CN102968813A - Surface sampling method of triangular patch mesh model - Google Patents
Surface sampling method of triangular patch mesh model Download PDFInfo
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- CN102968813A CN102968813A CN2012104222736A CN201210422273A CN102968813A CN 102968813 A CN102968813 A CN 102968813A CN 2012104222736 A CN2012104222736 A CN 2012104222736A CN 201210422273 A CN201210422273 A CN 201210422273A CN 102968813 A CN102968813 A CN 102968813A
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Abstract
The invention provides a surface sampling method of a triangular patch mesh model. The method includes generating a random number with a value range from 0 to a sum of areas of all triangular patches; accumulating the areas of the triangular patches from small to large until an accumulated value is larger than the random number for the first time, and selecting the triangular patch corresponding to the accumulation; and performing random sampling on the selected triangular patch to obtain sampling points. According to the surface sampling method of the triangular patch mesh model, the quantity of the sampling points is controlled according to the areas of the triangular patches, so that the triangular patches with larger areas can be sampled repeatedly, the sampling points can accurately reflect structural characteristics of a three-dimensional model, the stability is achieved, and the method is suitable for application field of three-dimensional model detection and the like.
Description
Technical field
The present invention relates to the computer graphics techniques field, relate in particular to a kind of surperficial method of sampling of triangular surface patch grid model.
Background technology
The triangular surface patch grid model represents the spatial surface that a class represents with triangle gridding in computer system.One of them typical example utilizes triangle gridding to represent three-dimensional model (three-dimensional model described herein namely all is the three-dimensional model that represents with triangle gridding) exactly.In recent years, three-dimensional model is explosion type ground always and increases, and how to retrieve quickly and efficiently the model that needs from the solid model of magnanimity, and is reused an active demand that becomes the three-dimensional model design field.Content-based three-dimensional model search is the effectively important technical of retrieval of current realization three-dimensional model, and its geometrical property according to three-dimensional model (that is, shape facility and architectural feature) is carried out the extraction of characteristic information.Content-based three-dimensional model searching system generally includes the extraction of model preprocessing, proper vector (characteristic information that extracts generally exists in the mode of vector) and three steps of similarity matching of model from three-dimensional modeling data.
Wherein, pretreatment operation can be standardized the three-dimensional model of separate sources and extract the comparatively data of core, influential property, so that the data after the standardization have more comparability and accuracy.But after the pretreatment operation, because carrying out proper vector, the too huge inconvenience such as the point of three-dimensional model and dough sheet amount extract, thereby in the existing method, usually before extracting the proper vector operation, three-dimensional model carrying out the pseudorandom sampling, the sampled point according to gained extracts proper vector again.As seen, three-dimensional model (in this article, triangular surface patch grid model namely) the surperficial method of sampling is the important step in the three-dimensional model search, the result of triangular surface patch grid model surface sampling has determined whether the proper vector that content-based retrieval aspect of model extraction algorithm obtains can express the shape content feature of three-dimensional model, and directly affects the accuracy of three-dimensional model search.In addition, the surperficial sampling algorithm of triangular surface patch grid model also can be applicable in the multiple application such as structure, three-dimensional model gridding compression of three-dimensional model point cloud.
The surperficial method of sampling of the triangular surface patch grid model of main flow comprises at present: uniform sampling point algorithm and surface, the pseudo random number Monte Carlo method of sampling.Wherein, uniform sampling point algorithm can guarantee that sampled point distributes at the dough sheet surface uniform, but this algorithmic theory of randomness is not strong; Simultaneously, equally distributed sampled point all extracts the sampled point of same quantity in all dough sheets, can not give prominence to the architectural feature that embodies the triangular surface patch grid model.Therefore in the surperficial method of sampling of triangular surface patch grid model, the range of application of surface, the pseudo random number Monte Carlo method of sampling is more extensive.Fig. 1 shows the flow process of surface, the pseudo random number Monte Carlo method of sampling, comprising: all tri patch T=(t that 1) will form whole model
1, t
2...., t
k) read in internal memory, the tri patch quantity that comprises of k representation model wherein; 2) generate pseudo random number; 3) according to pseudo random number, choose at random a dough sheet in these dough sheets; 4) utilize formula
Calculating sampling point in the tri patch of choosing; 5) sampled point with all dough sheets is stored in the sampled point matrix; Whether the number of 6) judging sampled point reaches the upper limit, if do not reach, then jumps to 2) continue to carry out; If reach, then finish sampling algorithm.
