CN100468461C - Real time drawing method of vivid three dimensional land form geograpical model - Google Patents

Real time drawing method of vivid three dimensional land form geograpical model Download PDF

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CN100468461C
CN100468461C CNB2005100868335A CN200510086833A CN100468461C CN 100468461 C CN100468461 C CN 100468461C CN B2005100868335 A CNB2005100868335 A CN B2005100868335A CN 200510086833 A CN200510086833 A CN 200510086833A CN 100468461 C CN100468461 C CN 100468461C
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landform
algorithm
terrain
real
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CN1753033A (en
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王莉莉
史逊
刘贤梅
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Beihang University
Beijing University of Aeronautics and Astronautics
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Abstract

The invention is a method for real-time drawing geometric model of realistic 3D topography, characterized in comprising the following steps of: (1) preprocessing topographical data to its structure accord to the follow-up operation; (2) adopting a topographical planning algorithm of making file-file real-time switching based on traditional LRU algorithm and the method of integrating viewpoint interests to complete the real-time planning for large-scale topographical files; (3) simplifying topographical model based on geometric Mip Map topographical network implementing and generating algorithm;(4) displaying topographical feature based on multi-grain GPU topographical Bump Map rendering algorithm; (5) realizing topographical data conversion based on four-tree ergodic topographical partial-replacing algorithm. The invention solves the problem of the drawing speed of topographical model being low, raising the drawing efficiency and achieving the purpose of real-time drawing dynamical topography.

Description

The real-time drawing method of vivid three dimensional land form geograpical model
Technical field
The present invention relates to a kind of real-time drawing method of three dimensional land form geograpical model.
Background technology
The terrain rendering technology mainly comprises the concrete method for drafting that adopts in landform resource data tissue, drawing data tissue and the drawing process, and landform resource data tissue is meant the storage mode to the terrain data that obtains.Base area graphic data obtaining means difference, typical terrain data is with equidistant face of land elevation grid DEM sampling, as shown in Figure 1a, this part data is without the optimization process towards drafting, and data volume is big, redundancy, but data precision is good, often is applied in science calculating or the military policy.Towards reorganizing of drawing, the purpose of doing like this is to reduce to draw fixed point quantity and improve and draw efficient on the basis that does not influence display effect and verisimilitude to the drawing data tissue as far as possible with that resource data of disciple of obtaining.The data organization in this stage generally is divided into regular grid and irregular grid according to the characteristics that generate how much dough sheets, and one is based on the shortcut calculation of quad-tree structure, and the data layout quadrangularly after the reconstruct or the array distribution of regular triangle are shown in Fig. 1 b; Two are based on the shortcut calculation of the triangulation network, and the data layout after the reconstruct becomes the array distribution of sealene triangle, shown in Fig. 1 c.The former speed is fast, but simplifies effect not as the latter, and it is optimum that the latter's effect should reach, but speed is than the former slow one even several magnitude.Method for drafting is meant and will be plotted on the display screen through video card by drafting platforms such as OpenGL or DirectX through the terrain data after optimizing.
At present in the external disclosed document, Lindstrom P, Koller D, Ribarsky Wetal. " Real-Time continuous level of detail render of height fields " InSIGGRAPH, 96Proc, New Orleans, Louisiana USA, 1996. have early provided the real-time landform shortcut calculation of quad-tree structure.Domestic Wang Hong force, " a dynamic multiple resolution ratio relief block relevant " with viewpoint, computer-aided design (CAD) and figure journal, 2000,12 (8) have proposed the viewpoint correlation model based on the multiresolution relief block; Pan Liliang, " based on the Primary Study of the extensive sense of reality outdoor scene real-time rendering technology of LOD " Chinese development of games net 2003.4 have proposed to use viewpoint relevant and decide the LOD algorithm of the due level of detail of landform with the relevant technology of the fluctuating quantity of landform own.
