOD per a view-space error metric. A quadtree structure may facilitate identification of terrain blocks  25  used for a current scene. Only identified terrain blocks  25  are loaded into system memory (e.g., into working set  66 ,  FIG. 1B ) for rendering. As additional detail is required for a particular spatial area within a scene, the associated terrain block “splits” into four higher-LOD blocks (e.g., referring to  FIG. 4 , additional x-direction, y-direction and xy-direction data, that corresponds with an existing lower LOD block, is loaded). Also, blocks deemed unnecessary for the current scene are unloaded from memory in a data culling process, to eliminate unnecessary wavelet-encoded terrain-block data accesses and terrain-block rendering processes outside of the view angle. A quadtree structure may also facilitate data culling. 
     Terrain blocks  25  may form a wavelet-encoded height field such that x and y locations of each data point may only be implicit, based on sequence of data points within a block, providing a compact height field format for terrain geometry storage and vertex processing. Processes may be used, for example, to convert a scene&#39;s terrain block height fields to a smoothly-continuous and efficiently-renderable form. Such processes may be: (a) geomorphing of terrain block height values to provide smooth switching between LOD levels, (b) appending x- and y-axis values to each height value to create a true 3D vertex, (c) arranging the vertices of each terrain block into triangle strips for efficient processing by a typical hardware Graphics Processor Unit (GPU) while (d) tying edge vertices between adjacent terrain blocks with differing LOD. See also  FIG. 2B . 
     In process (a), the height values of each terrain block  25  are geomorphed to provide smooth height transitions between terrain block levels of detail. Since wavelet decomposition process removes spatial components as LOD decreases, height values of blocks at varying LODs may vary, representing the actual spatially filtered height value at each LOD. Geomorphing linearly varies height values of an entire terrain block  25  based on a distance of a viewpoint from the block. A “lifespan” may be attributed to a spatial area at a particular LOD: additional terrain blocks  25  must be loaded to add detail for the area (corresponding to an increasing LOD) for an approaching viewpoint; terrain blocks may be deleted (corresponding to lower LOD) for a receding viewpoint. Geomorphing varies height values of terrain blocks  25  smoothly; accordingly, displayed output does not abruptly change, which can cause “vertex popping” artifacts, when a spatial area switches from one LOD to another. 
       FIG. 7A  illustrates a data preparation process  500  for reconstruction using terrain height fields. Process  500  may be used, for example, as part of process  110  of  FIG. 2A  and  FIG. 2B , and is for example performed by computer  52  under the control of loaded 3D run-time terrain renderer software  62 ′,  FIG. 1B . Process  500  creates a delta block  535  of data (see also  FIG. 8 ) to hold differences between height values between a terrain block  25 ( 25 ) at one LOD (LOD n) and another terrain block  25 ( 26 ) at a higher LOD (LOD n+1). Process  500  begins with terrain block  25 ( 25 ) already loaded into memory (e.g., memory  54 ,  FIG. 1B ) in step  510 . Step  520  creates an expanded terrain block  25 ( 25 )′ that includes each data point  515  of terrain block  25 ( 25 ), and includes data points  517  that correspond to positions between each pair of data points in terrain block  25 ( 25 ). Data points  517  are created by interpolating data points  515 . Expanded terrain block  25 ( 25 )′ thus includes the number of data points that are included in a terrain block at LOD n+1. Step  530  loads terrain block  25 ( 26 ) into memory. Step  540  creates delta block  535 ; each data point  545  of delta block  535  corresponds to a difference between each data point  525  in terrain block  25 ( 26 ) and the corresponding data point  515  or  517  in expanded terrain block  25 ( 25 )′. Process  500  may be used each time a block of higher LOD data is loaded into memory, to create delta blocks that are used during geomorphing, as described below. 
       FIG. 7B  illustrates a geomorphing process  550  for reconstruction using terrain height fields. Because the terrain rendering process is block based, a computer (e.g., computer  52 ) may evaluate a viewpoint-to-block distance parameter α for each terrain block  25 —rather than for each height value (vertex)—for LOD determination, reducing CPU involvement in the rendering process. Process  550  is a linear height adjustment utilizing distance parameter α that is scaled to a value between 0.0 and about 1.0 depending on distance of a terrain block  25  from a viewpoint (e.g., viewpoint  410  or viewpoint  460 , see  FIG. 5  and  FIG. 6 ) relative to terrain blocks  25  of a greater or lesser LOD. 