Although in sampling process, choose on the dough sheet probability of same point very little, but the lack of uniformity because pseudo-random sequence randomness is strong, so that sampled point is at the model surface skewness, may in a territory, there be too much sampled point, particularly more at dough sheet and situation down-sampling effect that sampled point is relatively less is very bad, so just can not well utilize sampled point to represent the information of this dough sheet, thereby affect the extraction of shape facility information, thereby cause retrieval precision to descend and result for retrieval unstable.
In sum, the existing surperficial method of sampling can not satisfy the architectural feature that sampled result can embody the triangular surface patch grid model to the sampling of triangular surface patch grid model, possesses simultaneously again sampling randomness and Sampling uniformity.
Summary of the invention
For the problems referred to above, the invention provides a kind of surperficial method of sampling of triangular surface patch grid model.Can guarantee that acquisition can embody the sampled result of the architectural feature of triangular surface patch grid model under sampling randomness and the inhomogeneity prerequisite.
According to one embodiment of the invention, a kind of surperficial method of sampling of triangular surface patch grid model is provided, comprising:
Step 1), be the interval random number α that generates with [0, S]
i, wherein
S is the area summation of all tri patchs:
S
iRepresent single tri patch t
iArea, i ∈ [1, k], k represents the quantity of tri patch;
Step 2), the area of tri patch is added up from small to large, until cumulative value is first greater than α
i, select this time corresponding tri patch that adds up;
Step 3), carry out the collection of random point at selected tri patch, obtain sampled point.
In one embodiment, step 1) adopts following formula to calculate the area of single tri patch:
Wherein, s represents half of tri patch girth, (A, B, C) represent the summit of this tri patch in rectangular coordinate system in space, || AB|| represents the length of side on the AB limit of tri patch, || BC|| represents the length of side on the BC limit of tri patch, || CA|| represents the length of side on the CA limit of tri patch.
In one embodiment, step 3) adopts following formula to carry out the collection of random point:
Wherein, the summit of (A, B, C) selected tri patch of expression in rectangular coordinate system, r
1And r
2That span is two random numbers of 0 to 1.
In one embodiment, in step 2) frontly also comprise the steps:
All tri patchs are carried out the order ordering by size.
In a further embodiment, use quick sorting algorithm that all tri patchs are carried out the order ordering by size.
In one embodiment, also comprise before the step 1):
All tri patchs that step 0), will form whole triangular surface patch grid model read in internal memory.
In one embodiment, also comprise the steps: after the step 3)
Store resulting sampled point, repeating step 1) to step 3), until obtain the sampled point of requirement.
In a further embodiment, sampled point can be stored in the sampled point matrix or in the sampled point array.
Compare with prior art, how many present invention is by size the controlling its sampled point according to the dough sheet area, can embody better the architectural feature of triangular surface patch grid model and have stability, can improve the precision of three-dimensional model searching system, more be applicable to the retrieval of three-dimensional model.
