CN102509339A - Method for simplifying vertex clustering of three-dimensional models with texture constraint - Google Patents
Method for simplifying vertex clustering of three-dimensional models with texture constraint Download PDFInfo
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- CN102509339A CN102509339A CN2011103042820A CN201110304282A CN102509339A CN 102509339 A CN102509339 A CN 102509339A CN 2011103042820 A CN2011103042820 A CN 2011103042820A CN 201110304282 A CN201110304282 A CN 201110304282A CN 102509339 A CN102509339 A CN 102509339A
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Abstract
The invention provides a method for simplifying a vertex clustering of three-dimensional models with texture constraint. The method comprises the steps of: expanding the vertexes from a geometric space to a fifth-dimensional space including texture coordinates in consideration of algorithm efficiency in the self-adaptive division processes of the vertexes; dividing the vertexes according to the positions of the vertexes in the geometric space and the texture space in the self-adaptive division processes of the vertexes; in error measurement, respectively computing geometric errors and texture errors, if the error value is more than a given threshold, splitting the current node; and in the self-adaptive division processes of the vertexes, in consideration of saving the storage resources and improving the algorithm efficiency, adopting the relatively important vertex in an original model as a clustering representative instead of computing the geometric position of a new vertex through iteration. The method for simplifying vertex clustering of three-dimensional models with texture constraint organically integrates texture error measurement and geometric simplification, realizes rapid simplification of a mass of complex three-dimensional models and supports efficient three-dimensional visualization of city virtual scenes.
Description
Technical field
The present invention relates to three-dimensional geographic information visualization technique field, particularly relate to a kind of to the complex three-dimensional model vertices cluster short-cut method under the texture error condition.
Background technology
Texture is an important attribute information of three-dimensional model, is directly connected to the authenticity that three-dimensional model is expressed in virtual reality.In the model simplification process, even the maintenance of the geometric properties of model is good again, if can't guarantee the correctness of texture, its visual effect will be had a greatly reduced quality.
Although along with the continuous development of virtual reality technology, present existing three-dimensional model simplifying technology is very ripe aspect the model geometric simplification, for the research that keeps the model textural characteristics in the simplification process and few.
For the texture error metrics, the method a kind of commonly used that relevant document proposes is with (X, Y; Z) three-dimensional metric algorithm expansion accounts for (X, Y, Z; R, G is in 6 dimension spaces B); Garland, M. Multi-Resolution Modeling:Survey future opportunities [C]. Proceedings of the Eurographics ' 99. 1999; Shen Xukun, Zhao Xuewei, Zhao Qinping. a kind of lattice simplified and compression progressive transmission method [J] of keeping characteristics. computer research and development, 2007, Vol.44 (7): 1097-1104; Feng Xiang, Zhou Mingquan. the three-dimensional model simplifying algorithm [J] of band texture. computer-aided design (CAD) and graphics journal, 2009, Vol.21 (6): 842-846.Its ultimate principle is following: according to the texture coordinate on summit (u, v) on texture image, find colouring information corresponding to this summit (r, g, b).In the model simplification process, according to simplified model M
1With master pattern M
2The summit corresponding relation, define its texture error and be the distance error in its vertex color space, shown in the following formula, (r wherein
1, g
1, b
1), (r
2, g
2, b
2) be respectively the color value of vertex v 1, v2:
Wherein vertex v 1, v2 belong to model M respectively
1, M
2
This error metrics method can play certain binding effect to the model simplification process, can keep the textural characteristics of model to a certain extent, but still can not be satisfied with the needs of practical application.Its weak point is mainly reflected in following two aspects:
(1) reduces model simplification efficient.Adopt this texture error metrics method to instruct the model simplification process, need obtain vertex color corresponding on the texture image based on texture coordinate.Therefore, need frequent the model data texturing to be loaded into internal memory, and need carry out each summit (u, v) → (map operation b) has increased the resource overhead of shortcut calculation undoubtedly greatly, has increased the time of model simplification for r, g.
