CN105844703A - Three-dimensional terrain simplified algorithm based on high precision DEM data - Google Patents

Abstract

The invention discloses a three-dimensional terrain simplified algorithm based on high precision DEM data, comprising following steps: 1) designing a quad-tree data structure; 2) calculating viewpoint irrelevant error of a triangular irregular network; 3) performing subdivision on quad-tree junction points; 4) performing terrain simplified error judgment. Compared with common DEM, the algorithm has a special design for the quad-tree data structure in that not only point, edge and triangle linked lists are defined, but also the center point boundary of blocks and error measurement values of blocks are defined; after the viewpoint irrelevant error of the triangular irregular network is calculated, further subdivision to the error values is performed and further error judgment is made; as establishing wide-range, large-scale real-time, and interactive virtual terrain environment is simplified, junction point complexity is simplified when importance measurement of each junction point is calculated so that terrain drawing efficiency is increased and the obtained effect picture has delicate and real terrain details.

Description

A kind of dimensional topographies based on high accuracy DEM data simplify algorithm

Technical field

The present invention relates to a kind of algorithm, a kind of dimensional topographies based on high accuracy DEM data simplify algorithm, belong to Image processing technique field.

Background technology

For more efficient generation height emulation, transmission line of electricity dimensional topography scene extensive, high-precision, frequently with landform Digital elevation data (DEM), when using these massive terrain data to set up relief model, generally comprise hundreds of millions of triangles Shape, and network data is simplified by a way exactly that solve triangle grid model data volume big.Regular grid structure by Simply having obtained relatively broad application in data structure, common DEM just employs regular grid, and tree construction is rule mesh In network terrain rendering through frequently with data structure, quaternary tree is commonly used for the simplification of landform.

Tree construction can carry out piecemeal easily, greatly reduce the terrain rendering time landform, accelerates Terrain Simplification, But but take substantial amounts of memory headroom, and the sealene triangle (TIN) expressed based on tree construction can be good at realizing right Scene data approximates, and visual continuity is relatively good, but its triangulation network algorithm exists the defect that execution efficiency is low.

Summary of the invention

It is an object of the invention to provide a kind of dimensional topographies based on high accuracy DEM data and simplify algorithm, big setting up Scope, large-scale in real time, Virtual Terrain Environment that can be mutual, it is thus achieved that preferably while approximation initial land form, improve and calculate The execution efficiency of method.

For reaching above-mentioned purpose, these dimensional topographies based on high accuracy DEM data simplify algorithm, comprise the following steps:

(1) on the basis of high accuracy DEM data, set up based on quad-tree structure DEM model, and defining point, limit, triangle Face chained list, and the central point border of block and the error metric value of block；

(2) according to the design of step (1), calculate the unrelated error amount of viewpoint of TIN, do not advise according to obtain Then the unrelated error of the viewpoint of the triangulation network carries out the calculating of projection error, to improve terrain rendering precision；

(3) the unrelated error amount of viewpoint of the TIN obtained in step (2) is compared with the threshold value of setting, greatly In then inserting this viewpoint, surround ball scope less than then expanding further；

(4) the whole landform choosing the multiple viewpoints of insertion is node, judges according to imposing a condition whether node meets condition Requirement, if meeting, is then leafy node；It is unsatisfactory for, then this node is divided into 4 child nodes, judges 4 sons by the method for recurrence Whether node meets leafy node condition, until only can not be further divided into, its distinguishing rule be according to calculated by preceding step not The node error amount e (C that the unrelated error amount of viewpoint of regular triangular net determines_i), for determining the simplification degree of terrain rendering.

Further, the viewpoint unrelated error S (C of TIN in step (2)_i), can be calculated by equation below:

$S\left(C_i\right)={\∫}_{d\left(C_i\right)}|h(x,y)-A\left(\mathrm{Star}\left(p\right)\right)|\mathrm{dxdy}---\left(1\right)$

Wherein, and h (x, y) is landform altitude function, and A (Star (p)) is the mean error plane of node definition, irregular three The unrelated error of viewpoint of angle net can be calculated by formula (1), d (C therein_j) scope determined by error nesting ball, for specific For physical points, its projection error and the unrelated error of actual view is directly proportional and it is the most remote away from viewpoint, projection error is the least, its Computing formula is:

${\mathrm{\ρ}}_i=\mathrm{\λ}\frac{S\left(C_i\right)}{||p_i-e||}---\left(2\right)$

Wherein, for P_iFor node, e is viewpoint, and λ is projection coefficient, is that actual object size is in projector space projective transformation After amplification；

Further, in step (3), size to the unrelated error amount of sealene triangle obtained according to (2) formula is entered One step segmentation, node continues the condition of segmentation and is:

$\begin{array}{c}{\mathrm{\ρ}}_i>\mathrm{\τ}\⇔\mathrm{\λ}\frac{S\left(C_i\right)}{||p_i-e||-R_i}>\mathrm{\τ}\\ \⇒\frac{\mathrm{\λ}}{\mathrm{\τ}}S\left(C_i\right)>||p_i-e||-R_i\\ \⇒{\left(\frac{1}{k}S\right(C_i)+R_i)}^2>{||p_i-e||}^2\end{array}---\left(3\right)$