Description of drawings
Fig. 1 is surface, pseudo random number Monte Carlo method of sampling process flow diagram;
Fig. 2 is the surperficial method of sampling process flow diagram of according to an embodiment of the invention triangular surface patch grid model;
Fig. 3 is the sampled point synoptic diagram of tri patch;
Fig. 4 .1-4.3 is respectively the synoptic diagram of three-dimensional model M102, M115, M103;
Fig. 5 adopts according to the surperficial method of sampling of triangular surface patch grid model of the present invention and the accuracy of surface, the pseudo random number Monte Carlo method of sampling Fig. 4 .1 to compare broken line graph;
Fig. 6 .1 is the point cloud chart that adopts the surperficial method of sampling according to triangular surface patch grid model of the present invention to obtain to the three-dimensional model among Fig. 4 .2;
Fig. 6 .2 is the point cloud chart that arrives that the three-dimensional model among Fig. 4 .2 is adopted surface, the pseudo random number Monte Carlo method of sampling;
Fig. 6 .3 is the partial enlarged drawing of Fig. 6 .1;
Fig. 6 .4 is the partial enlarged drawing of Fig. 6 .2;
Fig. 7 adopts according to the surperficial method of sampling of triangular surface patch grid model of the present invention and the stability of surface, the pseudo random number Monte Carlo method of sampling Fig. 4 .1 to compare broken line graph;
Fig. 8 adopts according to the surperficial method of sampling of triangular surface patch grid model of the present invention and the stability of surface, the pseudo random number Monte Carlo method of sampling Fig. 4 .3 to compare broken line graph.
Embodiment
The present invention will be further described below in conjunction with the drawings and specific embodiments.
According to one embodiment of present invention, provide a kind of triangular surface patch grid model surface method of sampling.The method is by calculating the area of each tri patch in the triangular surface patch grid model that is represented by tri patch, come how much the controlling of its sampled point according to the size of the tri patch area that calculates, the dough sheet that area is large must cover all information that could represent its dough sheet with more sampled point.
Fig. 2 shows the surperficial method of sampling of triangular surface patch grid model according to an embodiment of the invention, and its concrete steps comprise:
In rectangular coordinate system in space, for each tri patch, (A, B, C) represents three summits of this dough sheet, A, and B, C comprise respectively x, y, three (coordinate) components of z.
Calculating leg-of-mutton area has a lot of modes, because Heron's formula generally is applicable to calculate triangle area in computing machine, according to one embodiment of the invention, utilizes following formula to calculate S
i:
Wherein, s represents half of triangle girth; || AB|| represents the length of side on triangle AB limit; || BC|| represents the length of side on triangle BC limit; || CA|| represents the length of side on triangle CA limit.
Wherein, described sort method can use: bubble sort, quicksort, insertion sort etc.Because the time complexity of quicksort is minimum in sort algorithm, preferably uses quick sorting algorithm.
After the area according to each tri patch sequentially sorted it, in the front end of sequence T ' the very little dough sheet unit of many areas that distributing, the rear end then was the relatively large dough sheet of area.
1) be the interval random number α that generates with [0, S]
i, α
iIn equiprobable being distributed to [0, the S] space; Wherein, S is the area summation of all tri patchs:
2) with counter since 0, by sorted tri patch sequence T ', the area of tri patch is added up from small to large, until the value of counter is first greater than α
iThat is to say, adding upper panel S
iThe value of counter is more than or equal to α after the area of (span of i is between 1 to k)
i, and do not adding S
iThe value of this counter is less than α before
i, this dough sheet S then
iBe selected tri patch β
i
The reason that adopts the mode of above-mentioned Area-weighted to choose tri patch is: because from tiny dough sheet area accumulation until surpass α
iTill, can the easier counter upper limit α of surpassing so that in number axis [0, S], occupy the larger part adding counter of ratio
i, the dough sheet that namely area is larger can be chosen more frequently, that is to say, can represent the dough sheet that area is larger by more sampled point.
