CN103106687A - Adaptive computer generation method and device of three-dimensional ocean grid within vision scope - Google Patents

Adaptive computer generation method and device of three-dimensional ocean grid within vision scope Download PDF

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CN103106687A
CN103106687A CN201310042079XA CN201310042079A CN103106687A CN 103106687 A CN103106687 A CN 103106687A CN 201310042079X A CN201310042079X A CN 201310042079XA CN 201310042079 A CN201310042079 A CN 201310042079A CN 103106687 A CN103106687 A CN 103106687A
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video camera
ken
grid
ocean
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CN103106687B (en
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蒋永实
刘思江
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CHANGZHOU SCIENCE AND ART FUSION TECHNOLOGY RESEARCH INSTITUTE
Institute of Automation of Chinese Academy of Science
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CHANGZHOU SCIENCE AND ART FUSION TECHNOLOGY RESEARCH INSTITUTE
Institute of Automation of Chinese Academy of Science
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Abstract

The invention discloses a computer generation method of a three-dimensional ocean grid. The method comprises the steps of calculating and correcting a vision parameter of a camera according to a current vision parameter of the observation camera; calculating and correcting a sea level scope covered by vision of the camera; and subdividing the covered sea level scope and generating all vertices of the ocean grid and sending the vertices to a ground power unit (GPU) for drawing. The adaptive computer generation method and a device of the three-dimensional ocean grid within the vision scope are mainly used for ocean drawing under the circumstance of air observation. The covered sea level scope can be adaptively determined according to the vision scope of the observation camera, parts beyond the scope are eliminated, a part within the scope is taken as a whole for subdividing to generate the grid, and therefore integral and efficient ocean grid drawing is achieved.

Description

Computer generating method and the device thereof of three-dimensional ocean grid in the self-adaptation FOV (Field of View)
Technical field
The present invention relates to Computerized three-dimensional graphic plotting Computer Aided Design field, relate in particular to computer generating method and the device thereof of three-dimensional ocean grid in a kind of self-adaptation FOV (Field of View).
Background technology
It is an important branch in graphics that the real-time rendering of ocean is played up, particularly important in using at flight simulation, ship simulation.
Generally speaking, the method for ocean drafting mainly is divided into two large classes: based on the method for physics with based on the method for constructing.Generally realize simulation to the ocean by finding the solution the Navier-Stokes system of equations based on the method for physics, owing to calculating more complicated, but the scene scale of the method real time modelling is less, does not require real-time application scenario and more be applicable to film making etc.Mostly during real-time, interactive is used is the methods that adopt based on structure, the method is with the grid representation ocean face of a tiling, ocean statistics and frequency spectrum data based on actual observation, the structures such as employing Fourier transform meet the waveform function of ocean spectrum distribution, and the functional value stack of discretize is replaced to the surface grids of ocean, the driving grid fluctuates, thereby reaches the purpose of simulation ocean.
Flight simulation is the application scenario higher to requirement of real-time, so the method that also adopts based on structure is drawn in ocean wherein.Because the viewpoint position of flight simulation is often higher, the visual field is also comparatively broad, and this just requires for the grid plan of constructing the ocean broad equally, just can avoid can seeing in the high-altitude the not spontaneous phenomenon of coastal ocean; Due to the ambiguity of heading, this grid takes the space on all non-land again again, the visual sense of reality of guarantee.Above-mentioned two reasons will cause the ocean grid very huge, yet in most cases, only having seldom partly can be in sight, and this has just produced considerable redundant computation.Although can reduce amount of redundancy by the processing to grid LoDization, the consistance of the LoD of control mesh and assurance Different L oD needs again the extra computation resource.
In fact, only the part grid in FOV (Field of View) just can finally be drawn, and is presented on user's display screen.If can at first determine this scope, and grid is confined to not only can improve the practical efficiency of grid vertex in this scope, and more summit can be concentrated on and improve the ocean level of detail in this scope, strengthen visual effect.
Summary of the invention
The technical matters that (one) will solve
In view of this, fundamental purpose of the present invention is to provide a kind of suitable flight simulation this application scenario, take air observation under main visual angle situation, the ocean grid generation method that can adjust according to the FOV (Field of View) self-adaptation.