But the solution thinking of above-mentioned document has three defectives: first, do not consider the optimization problem of large-scale terrain, large-scale terrain emulation is demand common in the Simulation Application, but large-scale terrain loaded generally all to adopt once loads all landform, or simply adopt LRU (least recently used number of times) algorithm to be described, fundamentally do not consider the operation characteristic the when user roams for landform; The second, do not consider that the true to nature of landform play up, true to nature the playing up of landform is the verisimilitude of reality and the result of data complexity contradiction neutralization, promptly how with trying one's best few data description terrain effect true to nature.Relatively more classical problem comprises the simplification of triangle gridding, the elimination in T type crack, the loading of texture true to nature etc.In the programming of real world devices, triangle tabulation or triangle strip generating algorithm (pp.13-20, August 1995 for Deering Michael, " Geometry Compression " Computer Graphics) are generally adopted in leg-of-mutton generation.Becoming stronger day by day wherein along with the graphic display device function, adopt GPU (Graphic Processing Unit, a kind of hardware configuration in the graphics device) carries out fast that calculate on the summit and the texture loading becomes the important tool of playing up, apply it in the drafting of landform also fewer in recent years; The 3rd, do not consider that terrain data dynamically updates, landform is not unalterable in procedure for displaying, generally can be owing to wait cause specific to produce the variation of landform vertex position as blast, how these variations are achieved on general graphics system, above-mentioned document is not all paid attention to.Therefore, when causing present three dimensional land form geograpical model, render speed slowly, to draw efficient low, the defective of real-time drafting weak effect true to nature.
Summary of the invention
Technology of the present invention is dealt with problems: overcome the deficiencies in the prior art, a kind of real-time drawing method of vivid three dimensional land form geograpical model is provided, this method has solved the slow problem of relief block render speed, has improved drafting efficient, has reached the drafting purpose real-time true to nature of dynamic landform.
Technical solution of the present invention: the real-time drawing method of vivid three dimensional land form geograpical model, its characteristics are to comprise the following steps:
(1) terrain data pre-service, graphic data structure simplifiedly;
(2) adopt the landform dispatching algorithm of carrying out the real-time switching between file, finish the Real-Time Scheduling of shape file over the ground based on traditional lru algorithm and the method that combines based on viewpoint interest;
(3) implement generating algorithm based on how much Mip Map terrain mesh, simplify relief block;
(4) the GPU landform Bump Map based on many textures plays up algorithm, shows terrain feature;
(5) based on the local algorithm of replacing of the landform of the traversal of quaternary tree, realize the terrain data conversion.The pretreated step of described terrain data is as follows:
(1) to the original file data file division;
(2) file after will cutting apart is reset, and the file group after being about to cut apart renames according to geography information, and is kept in the file system.
The terrain data that the present invention uses comes from the GTOPO30 terrain data, and (specifying information, form, rights of using are referring to the operation manual website of USGS Http:// edcdaac.usgs.gov/gtopo30/README.asp), this landform comprises the Terrain Elevation data of the 1000 meters precision in the whole world, and 16 sampling precisions are divided into several blocks with the whole world, 6000*4800 sampled point of every block size.A such raw data called in behind the internal memory data volume is huge to be difficult to realize true-time operation, simultaneously 6000 kilometers scope people's FOV (Field of View) head and shoulders above.Therefore, must cut apart rearrangement to these source documents.File division is that file size is reduced to 512*512 or littler 256*256 by 6000*4800, here get 2 power time size and be processing speed (because computing machine adopts 2 systems to calculate), and the size of power value is generally according to application demand and machine performance decision in order to accelerate system.Rearrangement is that the file group after cutting apart is renamed according to geography information, and is kept in the file system.Because the source document of GTOPO30 comprises concrete latitude and longitude information, the initial longitude and latitude of the file after the process of rearrangement just can be cut apart by these information acquisitions.Can named file according to these information, shape as: gtopo30_E120_N40.dem represents east longitude 120 degree, and north latitude 40 degree are the terrain data of starting point.
Described landform dispatching algorithm step is as follows:
(1) get the current viewpoint position and towards, analyze the viewdata terrain block;
(2) the data cached and terrain blocks of data renewal landform cache list according to current landform generates the next frame data;
(3) renewal of buffer memory.
Though it is still also unrealistic that landform, is called in these files internal memory simultaneously through becoming less file group after the pre-service, also needs to carry out dynamic dispatching.Because people's the mobile of pilot is clocklike, and the restriction of visual range, because traditional LRU does not consider the characteristics repeatedly in the pilot roam procedure, the present invention improves algorithm on the basis of LRU, adopts the landform dispatching algorithm of carrying out the real-time switching between file based on traditional lru algorithm and the method that combines based on viewpoint interest.