(2) be not suitable for the complicated three-dimensional model of texture information.In the texture of three-dimensional model was expressed, the mapping relations of model vertices and texture image were not that (u v) arrives texture color (r, g, simple relation b) to texture coordinate.To with each 3d space under triangle, can be according to the texture coordinate on its summit, the 2D delta-shaped region of a correspondence of definition in texture, and in this 3D triangular element with the texture of this 2D delta-shaped region.The left side is the triangle under the 3d space in Fig. 1, in the XYZ coordinate system that with O is initial point foundation, and summit Q
1, Q
2, Q
3Dividing other coordinate is (x
1, y
1, z
1), (x
2, y
2, z
2), (x
3, y
3, z
3); The right is the corresponding 2D triangle texture region of this triangle, in the UV coordinate system, and summit Q
1, Q
2, Q
3Dividing other coordinate is (u
1, v
1), (u
2, v
2), (u
3, v
3).
If summit Q
1, Q
2, Q
3Corresponding texture color value is identical, and promptly three distances of summit in color space are 0.Suppose summit Q in the simplification process
1Be Q
2, Q
3Substitute the summit, if when adopting formula to carry out error metrics so, gained texture error amount also is 0.Yet under actual conditions, this visual impact that brings estimated value that simplifies the operation much larger than error metrics.
Therefore, adopt texture color to carry out error metrics and only be suitable for texture color distribution three-dimensional model comparatively uniformly, the three-dimensional model (like city complex three-dimensional BUILDINGS MODELS) comparatively complicated for texture is also improper.
To visible the earliest document: the Rossignac of the summit clustering method of three-dimensional model simplifying; J.; Borrel; P. Multi-Resolution 3D Approximations for Rendering [J]. Modeling in Computer Graphics, June-July 1993:455-465.This method key step is: based on factor spatial division that threedimensional model is shared such as the size of model meshes, complexities is a plurality of cubic units; Calculate the representative point in each cubic units, each summit in the cubic units is replaced with this representative point; The degeneration triangle that the replacement back produces removes.
To the weak point of above-mentioned summit clustering method, relevant document: Zhou Kun, Pan Zhigeng; Shi Jiaoying. a kind of new Mesh simplification algorithm based on the summit cluster [J]. robotization journal, 1999,1; Vol.25 (1): 1-8; Provided a kind of improved clustering method, carried out self-adaptation through Octree and divide, and measure the generation of controlling representative point through second order error.This method is very effective for the geometric properties that keeps model in the simplification process.But in this method, do not consider the attribute information of three-dimensional model, in the simplification process, can't keep the attributive character of three-dimensional model.
Summary of the invention
The objective of the invention is to simplify deficiency, propose a kind of three-dimensional model summit cluster short-cut method with the texture constraint to existing cluster.
Technical scheme of the present invention is a kind of three-dimensional model summit cluster short-cut method with the texture constraint, it is characterized in that, comprises the following steps:
Step 1, the weights on each summit in the Calculation of Three Dimensional model;
Step 2, big or small according to preset geometric units lattice size with the texture cell lattice, with three-dimensional model according to (X, Y; Z, U, V) five dimensions are divided, and promptly divide according to the geometric units lattice earlier and obtain some leaf nodes; According to the texture cell lattice above-mentioned some leaf nodes are further divided on this basis and obtained more leaf node, wherein (X, Y; Z) expression geometric space coordinate, (U, V) expression texture space coordinates;
Step 3 is checked each leaf node inner vertex number,
If number of vertices is empty or is 1, then do not do any operation;
If number of vertices greater than preset number threshold value, is then carried out the node splitting operation to leaf node;
If number of vertices is greater than 1 and be less than or equal to preset number threshold value; Weights according to step 1 gained summit; In leaf node, select the maximum summit of weights as the cluster representative point; Calculate the geometric error
and the texture error
that produce after the cluster, when geometric error
is carried out splitting operation during greater than the texture error threshold
preset greater than preset geometric error threshold value
or texture error
;
Step 4; The leaf node that splitting operation is produced returns execution in step 3; Number of vertices in all leaf nodes is empty or is 1 that perhaps geometric error
and texture error
are all in threshold range;
Step 5; For all geometric errors
and texture error
leaf node in threshold range all; Summit in the leaf node is replaced with the cluster representative point; And the renewal index data, then the triangle of degenerating is removed from the triangle tabulation of three-dimensional model.