(2) technical scheme
For achieving the above object, the invention provides the computer generating method of a kind of three-dimensional ocean grid, it comprises:
Step 101: according to the ken parameter of current observation video camera, calculate the ken parameter of revising video camera, and then determine to revise the ken of video camera;
Step 102: the sea level scope that the ken of calculating correction video camera covers;
Step 103: the sea level scope that the ken of revising video camera covers is segmented, generated whole summits of ocean grid, and the drafting that GPU carries out three-dimensional ocean grid is sent on whole summits of described ocean grid.
The invention allows for the computing machine generating apparatus of a kind of three-dimensional ocean grid, it comprises:
Determine device, be used for the ken parameter according to current observation video camera, calculate the ken parameter of revising video camera, and then determine to revise the ken of video camera;
Calculation element is used for calculating and revises the sea level scope that the ken of video camera covers;
Generating apparatus is used for the sea level scope that the ken of revising video camera covers is segmented, and generates whole summits of ocean grid, and the drafting that GPU carries out three-dimensional ocean grid is sent on whole summits of described ocean grid.
(3) beneficial effect
Can find out from technique scheme, the present invention has following beneficial effect:
1, the generation method of this Computerized three-dimensional provided by the invention ocean grid can be limited in the scope of expression ocean grid in visible FOV (Field of View), thereby reduces unnecessary calculating, improves the practical efficiency of grid vertex.
2, the generation method of this Computerized three-dimensional provided by the invention ocean grid can change according to the ken generating adaptively corresponding grid, and guaranteeing has the ocean face to exist at requisite space all the time, guarantees the sense of reality when redundancy is the least possible.
3, the generation method of this Computerized three-dimensional provided by the invention ocean grid, only segment the ocean grid in ken coverage, thereby more summit concentrated in FOV (Field of View), improves the ocean level of detail, strengthens visual effect.
Description of drawings
Fig. 1 is the computer generating method process flow diagram according to the three-dimensional ocean grid of the embodiment of the present invention;
Fig. 2 is the observation video camera and the ken mutual relationship figure that revises video camera according to the embodiment of the present invention;
Fig. 3 is with respect to the lift-over angle schematic diagram of revising video camera according to the observation video camera of the embodiment of the present invention;
Fig. 4 is the vertical field angle schematic diagram according to the observation video camera of the embodiment of the present invention and the correction video camera ken;
Fig. 5 is according to the correction video camera ken of the embodiment of the present invention and sea level schematic diagram;
Fig. 6 is according to the rectangular pyramid of the correction video camera ken formation of the embodiment of the present invention and the crossing situation schematic diagram on sea level;
Fig. 7 is for directly carrying out the divided method schematic diagram of linear interpolation according to the embodiment of the present invention to sea level institute coverage;
Fig. 8 is for again projecting the divided method schematic diagram on sea level according to the embodiment of the present invention to linear interpolation after the coverage normalization of sea level institute again;
Fig. 9 is for carrying out the divided method schematic diagram of the weighted linear interpolation of empirical parameter according to the embodiment of the present invention to sea level institute coverage;
Figure 10 is the practical application process flow diagram according to the generation method of the Computerized three-dimensional ocean grid of the embodiment of the present invention.
Embodiment
For make the purpose, technical solutions and advantages of the present invention more clear bright from, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in more detail.
As shown in Figure 1, the Computerized three-dimensional ocean grid generation method that proposes in the preferred embodiment of the present invention mainly comprises:
Step 101, according to the ken parameter of current observation video camera, calculate the ken parameter of revising video camera, and then determine to revise the ken of video camera;
The sea level scope that the ken of step 102, calculating correction video camera covers;
Step 103, covering sea level scope is segmented, generated whole summits of ocean grid and deliver to GPU and draw.