For example, at β
iUtilize following formula to carry out the collection of random point on the dough sheet:
Wherein, (A, B, C) expression dough sheet β
iThree summits, r
1And r
2From 0 to 1 two random numbers that generate.By shown in Figure 3, triangle β
iCan regard as by the fine rule of series of parallel in the BC limit and form, shown in dotted line.Suppose that an array records the fine rule area summation of crossing by sequential access from top to bottom successively, because square being directly proportional of triangle area and the length of side, so corresponding r
1Slice be in dotted line position among the figure.Utilize r
2Specify in the stochastic sampling point P on this slice.This shows that the position of sampled point is in the inner evenly distribution of triangle.
Adopting this formula to calculate random point is because the position of this formula gained sampled point can be in the inner evenly distribution of triangle.Two random number r
1And r
2Can guarantee the randomness of sampled point, repeated sampling not, reduce the overlapping of sampled point.
In step 5, resulting sampled point can be stored in sampled point matrix or the sampled point array, if the sampled point that gathers does not satisfy the required sampled point upper limit, then repeats above-mentioned steps 4-5, until need not to proceed to gather.Use for three-dimensional model search, this step is finally returned sampled point matrix or sampled point array, and the proper vector that is used for three-dimensional model is extracted.
What the present invention is directed to is the spatial surface that represents with tri patch, should be understood that the spatial surface with other geometirc graphical presentations can at first be divided into tri patch with this geometric figure, thereby also is suitable for the surperficial method of sampling provided by the invention.
Below the surperficial method of sampling of triangular surface patch grid model according to the present invention and current surface, the pseudo random number Monte Carlo method of sampling of generally using are compared.Three-dimensional model representative in the triangular surface patch grid model is as example, statistic record by many experiments, the surperficial method of sampling that can verify triangular surface patch grid model provided by the invention has more stability and representativeness than the surperficial method of sampling in pseudo random number Monte Carlo, is applicable to different types of triangular surface patch grid model and carries out the surface sampling.
The present invention acts on surface, the pseudo random number Monte Carlo method of sampling respectively on the identical three-dimensional model (these models all represent with triangle gridding) with surperficial sampling algorithm proposed by the invention, behind standardization and sampling vacuate, and the three-dimensional modeling data of opening in the three-dimensional model browser take OpenGL as too development behind the vacuate shows, observes the feature of the representative three-dimensional model which kind of surperficial method of sampling can be vivider.Simultaneously, the present invention has also selected the three-dimensional model of different dough sheet quantity to test.The dough sheet quantity of three-dimensional model as controllable variable, when quantity changes, is used two kinds of surperficial method of samplings and sampled, and sampled result utilizes the Osada algorithm to carry out the extraction of proper vector and the calculating of similarity.That is, with the thought of control variate method, under the identical prerequisite identical with similarity calculating method of, proper vector extraction algorithm identical at three-dimensional model, adopt the different surperficial method of samplings, the result is investigated.
Experiment one.
Using the dough sheet number shown in Fig. 4 .1 is that 226 M102 model is as experimental subjects, this three-dimensional model is adopted respectively the pseudorandom Monte Carlo surface method of sampling and method provided by the invention, by adjusting the ratio of sampling number and dough sheet number, observe two Algorithm Performances.The quantity of sampled point is set as respectively: 23,57,113,226,452,1130,4520,9040,18080, and then the ratio (rounding up) of sampled point and dough sheet number is respectively: 0.1,0.25,0.5,1,2,5,20,40,80.Sampled result utilizes this area Osada algorithm commonly used to carry out the extraction of proper vector, wherein, use the D2 distance of Osada algorithm as the shape function of feature extraction, and use Euclidean distance to calculate the sample similarity of rear proper vector of same model, same sampling number.In theory, same model is carried out double sampling, the difference of calculating the D2 distance should be 0, and in the actual computation, the difference of D2 distance is less, illustrates then that the method for sampling is unreasonable to think.