And the weights account form on summit is following,
If summit weights scope
W ∈(
0,1), weights more greatly then represent this summit important more, for the arbitrary summit that is not positioned at boundary in the three-dimensional model
Q, relevant triangle set is arranged
T S =
t 0 , t 1 ... T m , suppose the triangle set
T S Intermediate cam shape
t i With
t j Adjacent, definition
As follows
Wherein
n i ,
n j Be respectively triangle
t i ,
t j Normal vector,
DotBe the vector dot computing,
w Ij The value scope is (0,1),
w Ij Be worth big more, the expression triangle
t i With
t j Angle more little, the summit
QWeights
wBe expressed as:
For the summit that is positioned at boundary, its weights are directly given maximal value 1.
And in the step 1, it is following to judge whether the summit is positioned at the concrete implementation of boundary,
If summit
QRelevant limit set is arranged
L S Gather with triangle
T S If, the limit set
L S In have the limit
lSatisfy the triangle set
T S In have only unique triangle
tComprise this limit, so this summit
QIt promptly is frontier point; If limit set
L S In all limits do not satisfy this condition, this summit is not a frontier point so.
And in the step 3, the computational geometry error adopts the error of curvature measure, and concrete implementation is following,
Be set in the vertex set in the leaf node
Q S =
Q w , Q 0 , Q 1 Q n , summit wherein
Q w Be cluster representative point, vertex set
Q S Other any summits in interior
Q i Relevant triangle set is arranged
Ts=
t 0 , t 1 ... T m , triangle is gathered
TsIn all vertexs of a triangle
Q i Use the summit
Q w Obtain the triangle set after the replacement
Ts '=
t 0 ', t 1 ' ... T m '; If triangle set
TsIntermediate cam shape
t j Normal vector do
n j , the triangle set
Ts 'Intermediate cam shape
t j 'Normal vector do
n j ', this summit
Q i Geometric error do
Wherein
The computing of expression vector dot,
jValue is 0,1,
m
This vertex set
Q S Geometric error after the cluster does
Wherein, max{} representes to get maximal value,
iValue is 0,1,
n
And in the step 3, the concrete implementation of calculating the texture error is following,
Be set in the vertex set in the leaf node
Q S =
Q w , Q 0 , Q 1 Q n , summit wherein
Q w Be cluster representative point, summit
Q w Texture coordinate be (
u w , v w ), vertex set
Q S Other any summits in interior
Q i Texture coordinate be (
u i , v i ), with the summit
Q i Use the summit
Q w Texture error after the replacement does
This vertex set
Q S Texture error after the cluster does
Wherein, max{} representes to get maximal value,
iValue is 0,1,
n
The invention property ground as the texture error metrics, makes three-dimensional model simplifying have stronger binding character and higher efficient the texture coordinate space length; The texture error metrics method of complex three-dimensional model is got up with how much simplification organic unities, realized the quick simplification of magnanimity complex three-dimensional model, and effectively kept the textural characteristics after the model simplification.The present invention can support the efficient three-dimensional visualization of city virtual scene.
Description of drawings
Fig. 1 is a three-dimensional model texture graph of a relation.
Fig. 2 is the process flow diagram of the embodiment of the invention.
Embodiment
Embodiment adopts method of the present invention, uses C Plus Plus to write the summit cluster short-cut method of band texture constraint, comes practical implementation through typical 3 D complex building model.Consider that the 3 D complex BUILDINGS MODELS all is to carry out modeling according to true ratio, the redundant data amount of model is limited, for guaranteeing reduced mass preferably, simplify the result data amount maintain master pattern 30% ~ 50% between.
For the purpose of reference implementation, provide the embodiment flow process following, referring to Fig. 2:
Step 1 is calculated the weights on each summit.