Current observation video camera refers in the Computerized three-dimensional scene to be used for the virtual video camera observed, and its viewed content determines the 3-D view that final user sees on display screen, and namely its content of observing is used for showing.Revising video camera, is the virtual video camera in the Computerized three-dimensional scene, and the sea level scope that its FOV (Field of View) covers is the scope of drawing three-dimensional ocean grid, therefore revises the scope that video camera is not used in the three-dimensional ocean grid that shows and be used for determining needing drawing.Observe video camera any rotation can occur, pitching can occur under world coordinate system or local coordinate and revise video camera, but only go off course under world coordinate system, and lift-over does not occur under world coordinate system and local coordinate, world coordinate system is specified the whole three-dimensional coordinate system of justice, and local coordinate system means to revise video camera or observes video camera is the defined corresponding local coordinate of initial point.The ken of revising video camera has comprised the ken of observing video camera.The ken parameter of observing video camera and revising video camera comprises the sensing of the ken, the vertically length ratio of field of view angle, transverse and longitudinal and cross-sectional distance far away etc., the ken of revising video camera is pointed to, cross-sectional distance far away, three-dimensional space position are identical with the observation video camera, and other ken parameter is definite by observing video camera.
Observe video camera and revise the ken of video camera and mutual relationship as shown in Figure 2:
Point E is viewpoint position, namely observes the residing three dimensions point of video camera;
The ken that video camera is observed in rectangular pyramid E-ABCD representative, bottom surface ABCD is rectangle, the ratio of limit AB, BC is the length ratio R of ken transverse and longitudinal obs=| AB|/| BC|; Point O is the mid point of rectangle ABCD, and the sensing of line EO is the sensing of the ken
Figure BDA00002809819000041
And vertical with the bottom surface, the length of EO is cross-sectional distance far away; The mid point of limit AB, CD is respectively F, G, and line EF, EG ∠ FEG are vertical field angle of this ken, and establishing angle is θ obs
The ken of video camera is revised in rectangular pyramid E-KLMN representative, and bottom surface KLMN is rectangle, and the ratio of limit KL, LM is the length ratio R of ken transverse and longitudinal rev=| KL|/| LM|; Point O is the mid point of rectangle KLMN, and the sensing of line EO is the sensing of the ken
Figure BDA00002809819000042
And vertical with the bottom surface, the length of EO is cross-sectional distance far away; The mid point of limit KL, MN is respectively P, Q, and line EP, EQ ∠ PEQ are vertical field angle of this ken, and establishing angle is θ rev
The ken rectangular pyramid E-ABCD that observes video camera can go off course, any rotation of pitching or lift-over changes, and the ken rectangular pyramid E-KLMN that revises video camera can occur pitching, only occur in world coordinate system driftage, the lift-over in any coordinate system does not occur, so limit KL or MN parallel with surface level in world coordinate system all the time; Simultaneously, revise the compact ken rectangular pyramid bottom surface ABCD that observes video camera that surrounds of ken rectangular pyramid bottom surface KLMN of video camera, namely the latter's summit is dropped on the former limit all the time.
To observing the definition of video camera and correction video camera, step 101 specifically comprises the following steps based on above-mentioned:
Step 1011: calculate and observe video camera with respect to the lift-over angle of revising video camera.
The ken parameter of observing video camera is known and definite, various rotations occur for it can cause the variation of revising video camera, constantly observe the corresponding correction video camera of video camera for obtaining certain, need at first to calculate and observe video camera with respect to the lift-over angle of revising video camera, as shown in Figure 3:
The definition of each point is identical with Fig. 2, definition It is vectorial for observing making progress of the video camera ken,
Figure BDA00002809819000052
For revising the upwards vector of video camera, angle ∠ FOP is for observing video camera with respect to the roll angle of revising video camera, and establishing angle is α.But the α value is difficult for directly calculating, this be because, although vector
Figure BDA00002809819000053
Can be obtained by the local coordinate Y-axis of observing video camera, and vector
Figure BDA00002809819000054
Be the amount that required correction video camera comprises, can't directly obtain.
Consider that lift-over can not occur to revise video camera, therefore put plane that E, O, P determine perpendicular to the surface level of world coordinate system.Suppose vector of unit length Perpendicular to the surface level of world coordinate system, so
Figure BDA00002809819000056
In the EOP of plane; If vector
Figure BDA00002809819000057
KL is parallel with the limit, so
Figure BDA00002809819000058
In plane KLMN (or ABCD), and If establish
Figure BDA000028098190000510
With
Figure BDA000028098190000511
Angle is β, has,
α=|β-90°|
Separately, vector
Figure BDA000028098190000512
With Yi Zhi has,
Figure BDA000028098190000514
Obtain vector
Figure BDA000028098190000515
With
Figure BDA000028098190000516
After, can calculate both angle β, thereby obtain roll angle α.