Wherein k=τ/λ, through the optimization of formula (3), algorithm can reach more satisfactory calculating effect, for unrelated mistake The size of difference, it is possible to compare with threshold value, more than then inserting this viewpoint, surrounds ball scope less than then expanding further；

Further, step (4) is Terrain Simplification error judgment, and first choosing with regard to whole landform is node, then judges Whether node meets certain condition, is if it is considered leafy node, otherwise this node four is divided into 4 child nodes, with passing The method returned judges whether 4 child nodes meet leafy node condition, until only can not be further divided into, its algorithmic procedure is as follows:

Root node is stacked, if stack is not empty, and stack node is less than e (C_i), then node is put into a set, algorithm terminates； If stack is not empty, but stack node is more than or equal to e (C_i), then return a upper program, continue to be divided into child node, until stack node is little In e (C_i), then node is put into a set, algorithm terminates；If stack is empty, then algorithm terminates.

e(C_i) computing formula be:

$e\left(C_i\right)=k\·\frac{l\×L\×\mathrm{\λ}}{2\×\tan \frac{\mathrm{\α}}{2}\×d}\·S\left(C_i\right)---\left(4\right)$

Wherein α is the subtended angle of viewpoint, and L is the length of side of projection plane, and l is to be thrown line segment length, and d is in viewpoint and this line segment The distance of the heart, λ is the pixel count on a projection plane of the unit length in object space, and k is a variable coefficient.

Compared with common DEM, quaternary tree data structure is specifically designed by this algorithm, define not only point, limit, Triangular facet chained list, also makes definitions to the central point border of block and the error metric value of block, is regarding TIN After the unrelated error of point makes calculating, segmentation further to error amount, and make further error judgment, to setting up big model Enclose, large-scale in real time, can be while mutual Virtual Terrain Environment simplifies, by calculating the importance of each node When estimating, simplify the complexity of node, improve terrain rendering efficiency, and the design sketch topographic details obtained is careful truly.

Accompanying drawing explanation

Fig. 1 is the algorithmic procedure flow chart of step of the present invention (4).

Detailed description of the invention

The invention will be further described below.

These dimensional topographies based on high accuracy DEM data simplify algorithm, comprise the following steps:

(1) on the basis of high accuracy DEM data, set up DEM model based on quad-tree structure, and defining point, limit, three Edged surface chained list, and the central point border of block and the error metric value of block, design process is as follows:

The purpose more than designed is in the level of detail model of landform, cuts out what comes into a driver's for landform in addition easily Cut and calculate with error transition, in order to accelerate to draw speed.

(2) according to the design of step (1), calculate the unrelated error amount of viewpoint of TIN, do not advise according to obtain Then the unrelated error of the viewpoint of the triangulation network carries out the calculating of projection error, to improve terrain rendering reliability；

(3) the unrelated error amount of viewpoint of the TIN obtained in step (2) is compared with the threshold value of setting, greatly In then inserting this viewpoint, surround ball scope less than then expanding further；

(4) the whole landform choosing the multiple viewpoints of insertion is node, judges according to imposing a condition whether node meets condition Requirement, if meeting, is then leafy node；It is unsatisfactory for, then this node is divided into 4 child nodes, judges 4 sons by the method for recurrence Whether node meets leafy node condition, until only can not be further divided into, its distinguishing rule be according to calculated by preceding step not The node error amount e (C that the unrelated error amount of viewpoint of regular triangular net determines_i), for determining the simplification degree of terrain rendering.

The viewpoint unrelated error S (C of TIN in step (2)_i), can be calculated by equation below:

$S\left(C_i\right)={\∫}_{d\left(C_i\right)}|h(x,y)-A\left(\mathrm{Star}\left(p\right)\right)|\mathrm{dxdy}---\left(1\right)$

Wherein, and h (x, y) is landform altitude function, and A (Star (p)) is the mean error plane of node definition, irregular three The unrelated error of viewpoint of angle net can be calculated by formula (1), d (C therein_j) scope determined by error nesting ball, for specific For physical points, its projection error and the unrelated error of actual view is directly proportional and it is the most remote away from viewpoint, projection error is the least, its Computing formula is:

${\mathrm{\ρ}}_i=\mathrm{\λ}\frac{S\left(C_i\right)}{||p_i-e||}---\left(2\right)$

Wherein, for P_iFor node, e is viewpoint, and λ is projection coefficient, is that actual object size is in projector space projective transformation After amplification；

In step (3), the size to the unrelated error amount of sealene triangle obtained according to (2) formula is segmented further, Node continues the condition of segmentation:

$\begin{array}{c}{\mathrm{\ρ}}_i>\mathrm{\τ}\⇔\mathrm{\λ}\frac{S\left(C_i\right)}{||p_i-e||-R_i}>\mathrm{\τ}\\ \⇒\frac{\mathrm{\λ}}{\mathrm{\τ}}S\left(C_i\right)>||p_i-e||-R_i\\ \⇒{\left(\frac{1}{k}S\right(C_i)+R_i)}^2>{||p_i-e||}^2\end{array}---\left(3\right)$