The purpose of three-dimensional model simplifying is under the model of guarantee simplifying and the similar as far as possible situation of master pattern, to delete the summit to greatest extent.Therefore in the process of summit cluster, the cluster representative point of selection should be that some can reflect model principal character and the summit that keeps model silhouette.The summit weights can reflect that this summit is for the importance that keeps the aspect of model.Generally, be positioned at variations such as model boundary, acute angle and comparatively significantly should give bigger weights in the summit of part, and should give less weights for the summit of the level and smooth part of model variation.According to this principle, embodiment is after importing three-dimensional modeling data, and the method for calculating the summit weights is following:
For ease of calculating, establish summit weights scope
W ∈(
0,1), weights more greatly then represent this summit important more, for the arbitrary summit that is not positioned at boundary in the three-dimensional model
Q, relevant triangle set is arranged
T S =
t 0 , t 1 ... T m , subscript 0,1,
Be used for identifying the triangle of set.Suppose the triangle set
T S Intermediate cam shape
t i With
t j Adjacent, definition
As follows
Wherein
n i ,
n j Be respectively triangle
t i ,
t j Normal vector,
DotBe the vector dot computing,
w Ij The value scope is (0,1),
w Ij Be worth big more, the expression triangle
t i With
t j Angle more little, geometric properties is obvious more.The summit
QWeights
wBe expressed as:
For the summit that is positioned at boundary, its weights are directly given maximal value 1.
In addition, because model boundary is the pith that keeps model silhouette, therefore for the summit that is positioned at boundary, its weights should be given maximal value 1.A kind of frontier point determination methods commonly used is following: establish the summit
QRelevant limit set is arranged
L S Gather with triangle
T S If, the limit set
L S In have the limit
l(limit Shuo Liang>=1) satisfies the triangle set
T S In have only unique triangle
tComprise this limit, this summit promptly is a frontier point so
QIf limit set
L S In all limits do not satisfy this condition, this summit is not a frontier point so.
During practical implementation, can also adopt other existing weights account forms.
Step 2, according to preset geometric units lattice size and texture cell lattice size, with three-dimensional model according to (X, Y, Z, U, V) five dimensions are divided, wherein (X, Y, Z) expression geometric space coordinate, (U V) representes texture space coordinates.
The geometric space that three-dimensional model is corresponding is its bounding box volume; Texture space is a two dimensional surface; Span is 0 to 1 on its X and the Y direction, and the geometric units lattice are geometric space volumes of user-defined least unit, and the texture cell lattice are texture space areas of user-defined least unit; For example defining geometric units lattice is 1 meter square, the texture cell lattice for long and wide be 0.1 texture area.During practical implementation, the user can set up on their own according to accuracy requirement.According to user-defined cell (comprising geometric space volume, texture space area) size, with master pattern according to (X, Y; Z; U, V) five dimensions are divided, and promptly divide according to the geometric units lattice earlier and obtain some leaf nodes; Divide according to texture space on this basis further division of above-mentioned some leaf nodes obtained more leaf node, accomplish initial division.The leaf node number that obtains after the initial division is an initial number, possibly divide the leafier child node of generation at subsequent step 3.
Step 3 is checked each leaf node inner vertex number,
If number of vertices is empty or is 1, then do not do any operation;
If number of vertices greater than preset number threshold value, is then carried out the node splitting operation to leaf node;
If number of vertices is greater than 1 and be less than or equal to preset number threshold value; Weights according to step 1 gained summit; In leaf node, select the maximum summit of weights as the cluster representative point; Calculate the geometric error
and the texture error
that produce after the cluster, when geometric error
is carried out splitting operation during greater than the texture error threshold
preset greater than preset geometric error threshold value
or texture error
.Certainly; If geometric error
and texture error
are all in threshold range; Be that geometric error
is less than or equal to preset geometric error threshold value
; And when texture error
is less than or equal to preset texture error threshold
; Need not carry out the node splitting operation to leaf node, the summit in the leaf node replaced with the cluster representative point in step 5.
The splitting operation that embodiment carries out leaf node is according to (X, Y, Z, U, V) five dimensions subdivision 2 again with present node
5Child node, promptly according to dimension X, Y, Z, U, V, each dimension is carried out the division of one-to-two.Summit in this leaf node is reentered in the leaf node that subdivision obtains, and will returns step 3 leaf node that each subdivision obtains is judged, whether continue division.Preset number threshold value, error threshold
,
size are relevant with modeling precision, can according to actual conditions suitable value be set by the user.