In step 1012: after obtaining to observe the roll angle α of video camera with respect to the correction video camera, calculate the length ratio of revising video camera ken transverse and longitudinal.As shown in Figure 3,
|KL|=|AB|·|cosα|+|BC|·|sinα|
|LM|=|AB|·|sinα|+|BC|·|cosα|
R again rev=| KL|/| LM| can obtain revising the length ratio of video camera ken transverse and longitudinal.
Step 1013: calculate vertical field of view angle of revising the video camera ken.As shown in Figure 4:
The definition of each point is identical with Fig. 2, and ∠ FEG is for observing vertical field angle of the video camera ken, and angle is θ obs∠ PEQ is for revising vertical field angle of the video camera ken, and angle is θ revHave,
|BC|=2·|EO|·|tan(θ obs/2)|
|AB|=|BC|·R obs=2·|EO|·|tan(θ obs/2)|·R obs
Have again
|LM|=|AB|·|sinα|+|BC|·|cosα|
{。##.##1},
θ rev=2·tan -1(0.5·|LM|/|EO|)=2·tan -1(0.5·(|AB|·|sinα|+|BC|·|cosα|)/|EO|)
=2·tan -1(|tan(θ obs/2)|·(R obs·|sinα|+|cosα|))
Step 1014: the parameters such as the sensing of the ken of revising video camera, cross-sectional distance far away, three-dimensional space position (namely putting E) are set, make it consistent with the corresponding parameter of observing video camera, thereby finally determine to revise the ken of video camera according to vertical field of view angle of the correction video camera that calculates, the ken that length ratio and the set ken are pointed to, far cross-sectional distance, three-dimensional space position are determined the correction video camera of transverse and longitudinal.
Step 102 specifically comprises the following steps:
Step 1021: rectangular pyramid that determine to revise four angle points compositions in video camera three-dimensional space position point of living in and ken cross section far away thereof;
Step 1022: all intersection points that calculate described rectangular pyramid and sea level;
Step 1023: determine to revise the sea level scope that the video camera ken covers according to described intersection point.Wherein revise the ken of video camera and sea level as shown in Figure 5:
Rectangular pyramid E-KLMN is the determined cone of the correction video camera ken that step 101 calculates, plane γ determines by one the plane that point and vector straight up pre-define, parallel with the surface level in world coordinate system, this determines that point can be any point in world coordinate system.。
The crossing situation of rectangular pyramid E-KLMN and plane γ has three kinds as shown in Figure 6:
(1) there is no intersection point;
(2) rib EN, EM and plane γ meet at U, V 2 points, and base LM, KN and plane γ meet at X, Y 2 points;
Article (3) four, rib EN, EM, EL, EK and plane γ meet at a U, V, X, Y.
For situation (1), revising the video camera ken and plane does not have intersection point, thinks that namely observing video camera does not observe the sea level at this moment, need not generate the ocean grid of this moment.
For situation (2) (3), four intersection points are all arranged, therefore think that observing video camera can observe the sea level this moment, and the quadrilateral area that intersection point UVXY is enclosed is as the zone that should generate the ocean grid.
In step 103, to cover the sea level scope as required in step 102, be sky, be perhaps the quadrilateral UVXY zone in the γ of plane.Quadrilateral UVXY zone is the sea level scope that need to segment the whole summits that generate the ocean grid.
The zone that quadrilateral UVXY surrounds is segmented, generated whole summits of ocean grid, can be by following three kinds of methods:
The first, the coverage of the ken on the sea level of described correction video camera directly carried out linear interpolation, generate the summit.As shown in Figure 7, be the top view above the γ of plane.The vertex position of quadrilateral UVXY is known, if the sampled point number on limit UV (or XY) is m and evenly distributes, sampled point number on limit UY (or VX) is the same evenly distribution of n, line intersects all summits that form thus, it is namely the ocean grid vertex that segmentation obtains, for example laterally sequence number i, the vertical some W of sequence number j, its position is
W=(1-j/n)·((i/m)·U+(1-i/m)·V)+(j/n)·((i/m)·Y+(1-i/m)·X)
Wherein, W, U, V, X and Y represent respectively the three-dimensional coordinate in three dimensions.The advantage of directly carrying out linear interpolation in quadrilateral UVXY is that computing velocity is fast, and shortcoming is evenly divided from the top view grid, but according to Perspective Principles, from observing camera angle, it is very sparse that segmentation grid nearby can seem.