     For example, in  FIG. 5B , terrain blocks  25 ( 23 ) that are adjacent to terrain blocks  25 ( 22 ) near line  426  should be scaled the same. This may be accomplished by assigning an α of about 1.0 to terrain blocks  25 ( 3 ) near line  426 , and assigning an α of about 0.0 to terrain blocks  25 ( 3 ) near line  426 . Likewise, terrain blocks  25 ( 22 ) that are adjacent to terrain blocks  25 ( 21 ) near line  424  may be scaled the same, so an α of about 1.0 is assigned to terrain blocks  25 ( 2 ) near line  424 , and an α of about 0.0 is assigned to terrain blocks  25 ( 1 ) near line  426 . The exact value of α assigned to each block is determined from the average distance of the block from viewpoint  410 . 
     Process  550  begins with delta block  535  having been created (e.g., by step  540  process  500 ) and with α determined in step  560 . Step  570  scales each data point  545  of delta block  535  by multiplying it by α. Step  580  subtracts the scaled values from the corresponding data points  525  of terrain block  25 ( 26 ), to create a rendered block  575 . Thus, geomorphing process  550  provides linear height value interpolation between reconstructed terrain block LODs, yielding continuous and spatially-filtered terrain heights as seen from viewpoint  410 . Process  550  may be repeated each time viewpoint  410  moves within scene  400  (because the movement of viewpoint  410  changes α). 
       FIG. 8  illustrates the steps performed in processes  500  and  550  from a terrain block data perspective. Terrain block  25 ( 25 )′ is created from LOD n terrain block  25 ( 25 ) in step  520  by adding interpolated data points  517  to the original data points  515  of terrain block  25 ( 25 ). After LOD n+1 terrain block  25 ( 26 ) is loaded in step  530 , delta block  535  is created in step  540  by subtracting each data point  515  or  517  of terrain block  25 ( 25 )′ from a corresponding data point  525  of terrain block  25 ( 26 ). After α for a specific scene is determined for block  25 ( 26 ), each data point  545  of delta block  535  is first multiplied by α in step  570 , then subtracted from a corresponding data point  525  of terrain block  25 ( 26 ) to create rendered block  575  in step  580 . 
     In process (b), height values with implicit x and y locations within the terrain block are converted to explicit 3D vertices having floating point x, y, and z coordinate values. The raster x and y coordinates become the 3D vertex x and z coordinates, respectively. The corresponding height value becomes the y coordinate. Since location of a terrain block  25  within a scene (e.g., scene  400 ) is known, offset values may be added to convert x and y coordinates of each height value within terrain block  25  to 3D x and z coordinates. 
     In process (c), vertices are transmitted to a GPU as a set of one or more packed triangle strip constructs.  FIG. 9A  illustrates generation of triangle strips from a terrain block  25 ( 30 ). A triangle strip may be, for example, a list of vertices wherein it is understood by a GPU that each of the last three vertices in the list at any time represents a triangle to be rendered; each new vertex added to the list forms a triangle with the two vertices that preceded it. Terrain block  25 ( 30 ) may be divided into a field area  600  that contains all internal vertices  620  of block  25 ( 30 ), and a trim area  610  that contains external vertices  630  (for example, external vertices  630  may be single rows and columns of vertices on the perimeter of block  25 ( 30 )). Dashed line  605  illustratively separates field area  600  from trim area  610  in  FIG. 9A . Arrows  602  indicate the general progression of triangle strip formation through field area  600 ; arrows  612  indicate the general progression of triangle strip formation through trim area  610 . Not all vertices  620 ,  630  of terrain block  25 ( 30 ) or all arrows  602 ,  612  are labeled, for clarity of illustration. 