Wherein k=τ/λ, through the optimization of formula (3), algorithm can reach more satisfactory calculating effect, for unrelated mistake The size of difference, it is possible to compare with threshold value, more than then inserting this viewpoint, surrounds ball scope less than then expanding further；

Step (4) is Terrain Simplification error judgment, and first choosing with regard to whole landform is node, then judges that node is the fullest Certain condition of foot, is if it is considered leafy node, otherwise this node four is divided into 4 child nodes, sentences by the method for recurrence Whether disconnected 4 child nodes meet leafy node condition, until only can not be further divided into, its algorithmic procedure is as follows:

Root node is stacked, if stack is not empty, and stack node is less than e (C_i), then node is put into a set, algorithm terminates； If stack is not empty, but stack node is more than or equal to e (C_i), then return a upper program, continue to be divided into child node, until stack node is little In e (C_i), then node is put into a set, algorithm terminates；If stack is empty, then algorithm terminates.

e(C_i) computing formula be:

$e\left(C_i\right)=k\·\frac{l\×L\×\mathrm{\λ}}{2\×\tan \frac{\mathrm{\α}}{2}\×d}\·S\left(C_i\right)---\left(4\right)$

Wherein α is the subtended angle of viewpoint, and L is the length of side of projection plane, and l is to be thrown line segment length, and d is in viewpoint and this line segment The distance of the heart, λ is the pixel count on a projection plane of the unit length in object space, and k is a variable coefficient.

Claims (4)

1. dimensional topographies based on high accuracy DEM data simplify algorithm, it is characterised in that comprise the following steps:

(1) on the basis of high accuracy DEM data, DEM model based on quad-tree structure, and defining point, limit, triangular facet are set up Chained list, and the central point border of block and the error metric value of block；

(2) according to the design of step (1), the unrelated error amount of viewpoint of TIN is calculated, according to irregular three obtained The unrelated error of viewpoint of angle net carries out the calculating of projection error, to improve terrain rendering precision；

(3) the unrelated error amount of viewpoint of the TIN obtained in step (2) is compared with the threshold value of setting, more than then Insert this viewpoint, surround ball scope less than then expanding further；

(4) the whole landform choosing the multiple viewpoints of insertion is node, judges according to imposing a condition whether node meets condition requirement, If meeting, then it it is leafy node；It is unsatisfactory for, then this node is divided into 4 child nodes, judges 4 child nodes by the method for recurrence Whether meeting leafy node condition, until only can not be further divided into, its distinguishing rule is irregular according to calculated by preceding step The node error amount e (C that the unrelated error amount of viewpoint of the triangulation network determines_i), for determining the simplification degree of terrain rendering.

A kind of dimensional topographies based on high accuracy DEM data the most according to claim 1 simplify algorithm, it is characterised in that The viewpoint unrelated error S (C of TIN in step (2)_i), can be calculated by equation below:

Wherein, (x, y) is landform altitude function to h, and A (Star (p)) is the mean error plane of node definition, TIN The unrelated error of viewpoint can be calculated by formula (1), d (C therein_j) scope determined by error nesting ball, for specific physics For Dian, its projection error and the unrelated error of actual view is directly proportional and it is the most remote away from viewpoint, projection error is the least, its calculate Formula is:

Wherein, for P_iFor node, e is viewpoint, and λ is projection coefficient, is that actual object size is after projector space projective transformation Amplification.

A kind of dimensional topographies based on high accuracy DEM data the most according to claim 1 simplify algorithm, it is characterised in that In step (3), the size to the unrelated error amount of sealene triangle obtained according to (2) formula is segmented further, and node continues The condition of segmentation is:

Wherein k=τ/λ, through the optimization of formula (3), algorithm can reach more satisfactory calculating effect, for unrelated error amount Size, it is possible to compare with threshold value, more than then inserting this viewpoint, surround ball scope less than then expanding further.

A kind of dimensional topographies based on high accuracy DEM data the most according to claim 1 simplify algorithm, it is characterised in that Step (4) is Terrain Simplification error judgment, and first choosing with regard to whole landform is node, then judges whether node meets certain Part, is if it is considered leafy node, otherwise this node four is divided into 4 child nodes, judges 4 son joints by the method for recurrence Whether point meets leafy node condition, until only can not be further divided into, its algorithmic procedure is as follows:

Root node is stacked, if stack is not empty, and stack node is less than e (C_i), then node is put into a set, algorithm terminates；If stack is not For sky, but stack node is more than or equal to e (C_i), then return a upper program, continue to be divided into child node, until stack node is less than e (C_i), then node is put into a set, algorithm terminates；If stack is empty, then algorithm terminates.

e(C_i) computing formula be:

Wherein α is the subtended angle of viewpoint, and L is the length of side of projection plane, and l is to be thrown line segment length, and d is viewpoint and this line segment center Distance, λ is the pixel count on a projection plane of the unit length in object space, and k is a variable coefficient.