The step of updating of above-mentioned buffer memory is as follows:
A. each blocks of data all has the statistics of access times in the buffer memory, if the landform that next frame needs is present in the buffer memory soon, then this statistical items adds one automatically;
B. according to current view point with towards with the pilot of previous frame with towards comparing, draw the data that next frame points to, if these data are present in the buffer memory, then statistical items adds one automatically;
C. on this basis, with needs but non-existent data add in the buffer memory, and same quantity data is picked out from current cache, principle is to select statistical items minimal data in the current cache, but this is hit;
D. if the data of picking out are less than the data of increase, promptly buffer memory is too little, then increases buffer memory quantity;
E. as if the data that do not have to pick out, then each frame is picked out the statistical items minimal data piece in the current cache automatically, and the current cache size is subtracted one, once keeps buffer memory can unrestrictedly not increase;
F. if system works on, then return repetition c, otherwise stop.
It is as follows that described Mip Map terrain mesh based on how much is implemented the generating algorithm step:
(1) for initiate terrain block, data is formed quad-tree structure, add up the maximum in each terrain piece summit, minimum, parameters such as error;
(2) according to the distance of current view point and terrain block encirclement ball center, judge the quaternary tree data that adopt which precision grade;
(3) according to adjacent terrain piece data precision level, generate the landform triangle strip, eliminate T type projection;
(4) triangle strip is input to GPU, carries out smoothing processing.
The landform file comprises the geological information of terrain sampling point, and these information are a big grid with topograph.In implementing drawing process, grid is turned to Triangle List or Triangle Strips by triangle and sends into and play up pipeline and play up speed with optimization.Nonetheless, display speed particularly still can not satisfy the demands under the situation that a plurality of ground shape file shows, therefore just needs to be optimized.The method that the present invention adopts is based on how much MipMap grid generating algorithm, each ground shape file is formed the institutional framework of quaternary tree in internal memory, bottom is the Data Patch that 17*17 summit formed, and last layer comprises 4 lower floor's subtrees, and recurrence generates until the whole summits of include file.For the ground shape file of 256*256, the subtree number of plies that a such tree comprises is 5 layers, and each layer represented a kind of precision of this Data Patch.The variance that needs to calculate each layer terrain data in the process that generates quaternary tree, information such as average height, these information are selected the data of a certain roughness levels to the distance at landform center according to viewpoint in real-time procedure for displaying.When a coarse rank is transferred to another coarse rank, can produce saltus step on the screen; Can not produce so-called crack problem at intersection simultaneously and work as adjacent landform degree of roughness, address this problem the Shader code that to use GPU.
It is as follows that described GPU landform Bump Map based on many textures plays up algorithm steps:
(1) according to the vector plot and the morphosequent figure of terrain block data generation Bump Mapping, this algorithm pretreatment stage before operation is finished;
(2) calculate face of land planar process vector;
(3) according to the normal vector on planar process vector calculation summit, vertex data place;
(4) the normal vector storage is imported as the Bump Mapping normal direction texture of this algorithm hereof;
(5), calculate the weights that this fixed point is used face of land texture according to the height on landform summit;
(6) utilize the pixel processing unit (Pixel Shader) of GPU to synthesize texture and calculate illumination;
(7) carry out bump pinup picture algorithm.
The landform of described traversal based on quaternary tree is local, and to replace algorithm steps as follows:
(1) obtains and wait to replace the landform geographic position;
(2) according to above-mentioned topographical position index quaternary tree;
(3) upgrade graphic data partly;
(4) recomputate normal vector information.
The present invention's advantage compared with prior art is:
(1) at the form height number of passes is big according to scale accurately, can not disposablely call in the problem of internal memory, according to the zone terrain data is divided into a plurality of files, be kept in the file system or in the Database Systems, employing is carried out real-time switching, scheduling between file based on traditional lru algorithm and the method that combines based on viewpoint interest, has reached flexibly the effectively effect of managing large scale terrain data;
(2) big at three dimensional land form geograpical model vertex data amount, the problem that render speed is slow, setting up on the basis of tree data structure, use is based on the mipmap method of geometry, form the summit of minimum number in real time according to viewpoint and local lineament, and carry out smoothing processing to change the landform saltus step cause because of viewpoint by hardware based summit handoff algorithms, reach relief block and drawn the well balanced of effect and render speed;
(3) at existing topography and landform character complexity, use how much dough sheets to describe fully, be difficult to guarantee the problem of the real-time of its verisimilitude and drafting, adopted GPU terrain rendering method based on many textures, and by bump map algorithm and texture blend, basic landforms texture and cultural traits texture are carried out real time fusion, both reached the effect of demonstration true to nature, also improved drafting efficient;
(4) at the application demand that needs dynamically to change the partial top point coordinate in the terrain rendering, employing is based on the traversal of quaternary tree, location partial top point data, by the data after realizing upgrading based on the interpolation algorithm of graphic hardware and the fusion of ambient data, to reach the real-time rendering purpose of dynamic landform.