The second, to described correction video camera linear interpolation again after the coverage on the sea level is carried out normalization, and again project the sea level, to generate whole summits of ocean grid.As shown in Figure 8, lift-over can not occur owing to revising video camera, therefore according to symmetry, limit EU, EV are equal in length, and EX, EY are equal in length; But EU and EY might not equate.Therefore at first EU, EV, EX, EY are normalized to vector of unit length
Figure BDA00002809819000071
And in quadrilateral U ' V ' X ' Y ' according to the first method linear interpolation go out have a few, then point is projected in quadrilateral UVXY, as putting certain interpolation point W ' line in E and quadrilateral U ' V ' X ' Y ', intersect with quadrilateral UVXY and obtain a segmentation point W.
The second divided method can overcome the defective of the first divided method fully, but calculated amount can increase.
The 3rd, the coverage of described correction video camera on the sea level carried out the weighted linear interpolation of empirical parameter, generate whole summits of ocean grid.As shown in Figure 9, when namely quadrilateral UVXY being carried out grid subdivision, give weights for vertical interpolation, the segmentation on making vertically is close to myopia point place (limit UV), and namely the closer to myopia point place (limit UV), vertically the upper grid of dividing is narrower.The following expression of simple weighted strategy:
W=(1-(j/n) 2)·((i/m)·U+(1-i/m)·V)+(j/n) 2·((i/m)·Y+(1-i/m)·X)
This method can to a certain degree overcome the defective of first method, and calculated amount is less than second method from experience but not principle.
After the sea level range subdivision obtains all ocean grid vertexes, vertex data is delivered to GPU, undertaken by GPU that height is replaced, whole grid is also finally drawn out in the operation such as painted.
The generation method of Computerized three-dimensional of the present invention ocean grid, three steps that comprise, each frame refreshes and all should sequentially carry out one time with new data more in theory, can omit or skip some work according to specified conditions in practical application, as Figure 10 according to as shown in the practical application process flow diagram of the Computerized three-dimensional ocean grid generation method of the embodiment of the present invention.
Step 201,202 corresponding diagram 1 steps 101 in Figure 10 are specially:
Step 201: whether the picture that judgement observation video camera photographs is compared with previous frame and is changed, if execution in step 202, otherwise the execution of end the method;
Step 202: according to the ken parameter of the ken calculation of parameter correction video camera of current observation video camera;
Step 203,204 corresponding diagram 1 steps 102 in Figure 10 are specially:
Step 203: whether intersect on the ken and the sea level of revising video camera, if intersect execution in step 204, otherwise finishes the execution of the method;
Step 204: the sea level scope that the ken of calculating correction video camera covers.
Step 205 corresponding diagram 1 step 103 in Figure 10 is specially:
Step 205: covering sea level scope is segmented the whole summits that generate the ocean grid, and GPU is sent on whole summits draw.
In sum, the present invention calculates by the ken parameter according to current observation video camera the ken parameter of revising video camera; The sea level scope that the ken of calculating correction video camera covers; Covering sea level scope is segmented, generated whole summits of ocean grid and send GPU to draw, realize that finally the ocean grid of self-adaptation FOV (Field of View) generates and draws, whole process is completed.
Above-described specific embodiment; purpose of the present invention, technical scheme and beneficial effect are further described; institute is understood that; the above is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any modification of making, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (10)

1. the computer generating method of a three-dimensional ocean grid, it comprises:
Step 101: according to the ken parameter of current observation video camera, calculate the ken parameter of revising video camera, and then determine to revise the ken of video camera;
Step 102: the sea level scope that the ken of calculating correction video camera covers;
Step 103: the sea level scope that the ken of revising video camera covers is segmented, generated whole summits of ocean grid, and the drafting that GPU carries out three-dimensional ocean grid is sent on whole summits of described ocean grid.
2. the computer generating method of three-dimensional ocean according to claim 1 grid, is characterized in that, described observation video camera refers to be used for observing three-dimensional virtual video camera in the Computerized three-dimensional scene.