Experimental data as shown in Figure 5.Adopting the distance of surface, pseudorandom Monte Carlo method of sampling gained when sampling number is considerably less is very large (that is, so that same three-dimensional model is dissimilar), this be can't representative model because sampling number is very few overall picture.Adopt surface, the pseudorandom Monte Carlo method of sampling when stochastic sampling is counted greater than three-dimensional model dough sheet number after apart from monotone decreasing, level off to 0, and before not reaching three-dimensional model dough sheet number, sampling number also has the interval of one section fluctuation, be not that completely monotone is successively decreased, this is because surface, pseudorandom Monte Carlo method of sampling randomness is strong, but it is whole well to cover three-dimensional model, and the sampled point result is not bery stable each time causes.Only have when sampling number is counted greater than the three-dimensional model dough sheet, the pseudo random number sampling method could the basic feature of summarizing three-dimensional model, and each face at three-dimensional model of that is to say has at least a sampled point representative to be only to approach accurately.
The surperficial method of sampling of triangular surface patch grid model provided by the invention is in sampled point and the very little situation of the ratio of dough sheet number, and distance is also smaller, and is monotone decreasing always and levels off to 0 situation.Surperficial method of sampling of triangular surface patch grid model provided by the invention is described for this so that sampled point has better covered the surface of three-dimensional model, can represent than surface, pseudorandom Monte Carlo method of sampling use sampled point still less the feature of three-dimensional model.
When the dough sheet number is larger, the M103 model shown in Fig. 4 .3 (31432 dough sheets) is for example got 31432*40 point after calculating the area of each dough sheet more at random, then calculates the D2 distance, in fact when data volume is large, be necessary to reduce sampled point for improving counting yield.Consequently, during less than the dough sheet number, more accurate by the distance that method provided by the invention calculates at sampled point.
Experiment two.
Choose the M115 model shown in Fig. 4 .2, with the surperficial method of sampling of the pseudorandom Monte Carlo surface method of sampling and triangular surface patch grid model provided by the invention it is carried out the sampling of three-dimensional model surface respectively, the three-dimensional model browser of utilization take OpenGL as instrument opened sampled point, obtains the three-dimensional model point cloud chart.
Fig. 6 .1 shows the point cloud chart that adopts the surperficial method of sampling according to triangular surface patch grid model of the present invention to obtain to the three-dimensional model among Fig. 4 .2, and Fig. 6 .2 shows the point cloud chart that adopts surface, the pseudo random number Monte Carlo method of sampling to obtain to the three-dimensional model among Fig. 4 .2.Can find out intuitively: the feature that the surperficial method of sampling of triangular surface patch grid model provided by the invention more can be given prominence to three-dimensional model than the surperficial method of sampling in pseudorandom Monte Carlo.The skeleton moulding of choosing for this model, from Fig. 6 .1 and 6.2 about the partial enlarged drawing of thigh bone, be to find out in Fig. 6 .3 and 6.4, the surperficial method of sampling provided by the invention can well be given prominence to the planform of thigh bone, and surface, the pseudorandom Monte Carlo method of sampling can only provide the general profile of thigh bone, at detailed structure up-sampling poor-performing, and sampling point distributions is uneven.Thereby method provided by the invention can better embody the structure of three-dimensional model.
Experiment three.
Use 8192 points of sampling respectively of the M102 model shown in Fig. 4 .1, every kind of method of sampling carry out 10 times with self calculating similarity, the result is as shown in Figure 7.
As seen from Figure 7, in the situation of dough sheet less (the dough sheet number is 226), the stability of the surperficial method of sampling of triangular surface patch grid model provided by the invention is higher than the stability of the surperficial method of sampling in pseudorandom Monte Carlo, but the degree of accuracy difference of them is also little, this is because dough sheet is less, stochastic sampling point is more, can have several sampled points to occur on each dough sheet.
Choose again a more three-dimensional model of dough sheet and carry out self comparison, the dough sheet number of M103 shown in Fig. 4 .3 is 31432, it is carried out vacuate sampling, when getting equally 8192 sampled points and working as sampling number less than model dough sheet number, the comparison of two kinds of algorithm stabilities.As shown in Figure 8.