Description of drawings
Fig. 1 is the existing figure of terrain data basic organizational structure, wherein Fig. 1 a is that typical terrain data is with equidistant face of land elevation grid DEM sample graph, Fig. 1 b is rule-based triangularization array distribution figure, and shown in Fig. 1 b, Fig. 1 c is the array distribution figure of sealene triangle;
Fig. 2 is large-scale terrain dispatching algorithm modular structure figure of the present invention;
Fig. 3 is the Mip Map terrain mesh rough schematic view based on geometry of the present invention;
Fig. 4 is an elimination T type projection synoptic diagram of the present invention;
Fig. 5 plays up the algorithm synoptic diagram for the GPU landform Bump Map based on many textures of the present invention;
Fig. 6 is the local algorithm synoptic diagram of replacing of the landform of the traversal based on quaternary tree of the present invention.
Embodiment
The present invention is described in more detail below in conjunction with embodiment.
With the original dem data file of the Chinese landform of current reflection, horizontal indulging is that 1024*1024 summit is example.
1. at first carry out pre-service, the data file is cut apart, this document is split into the file sequence set of 256*256 size, and the file group after will cutting apart again renames according to geography information, and preserves in 4 ground shape files, supposes file a, b, c, d.
2. adopt the landform dispatching algorithm of carrying out the real-time switching between file based on traditional lru algorithm and the method that combines based on viewpoint interest then, finish the Real-Time Scheduling of shape file over the ground.Traditional lru algorithm is considered least-recently-used terrain information, when not having the space in the buffering, least-recently-used terrain block is picked out internal memory.This method is widely used in the scheduling memory program, but does not consider the characteristics in the landform navigation process.When people are positioned at a certain viewpoint, and when moving by a certain route, the position that always can predict the next frame viewpoint according to travel direction, according to interest, viewpoint can be rotated, and this has just increased the complicacy of prediction.The present invention can incorporate this prediction in the algorithm in conjunction with the lru algorithm of viewpoint motion interest.As shown in Figure 2, the landform dispatching algorithm is as follows:
(1) drawing program starts, and initialization terrain data buffer memory is preloaded near the terrain data of initial point; When initial, initial point is positioned at region, file a place, and the scope that this moment, viewpoint can reach only is a region, only stores the data message of a in the then initialized landform buffer memory;
(2) obtain the current viewpoint position and towards, analyze the viewdata terrain block; In the procedure for displaying, if viewpoint is positioned at a, the b intersection, this moment, content comprised a, two terrain datas of b;
(3) upgrade the landform cache list according to the data cached and terrain blocks of data of current landform since b terrain data this moment not among buffer memory, so algorithm will load the b data in buffer memory.Generate the next frame data;
(4) renewal of buffer memory is the emphasis among the present invention, and concrete steps are as follows:
A. each blocks of data all has the statistics of access times in the buffer memory, if the landform that next frame needs is present in the buffer memory soon, then this statistical items adds one automatically;
B. according to current view point with towards with the pilot of previous frame with towards comparing, go out the possible data of next frame according to trend prediction, if these data are present in the buffer memory, then statistical items adds one automatically;
C. on the basis of above-mentioned a, b, with needs but non-existent data add in the buffer memory, and same quantity data is picked out from current cache, principle is to select statistical items minimal data in the current cache, but this is hit;
D. if the data of picking out are less than the data (being that buffer memory is too little) of increase, then increase buffer memory quantity, generally double, be that the current cache size only is 1 landform, and because a, b is being shown, and buffer memory quantity must increase, increase strategy and be 2 times to original size, if original size is 4 landform, the landform size after then increasing is 8;
E. as if the data that do not have to pick out, then each frame is picked out the statistical items minimal data piece in the current cache automatically, and the current cache size is subtracted one, once keeps buffer memory can unrestrictedly not increase;