The key factor of three-dimensional model summit and 2 d texture mapping be the summit texture coordinate (u, v).For the summit (u, v) value differs bigger 3D triangle, its texture information that between 2D triangle corresponding on the texture, comprises is also more, it is big more to delete the texture error that this triangle brings; Otherwise, for the summit (u, v) value differs less 3D triangle, its texture information that between 2D triangle corresponding on the texture, comprises is also less, it is more little to delete the texture error that this triangle brings.Therefore, the present invention is carrying out in the three-dimensional model simplifying process, can geometric space be expanded to comprise texture coordinate (X; Y; Z, U is in quintuple space V); According to the summit corresponding relation of simplified model and master pattern, define its texture error for its summit in the texture coordinate space apart from difference:
Wherein, wherein vertex v 1, v2 belong to simplified model M respectively
1, master pattern M
2, (u
1, v
1), (u
2, v
2) be vertex v 1, the apex coordinate of v2.
Based on this texture error metrics criterion, in the process of carrying out model simplification, preferentially delete the less summit of texture coordinate distance, keep the bigger summit of texture coordinate distance, thereby make that simplifying the result can keep more textural characteristics.
Adopt the method for texture coordinate space length as error metrics; With take the texture color space length and compare as the error metrics method; Not only its binding character is stronger, and because the operation that need all not obtain color to each summit, and a dimension has been lacked than color space in the texture coordinate space; The complexity of algorithm also can be lower in difference calculation process runs, thereby improved the efficient of model simplification algorithm.
The geometric error that comprises of error metrics is measured and texture error metrics two parts.Embodiment adopts error of curvature measure of the prior art for geometric error tolerance, and is specific as follows:
Suppose to be positioned at the vertex set of a leaf node
Q S =
Q w , Q 0 , Q 1 Q n , summit wherein
Q w Be cluster representative point, summit
Q 0 , Q 1 Q n Be that leaf node is interior in addition
n+ 1 node.Vertex set
Q S Other any summits in interior
Q i Relevant triangle set is arranged
Ts=
t 0 , t 1 ... T m , triangle is gathered
TsIn all vertexs of a triangle
Q i Use the summit
Q w Obtain the triangle set after the replacement
Ts '=
t 0 ', t 1 ' ... T m '; If triangle set
TsIntermediate cam shape
t j Normal vector do
n j , the triangle set
Ts 'Intermediate cam shape
t j 'Normal vector do
n j ', this summit
Q i Geometric error do
Wherein
The computing of expression vector dot,
jValue is 0,1,
m
This vertex set
Q S Geometric error after the cluster does
Wherein, max{} representes to get maximal value,
iValue is 0,1,
n
During practical implementation, the computational geometry error can also adopt additive method, such as distance error tolerance, and angular error tolerance or the like.
The basic skills of texture error metrics is following:
Be set in the vertex set in the leaf node
Q S =
Q w , Q 0 , Q 1 Q n , summit wherein
Q w Be cluster representative point, summit
Q w Texture coordinate be (
u w , v w ), vertex set
Q S Other any summits in interior
Q i Texture coordinate be (
u i , v i ), with the summit
Q i Use the summit
Q w Texture error after the replacement does
This vertex set
V S Texture error formula after the cluster is identical with geometric error.This vertex set
Q S Texture error after the cluster does
Wherein, max{} representes to get maximal value,
iValue is 0,1,
n
Step 4, the leaf node that splitting operation is produced returns execution in step 3, satisfies one of following two conditions up to all leaf nodes:
(1) number of vertices in the leaf node is empty or is 1;
(2) number of vertices in the leaf node is greater than 1 and be less than or equal to preset number threshold value, and geometric error
and texture error
are all in threshold range.Promptly in leaf node, select the maximum summit of weights as the cluster representative point; Calculate the geometric error
and the texture error
that produce after the cluster; Geometric error
is less than or equal to preset geometric error threshold value
, and texture error
is less than or equal to preset texture error threshold
.
Step 5; For all geometric errors
and texture error
leaf node in threshold range all; Summit in the leaf node is replaced with the cluster representative point; And the renewal index data, then the triangle of degenerating is removed from the triangle tabulation of three-dimensional model.