As seen from Figure 8, floating of surface, the pseudorandom Monte Carlo method of sampling is larger, and the surperficial method of sampling of the triangular surface patch grid model that the present invention proposes is unsteady relatively mild.Can find out from the ordinate of broken line graph 8, in the situation of vacuate, be sampling number during less than the dough sheet number, the Area-weighted algorithm can better be distributed on the whole dough sheets of three-dimensional model, and its distance is also [0,0.1] between float, and for the pseudorandom Monte Carlo surface method of sampling, its randomness is strong but can not well cover the surface of three-dimensional model, so its distance is [0,0.6] between float, the interval is larger.
Can be found out by experiment one to three, regardless of dough sheet number and sampling number relation, the surperficial method of sampling of the triangular surface patch grid model that the present invention proposes all has better stability, and more can embody the feature structure as the three-dimensional model of triangular surface patch grid model, more be applicable to the retrieval of three-dimensional model.
Should be noted that and understand, in the situation that does not break away from the desired the spirit and scope of the present invention of accompanying claim, can make to the present invention of foregoing detailed description various modifications and improvement.Therefore, the scope of claimed technical scheme is not subjected to the restriction of given any specific exemplary teachings.
Claims (8)
1. the surperficial method of sampling of a triangular surface patch grid model comprises: step 1), be the interval random number α that generates with [0, S]
i, wherein
S is the area summation of all tri patchs:
S
iRepresent single tri patch t
iArea, i ∈ [1, k], k represents the quantity of tri patch;
Step 2), the area of tri patch is added up from small to large, until cumulative value is first greater than α
i, select this time corresponding tri patch that adds up;
Step 3), carry out the collection of random point at selected tri patch, obtain sampled point.
2. method according to claim 1, wherein step 1) adopts following formula to calculate the area of single tri patch:
Wherein, s represents half of tri patch girth, (A, B, C) represent the summit of this tri patch in rectangular coordinate system in space, || AB|| represents the length of side on the AB limit of tri patch, || BC|| represents the length of side on the BC limit of tri patch, || CA|| represents the length of side on the CA limit of tri patch.
3. method according to claim 1 and 2, step 3) adopts following formula to carry out the collection of random point:
Wherein, the summit of (A, B, C) selected tri patch of expression in rectangular coordinate system, r
1And r
2That span is two random numbers of 0 to 1.
4. method according to claim 1 and 2 is in step 2) frontly also comprise the steps:
All tri patchs are carried out the order ordering by size.
5. method according to claim 4 wherein uses quick sorting algorithm that all tri patchs are carried out the order ordering by size.
6. method according to claim 1 and 2 wherein also comprises before the step 1):
All tri patchs that step 0), will form whole triangular surface patch grid model read in internal memory.
7. method according to claim 1 and 2 wherein also comprises the steps: after the step 3)
Store resulting sampled point, repeating step 1) to step 3), until obtain the sampled point of requirement.
8. method according to claim 7, wherein sampled point can be stored in the sampled point matrix or in the sampled point array.
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| WO2022193080A1 (en) * | 2021-03-15 | 2022-09-22 | 深圳市大疆创新科技有限公司 | Point cloud processing method and apparatus, and computer-readable storage medium |
| CN113378325A (en) * | 2021-06-30 | 2021-09-10 | 广东科学技术职业学院 | Area method-based grid patch retrieval method for curved surface part measuring points |
| WO2023103828A1 (en) * | 2021-12-09 | 2023-06-15 | 西安交通大学 | Single-point sampling optimization method and system for frequency response measurement |
| CN114821541A (en) * | 2022-06-23 | 2022-07-29 | 深圳大学 | Road surface damage detection method based on grid model and related equipment |
| CN114821541B (en) * | 2022-06-23 | 2022-10-04 | 深圳大学 | Road surface damage detection method based on grid model and related equipment |
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