     Vertices  620  of field area  600  may be transmitted to a GPU as a single triangle strip.  FIG. 9B  illustrates initiation of a triangle strip from a portion of terrain block  25 ( 30 ). The vertices that form the beginning of the triangle strip are numbered in the order that they are transmitted. Vertices V 1 , V 2  and V 3  form the first triangle in the strip; vertices V 2 , V 3  and V 4  form the second triangle, and so forth until vertex V 12  is transmitted. After vertex V 12 , the triangle strip cannot continue with the vertices labeled V 14 , V 15  and V 16 , because transmitting vertex V 14  after vertex V 12  would result in the rendering of a triangle consisting of vertices V 11 , V 12  and V 14 , which is not desired. Instead, vertex V 12  is transmitted again as vertex V 13 , forming a degenerate triangle composed of vertices V 11 , V 12  and V 13 . Next, vertex V 14  is transmitted, forming a degenerate triangle composed of vertices V 12 , V 13  and V 14 . Next, vertex V 14  is transmitted again as vertex V 15 , forming a degenerate triangle composed of vertices V 13 , V 14  and V 15 . Next, vertex V 16  is transmitted, forming a degenerate triangle composed of vertices V 14 , V 15  and V 16 . The degenerate triangles may be rendered by the graphics processor, but have zero size, so they do not appear as output. Vertex V 17  is transmitted after vertex V 16 , to form a triangle composed of vertices V 15 , V 16  and V 17 , to restart the regular formation of triangles across terrain block  25 ( 30 ) in the direction of arrows  602 , continuing with vertices V 18  and V 19 , as shown. 
     Other sequences of vertex output may be used in place of the specific sequence listed above, depending for example on specific GPU or GPU driver requirements. Vertex sequencing may occur in a different order, or differing sequences of vertex output may form degenerate triangles in a different number or position than those described above. Transmission of the last vertex in field area  600  may terminate a triangle strip. 
     Trim areas are converted to triangle strips in a similar manner as field edges; however, triangle stripping of trim areas may involve reconciliation of edge effects that may form when, for example, a terrain block is adjacent to a terrain block of a differing LOD. Terrain blocks  25  of one LOD that adjoin terrain blocks  25  of a lower LOD may form T-junctions in the terrain mesh, leaving visual gaps in the subsequent rendering process. To provide a continuous terrain mesh, T-junctions are removed using a vertex-collapse technique. 
       FIG. 10A  illustrates a process of joining terrain blocks  25 ( 31 ) and  25 ( 32 ) that have differing LOD. Vertices V 20  and V 21  of terrain block  25 ( 31 ) are removed to eliminate T-junctions.  FIG. 10B  illustrates a composite terrain block  650  that forms when terrain blocks  25 ( 31 ) and  25 ( 32 ) are joined. Field areas  655  and  660  are converted to triangle strips as described above, and trim areas are converted to triangle strips along the paths of arrows  665  and  670 . Specific vertices may be transmitted so that the triangles indicated by solid lines in  FIG. 10B  are rendered, with certain vertices transmitted multiple times so that degenerate triangles form, to prevent unintended triangles from rendering. 
     Changes may be made in the above methods and systems without departing from the scope hereof. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall there between. It should therefore be apparent that the disclosed systems and methods may be altered without departing from the scope hereof, including the following claims. Such alterations may for example include:
         The discrete wavelet transform used to process the original height field data may be operated in either a lossless or lossy mode.   The wavelet encoding process used to reconstruct terrain blocks from the wavelet-encoded data may be such that original height field minima and maxima are preserved in the reconstructed data at all levels of detail.   A sparse height field reconstruction approach may be used wherein high-frequency wavelet coefficients are examined at run time, and coefficients indicating low energy content are used as an indicator for removing certain vertices from a reconstructed terrain block. Removing vertices reduces the terrain block vertex count, and remaining vertices are triangulated in the triangle stripping process.   The wavelet-encoded terrain data may be physically separated from the 3D terrain-block renderer and interconnected via a networked interface.   Any mesh structure describable by a height field may be processed by the systems and methods above.   Terrain block size is not limited to a 64×64 size but may be optimized to GPU hardware capabilities.   The discrete wavelet transform used to process the original height field data may use other wavelet subband filters.