Embodiment carries out the summit cluster operation with the leaf node that all satisfy the cluster standard, and the degeneration triangle that produces after the cluster is removed.In the prior art, gather with triangle in the data of three-dimensional model and represent the object external outline shape, be made up of the definition of a plurality of triangle surfaces, the definition of each tri patch comprises the three-dimensional coordinate on each summit of triangle and the method vector of tri patch.Index data is the corresponding index in summit in the three-dimensional model, needs to upgrade behind the replacement summit.The triangle tabulation is the set of three-dimensional model intermediate cam shape, expresses with the index on triangle sequence number and corresponding three summits.The triangle of degenerating is through after simplifying, and therefore the triangle that from three-dimensional model, shifts out needs correspondingly from the triangle tabulation, to remove.
Can find out through above practical implementation; Increase the simplification after texture retrains; Though certain increase is arranged on algorithm complex; But its efficient can satisfy the needs of practical application, and more crucial is to keep that for the textural characteristics of simplifying the result tangible effect is arranged, and is applicable to the three-dimensional building object model that some grain details are complicated.In addition, because the summit clustering method is a kind of method that does not keep topological structure, thereby is applicable to the model simplification of some non-manifolds, and simplify rapid speed.
Claims (5)
1. the three-dimensional model summit cluster short-cut method with the texture constraint is characterized in that, comprises the following steps:
Step 1, the weights on each summit in the Calculation of Three Dimensional model;
Step 2, big or small according to preset geometric units lattice size with the texture cell lattice, with three-dimensional model according to (X, Y; Z, U, V) five dimensions are divided, and promptly divide according to the geometric units lattice earlier and obtain some leaf nodes; According to the texture cell lattice above-mentioned some leaf nodes are further divided on this basis and obtained more leaf node, wherein (X, Y; Z) expression geometric space coordinate, (U, V) expression texture space coordinates;
Step 3 is checked each leaf node inner vertex number,
If number of vertices is empty or is 1, then do not do any operation;
If number of vertices greater than preset number threshold value, is then carried out the node splitting operation to leaf node;
If number of vertices is greater than 1 and be less than or equal to preset number threshold value; Weights according to step 1 gained summit; In leaf node, select the maximum summit of weights as the cluster representative point; Calculate the geometric error
and the texture error
that produce after the cluster, when geometric error
is carried out splitting operation during greater than the texture error threshold
preset greater than preset geometric error threshold value
or texture error
;
Step 4; The leaf node that splitting operation is produced returns execution in step 3; Number of vertices in all leaf nodes is empty or is 1 that perhaps geometric error
and texture error
are all in threshold range;
Step 5; For all geometric errors
and texture error
leaf node in threshold range all; Summit in the leaf node is replaced with the cluster representative point; And the renewal index data, then the triangle of degenerating is removed from the triangle tabulation of three-dimensional model.
2. according to claim 1 with the three-dimensional model summit cluster short-cut method of texture constraint, it is characterized in that: the weights account form on summit is following,
If summit weights scope
W ∈(
0,1), weights more greatly then represent this summit important more, for the arbitrary summit that is not positioned at boundary in the three-dimensional model
Q, relevant triangle set is arranged
T S =
t 0 , t 1 ... T m , suppose the triangle set
T S Intermediate cam shape
t i With
t j Adjacent, definition
As follows
Wherein
n i ,
n j Be respectively triangle
t i ,
t j Normal vector,
DotBe the vector dot computing,
w Ij The value scope is (0,1),
w Ij Be worth big more, the expression triangle
t i With
t j Angle more little, the summit
QWeights
wBe expressed as:
For the summit that is positioned at boundary, its weights are directly given maximal value 1.
3. like the three-dimensional model summit cluster short-cut method of the said band texture of claim 2 constraint, it is characterized in that: in the step 1, it is following to judge whether the summit is positioned at the concrete implementation of boundary,
If summit
QRelevant limit set is arranged
L S Gather with triangle
T S If, the limit set
L S In have the limit
lSatisfy the triangle set
T S In have only unique triangle
tComprise this limit, so this summit
QIt promptly is frontier point; If limit set
L S In all limits do not satisfy this condition, this summit is not a frontier point so.