F. if system works on, then return repetition c, otherwise stop.
3. implement generating algorithm based on how much Mip Map terrain mesh, simplify relief block, as shown in Figure 3, Figure 4, concrete steps are as follows:
(1) with the formation of the terrain data piece after the step (4) in landform dispatching algorithm tabulation and to the following operation of each piece circulation carrying out;
In scene graph behind the first adding landform b, do not have corresponding rendered object (specifically comprising data and the state of drawing landform, texture), therefore system will set up corresponding rendered object this moment: the institutional framework that each ground shape file is formed quaternary tree in internal memory, bottom is the DataPatch that 17*17 summit formed, last layer comprises 4 lower floor's subtrees, and recurrence generates until the whole summits of include file.For the ground shape file of 256*256, the subtree number of plies that a such tree comprises is 5 layers, and each layer represented a kind of precision of this Data Patch.
(2) for initiate terrain block, data are formed quad-tree structure, add up the maximum in each DataPatch summit, minimum, parameters such as error;
(3) according to the distance of current view point and terrain block encirclement ball center, judge the quaternary tree data that adopt which precision grade; After setting up rendered object, this relief block can normally be drawn.At first need during drafting to determine to adopt the data of that precision to send to demonstration, this is very necessary optimizing process.Data Patch from the most coarse (0 grade) to the meticulousst (n level), summit quantity differs 2^ (n-1) doubly, selecting under the coarse relatively situation of fine-grained mitigation system pressure greatly under the situation that the viewpoint error satisfies, thereby fundamentally improving render speed at large-scale data.The judgement of viewpoint error has multiple, and as based on projector space, based on screen space etc., because respective algorithms is a lot, specific algorithm is not at protection domain of the present invention.
(4) according to adjacent terrain piece data precision level, generate the landform triangle strip, eliminate T type projection; When the fine-grained of adjacent Data Patch can not produce T type projection simultaneously owing to adjacent summit is not corresponding, the solution of this problem can solve by this method: suppose that the adjacent and fine-grained of Patch 1 and Patch 2 is respectively 2 and 3.Because 3 grades meticulousr,, make Patch2 that adjacent with it triangle fixed point is selected 3 class precisions in order to guarantee display quality, all the other are constant, the triangle strip of Sheng Chenging can solve T projection problem preferably like this, and in like manner, the Patch that is adjacent between shape file also takes this method to eliminate the T projection.
(5) triangle strip is input to GPU, carries out smoothing processing.
4. it is as follows as shown in Figure 5, to carry out the Bump Mapping step that merges based on the multilayer texture of GPU:
Need before the operation to generate the landform vector information according to the vertex information of landform, promptly the normal vector at each place, landform summit also need provide the topographical features data file by the art designing.Normal vector is asked method: obtain the planar process vector on plane, place, summit earlier, and then according to the normal vector of on average obtaining this summit of planar process vector.The information of original texture is used on each summit, the corresponding face of land of topographical features data file.The present invention supports 3 tunnel concurrent original texture, and each summit can be chosen one wantonly, perhaps provides the weights of three's ratio separately.
(1) according to the vector plot and the morphosequent figure of landform blocks of data generation Bump Mapping, this pretreatment stage before operation is finished;
(2) calculate face of land planar process vector;
(3) according to the normal vector on planar process vector calculation summit, vertex data place;
(4) the normal vector storage is imported as Bump Mapping normal direction texture hereof;
(5), calculate the weights that this fixed point is used face of land texture according to the height on landform summit.Can import 3 face of land textures in real time, the weights here are exactly the proportion that three face of land textures are used on this summit, and weights are recorded in the independent file import as parametric texture;
(6) utilize the pixel processing unit (Pixel Shader) of GPU to synthesize texture and calculate illumination.Texture is synthetic: final color=texture 1 color * texture 1 weights+texture 2 color * textures 2 weights+texture 3 color * textures 3 weights;
(7) adopt bump pinup picture algorithm (this algorithm is ripe algorithm).