3. the computer generating method of three-dimensional ocean according to claim 1 grid, it is characterized in that, the ken parameter of described observation video camera and correction video camera comprises length ratio and the cross-sectional distance far away of the sensing of the ken, vertical field of view angle, transverse and longitudinal, and the ken parameter of revising video camera is definite by the ken parameter of observing video camera.
4. the computer generating method of three-dimensional ocean according to claim 1 grid, it is characterized in that, described correction video camera is the virtual video camera in the Computerized three-dimensional scene, and the sea level scope that its FOV (Field of View) covers is for being used for the scope of drawing three-dimensional ocean grid.
5. the computer generating method of three-dimensional ocean according to claim 1 grid, it is characterized in that, the ken of described correction video camera is only gone off course under world coordinate system, and lift-over all can not occur under world coordinate system and local coordinate, and the ken of correction video camera comprises the ken of described observation video camera.
6. the computer generating method of three-dimensional ocean according to claim 1 grid, is characterized in that, according to the ken parameter of the ken calculation of parameter correction video camera of current observation video camera, and then determines that the ken of revising video camera specifically comprises in step 101:
Step 1011: calculate and observe video camera with respect to the lift-over angle of revising video camera;
Step 1012: according to the lift-over angle of calculating and observe vertical field of view angle of the video camera ken, the length ratio of transverse and longitudinal, calculate vertical field of view angle of revising video camera and the length ratio of transverse and longitudinal:
Step 1013: arrange that the ken of revising video camera is pointed to, cross-sectional distance far away, three-dimensional space position are pointed to the ken of observation video camera, cross-sectional distance far away, three-dimensional space position are consistent, and according to length ratio and the set ken of vertical field of view angle of the correction video camera that calculates, transverse and longitudinal are pointed to, cross-sectional distance far away, three-dimensional space position are determined the correction video camera the ken.
7. the computer generating method of three-dimensional ocean according to claim 1 grid, is characterized in that, described sea level is to determine point and the predefined plane of normal vector straight up by one, and is parallel with the surface level in world coordinate system.
8. the computer generating method of three-dimensional ocean according to claim 1 grid, is characterized in that, calculates in step 102 to revise the sea level scope that the video camera ken covers and specifically comprise:
Step 1021: rectangular pyramid that determine to revise four angle points compositions in video camera three-dimensional space position point of living in and ken cross section far away thereof;
Step 1022: all intersection points that calculate described rectangular pyramid and sea level;
Step 1023: determine the sea level scope that the ken of correction video camera covers according to described intersection point.
9. the computer generating method of three-dimensional ocean according to claim 1 grid, is characterized in that, in step 103, covering sea level scope segmented, and the mode that generates whole summits of ocean grid comprises three kinds:
The first, the sea level scope that the ken of described correction video camera covers is directly carried out linear interpolation, generate whole summits of ocean grid;
The second, the sea level scope that the ken of described correction video camera is covered is carried out after normalization linear interpolation again, and again projects the sea level, to generate whole summits of ocean grid;
The 3rd, the sea level scope that the ken of described correction video camera is covered is carried out the weighted linear interpolation of empirical parameter, to generate whole summits of ocean grid.
10. the computing machine generating apparatus of a three-dimensional ocean grid, it comprises:
Determine device, be used for the ken parameter according to current observation video camera, calculate the ken parameter of revising video camera, and then determine to revise the ken of video camera;
Calculation element is used for calculating and revises the sea level scope that the ken of video camera covers;
Generating apparatus is used for the sea level scope that the ken of revising video camera covers is segmented, and generates whole summits of ocean grid, and the drafting that GPU carries out three-dimensional ocean grid is sent on whole summits of described ocean grid.
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CN103700143B (en) * 2013-12-30 2017-07-07 四川九洲电器集团有限责任公司 A kind of Three-Dimensional Dynamic ocean simulation method drawn based on GPU multipass
CN104574518A (en) * 2014-12-26 2015-04-29 浙江大学 Semi-physical drawing method for large-scale ocean scene with rich details
CN104574518B (en) * 2014-12-26 2017-07-11 浙江大学 Extensive ocean scenes semi physical method for drafting with abundant details
CN106127853A (en) * 2016-06-17 2016-11-16 中国电子科技集团公司第二十八研究所 A kind of unmanned plane Analysis of detectable region method
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