4. like the three-dimensional model summit cluster short-cut method of claim 1 or 2 or 3 said band texture constraints, it is characterized in that: in the step 3, the computational geometry error adopts the error of curvature measure, and concrete implementation is following,
Be set in the vertex set in the leaf node
Q S =
Q w , Q 0 , Q 1 Q n , summit wherein
Q w Be cluster representative point, vertex set
Q S Other any summits in interior
Q i Relevant triangle set is arranged
Ts=
t 0 , t 1 ... T m , triangle is gathered
TsIn all vertexs of a triangle
Q i Use the summit
Q w Obtain the triangle set after the replacement
Ts '=
t 0 ', t 1 ' ... T m '; If triangle set
TsIntermediate cam shape
t j Normal vector do
n j , the triangle set
Ts 'Intermediate cam shape
t j 'Normal vector do
n j ', this summit
Q i Geometric error do
Wherein
The computing of expression vector dot,
jValue is 0,1,
m
This vertex set
Q S Geometric error after the cluster does
Wherein, max{} representes to get maximal value,
iValue is 0,1,
n
5. like the three-dimensional model summit cluster short-cut method of claim 1 or 2 or 3 said band texture constraints, it is characterized in that: in the step 3, the concrete implementation of calculating the texture error is following,
Be set in the vertex set in the leaf node
Q S =
Q w , Q 0 , Q 1 Q n , summit wherein
Q w Be cluster representative point, summit
Q w Texture coordinate be (
u w , v w ), vertex set
Q S Other any summits in interior
Q i Texture coordinate be (
u i , v i ), with the summit
Q i Use the summit
Q w Texture error after the replacement does
This vertex set
Q S Texture error after the cluster does
Wherein, max{} representes to get maximal value,
iValue is 0,1,
n
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| US9621924B2 (en) | 2012-04-18 | 2017-04-11 | Thomson Licensing | Vextex correction method and apparatus for rotated three-dimensional (3D) components |
| CN106600684A (en) * | 2016-11-29 | 2017-04-26 | 浙江科澜信息技术有限公司 | Oblique model organization construction method |
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| US9621924B2 (en) | 2012-04-18 | 2017-04-11 | Thomson Licensing | Vextex correction method and apparatus for rotated three-dimensional (3D) components |
| US9866840B2 (en) | 2013-01-10 | 2018-01-09 | Thomson Licensing | Method and apparatus for vertex error correction |
| CN104123696A (en) * | 2014-07-07 | 2014-10-29 | 北京理工大学 | Focus and context visualization method based on multiresolution |
| CN107077746A (en) * | 2014-09-12 | 2017-08-18 | 酷比特公司 | System, method and computer program product for network transmission and the Automatic Optimal of the 3D texture models of real-time rendering |
| CN104574508A (en) * | 2015-01-14 | 2015-04-29 | 山东大学 | Multi-resolution model simplifying method oriented to virtual reality technology |
| US10417821B2 (en) | 2015-05-07 | 2019-09-17 | Institut Mines Telecom | Method of simplifying a geometry model |
| CN105654536B (en) * | 2015-12-21 | 2019-04-12 | 浙江工商大学 | The method that time domain cluster is carried out to threedimensional model according to curvature |
| CN105654536A (en) * | 2015-12-21 | 2016-06-08 | 浙江工商大学 | Method for performing time domain clustering on three-dimensional model according to curvature |
| CN106372224A (en) * | 2016-09-07 | 2017-02-01 | 北京拓扑视景科技有限公司 | Three-dimensional model retrieving method and device |
| CN106372224B (en) * | 2016-09-07 | 2019-06-21 | 北京拓扑视景科技有限公司 | A kind of method for searching three-dimension model and device |
| CN106600684A (en) * | 2016-11-29 | 2017-04-26 | 浙江科澜信息技术有限公司 | Oblique model organization construction method |
| CN110291522A (en) * | 2017-11-30 | 2019-09-27 | 西门子工业软件有限公司 | The method for operating the CAD system model for being modeled to product to be manufactured |
| CN116402975A (en) * | 2023-01-13 | 2023-07-07 | 北京航空航天大学云南创新研究院 | Method and device for loading and rendering three-dimensional model in WEB platform environment |
| CN116402975B (en) * | 2023-01-13 | 2024-03-26 | 北京航空航天大学云南创新研究院 | Method and device for loading and rendering three-dimensional model in WEB platform environment |
| CN117113478A (en) * | 2023-07-28 | 2023-11-24 | 中水淮河规划设计研究有限公司 | BIM model light weight method |
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