5. as shown in Figure 6, local to replace algorithm steps as follows based on the landform of the traversal of quaternary tree:
(1) obtains and wait to replace the landform geographic position, promptly obtain the latitude and longitude information of landform initial vertex,, can obtain the position of this terrain data in quaternary tree according to this information;
(2) according to above-mentioned topographical position index quaternary tree;
(3) upgrade graphic data partly, promptly replace in the summit array of terrain data rendered object correspondence;
(4) recomputate normal vector information, obtain the planar process vector on plane, place, summit earlier, and then according to the normal vector of on average obtaining this summit of planar process vector.

Claims (5)

1, the real-time drawing method of vivid three dimensional land form geograpical model is characterized in that comprising the following steps:
(1) terrain data pre-service, graphic data structure simplifiedly;
(2) adopt the landform dispatching algorithm of carrying out the real-time switching between file, finish the Real-Time Scheduling of shape file over the ground based on traditional lru algorithm and the method that combines based on viewpoint interest;
(3) implement generating algorithm based on how much Mip Map terrain mesh, simplify relief block;
(4) the GPU landform Bump Map based on many textures plays up algorithm, shows terrain feature;
(5) based on the local algorithm of replacing of the landform of the traversal of quaternary tree, realize the terrain data conversion;
Landform dispatching algorithm step in the described step (2) is as follows:
(A) get the current viewpoint position and towards, obtain the terrain blocks of data;
(B) the data cached and terrain blocks of data renewal landform cache list according to current landform generates the next frame data;
(C) carry out the renewal of buffer memory, step of updating is as follows:
A. each blocks of data all has the statistics of access times in the buffer memory, if the landform that next frame needs is present in the buffer memory soon, then this statistical items adds one automatically;
B. according to current view point with towards with the pilot of previous frame with towards comparing, draw the data that next frame points to, if these data are present in the buffer memory, then statistical items adds one automatically;
C. on this basis, with needs but non-existent data add in the buffer memory, and same quantity data is picked out from current cache, principle is to select statistical items minimal data in the current cache, but this is hit;
D. if the data of picking out are less than the data of increase, promptly buffer memory is too little, then increases buffer memory quantity;
E. as if the data that do not have to pick out, then each frame is picked out the statistical items minimal data piece in the current cache automatically, and the current cache size is subtracted one, once keeps buffer memory can unrestrictedly not increase;
F. if system works on, then return repetition c, otherwise stop.
2, the real-time drawing method of vivid three dimensional land form geograpical model according to claim 1 is characterized in that: the pretreated step of terrain data in the described step (1) is as follows:
(1) to the original file data file division;
(2) file after will cutting apart is reset, and the file group after will cutting apart renames according to geography information, and is kept in the file system.
3, the real-time drawing method of vivid three dimensional land form geograpical model according to claim 1 is characterized in that: described step (3) is as follows based on how much the real-time generating algorithm step of Mip Map terrain mesh:
(1) for initiate terrain block, data is formed quad-tree structure, add up the parameter in each terrain piece summit;
(2) according to the distance of current view point and terrain block encirclement ball center, adopt the quaternary tree data that are suitable for this precision grade;
(3) according to adjacent terrain piece data precision level, generate the landform triangle strip, eliminate T type projection;
(4) triangle strip is input to GPU, carries out smoothing processing.
4, the real-time drawing method of vivid three dimensional land form geograpical model according to claim 1 is characterized in that: it is as follows that described step (4) is played up algorithm steps based on the GPU landform Bump Map of many textures:
(1) generates the vector plot and the morphosequent figure of Bump Mapping according to the landform blocks of data;
(2) calculate face of land planar process vector;
(3) according to the normal vector on planar process vector calculation summit, vertex data place;
(4) the normal vector storage is imported as the Bump Mapping normal direction texture of this algorithm hereof;
(5), calculate the weights that this fixed point is used face of land texture according to the height on landform summit;
(6) utilize the pixel processing unit Pixel Shader of GPU to synthesize texture and calculate illumination;
(7) carry out bump pinup picture algorithm.
5, the real-time drawing method of vivid three dimensional land form geograpical model according to claim 1 is characterized in that: the landform of described traversal based on quaternary tree is local, and to replace algorithm steps as follows:
(1) obtains and wait to replace the landform geographic position;
(2) according to above-mentioned topographical position index quaternary tree;
(3) upgrade graphic data partly;
(4) recomputate normal vector information.
CNB2005100868335A 2005-11-10 2005-11-10 Real time drawing method of vivid three dimensional land form geograpical model Expired - Fee Related CN100468461C (en)

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