CN103996221A - Plant organ mesh simplification method targeted for visualization calculation - Google Patents

Abstract

The invention relates to a plant organ mesh simplification method targeted for visualization calculation. With the triangular mesh model simplification of the plant organ being a target, the simplification and optimization of a mesh model are realized by utilizing and combining a quadric error measure simplification method and Laplace fairing operators comprehensively. The main method is that to begin with, simplifying the input triangular mesh model through the mesh simplification method based on quadric error measure, and then, carrying out fairing operation on the inner top point of the simplified mesh model by utilizing the Laplace fairing operators. The method well solves the technical problem that in the prior art, the quality of the mesh cannot be guaranteed at the same time the mesh is reduced, and when the model is simplified to be very few surface elements, relatively-large form distortion occurs; the simplified organ mesh model is still of good mesh quality; and the effect cannot be realized by the ordinary method.

Description

A kind of lattice simplified method of plant organ towards Visual calculation

Technical field

The invention belongs to field of Computer Graphics, especially relate to a kind of lattice simplified method of plant organ towards Visual calculation.

Background technology

Plant Geometric Modeling is the element task of digital plant research, the quantity of grid model and quality play decisive role to the digital plant Visual calculation of carrying out taking it as carrier, as crop canopies light distribution calculating, Realistic Rendering, plant growth and wilting deformation simulative etc.Compared with industrial circle, the botanical geometric model has the features such as systematicness is poor, complexity is high, colony's number of grid is large.

Be focus and the difficulties in intelligent CAD field towards the grid model optimization of Visual calculation, the algorithm adopting for different demands is also different always.In many engineering application, as finite element numerical simulation or complex model are played up, because the reasons such as the initial subdivision of grid, grid initially generate, data acquisition cause model quality poor, for raising the efficiency and precision, require grid cell sparse as far as possible under the prerequisite that ensures mesh quality, reduce model size.There is research to play up field towards high-level efficiency, inquire at generation level (LOD) model method meeting under constraint condition; How to carry out high-quality lattice simplified and optimization towards finite element simulation area research, to promote the efficiency and precision of analysis.In field of Computer Graphics, have two large class methods can realize this target---gridding and mesh simplification again.Again the target of gridding is a given triangle gridding, according to specific quality requirements, it is processed and obtains a new triangle grid model.Divide according to different objects, gridding method is divided into tactical rule, isotropy, anisotropy, compatible, gridding again based on feature etc. again.Mesh simplification is to remove the grid processing method of " redundancy " geometric units in order to reduce moulded dimension, and wherein most representative method is famous QEM shortcut calculation, has the plurality of advantages such as efficient, simple, low storage.Due to the relatively lagging behind property of plant Geometric Modeling and the complicacy of plant structure and organ, the research of the botanical geometric model grid optimization aspect is less, mainly contain the geometric model simplification method that the propositions such as Remolar are played up towards extensive forest, Xiao Baixiang etc. have proposed lattice simplified function for maize leaf, and Zhao Chunjiang etc. utilize self-adaptive gridding method to carry out mesh generation for plant organ.

From the prior art, have and just reduce from number of grid for the lattice simplified technology of plant, in reducing grid, do not ensure the quality of grid; And plant leaf blade boundary curve is comparatively mixed and disorderly, and often present belt shape, directly adopt the lattice simplified method of other field for plant leaf blade poor effect, poor robustness.

Summary of the invention

The technical matters that the present invention mainly solves is: solve when triangular mesh model is reduced to few bin and ensure that model does not produce larger distortion, to be applicable to the Visual calculation of digital plant.

Technical scheme proposed by the invention is: first adopt the lattice simplified method based on Quadric Error Metrics to simplify to the triangular mesh model M of input, be simplified grid model M '; Then adopt Laplacian method operator to carry out fairing operation to the internal vertex of simplifying grid model M '.

Grid model M is simplified to the lattice simplified method based on Quadric Error Metrics adopting to be comprised:

S31, input triangular mesh model M;

S32, calculates each vertex v _ideflation error degree matrix Q _i, note vertex v _ihomogeneous coordinates be [v _xv _yv _z1] ^t, definition v _ito it in abutting connection with triangle set P (v _i) Euclidean distance quadratic sum be Δ (v _i), computing formula is as follows:

$\mathrm{\Δ}\left(v_i\right)=\underset{p\∈P\left(v_i\right)}{\mathrm{\Σ}}{\left(p^T{v}_i\right)}^2={v_i}^T\left(\underset{p\∈P\left(v_i\right)}{\mathrm{\Σ}}{\mathrm{pp}}^T\right)v_i$

^p=[a b c d] ^trepresent by the defined plane of equation ax+by+cz+d=0, wherein a ²+ b ²+ c ²=1, definition for vertex v _ideflation error degree matrix;

S33, to every limit (v _i, v _j), calculate the target location of shrinking summit computing formula is as follows:

${\stackrel{\‾}{v}}_{\mathrm{ij}}{\left[\begin{array}{cccc}{q}_{11}& q_{12}& q_{13}& q_{14}\\ q_{12}& q_{22}& q_{23}& q_{24}\\ q_{13}& q_{23}& q_{33}& q_{34}\\ 0& 0& 0& 1\end{array}\right]}^{-1}\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]$

Wherein q _mntake from matrix (Q _i+ Q _j) (m, n) position, Q _i, Q _jfor vertex v _i, v _jcorresponding degree of error matrix, if above formula right-hand member square formation is irreversible, get the mid point on this limit, for border vertices, increase weights to keep border by penalty factor;

S34, with error as limit (v _i, v _j) contraction weights, and above-mentioned weights are arranged in heaps, minimum weights are set to heap top;

S35, deletes minimum weights limit, heap top, and shrinking this limit is summit renewal comprises vertex v _i, v _jentitlement value information;

S36, repeats above-mentioned steps S32 to step S35, till being met default number of vertex object simplified model M '.

Adopt Laplacian method operator to carry out fairing operation to the internal vertex of simplifying grid model M ', definition vertex v _iposition after optimizing formula is as follows:

Wherein, the in-degree that n is vertex v, v _ijfor v _ione ring summit, ω i _jfor lax weight coefficient, meet in fairing process, border vertices and given unique point are not carried out loose operations.

Preferably, lax weight coefficient ω i _jobtaining value method is: evenly weights: ω i _j=1/n, n is the in-degree of vertex v i; Or, discrete mediation weights: wherein λ i _j=(cot α i _j+ cot β i _j)/2, α _ij, β _ijbe respectively and simplify in Vee formation shape grid model M ' with limit (v _i, v _j) as two leg-of-mutton drift angles on base.

The invention has the beneficial effects as follows: complex mesh model is simplified and optimization process, can be reached promising result at aspects such as mesh quality, simplification efficiency and maintenance initial model features.Model after simplifying, for digital plant Visual calculation, in having ensured computational accuracy, is significantly improved to counting yield.

Brief description of the drawings

Can more clearly understand the features and advantages of the present invention by reference to accompanying drawing, accompanying drawing is schematically to should not be construed as the present invention is carried out to any restriction, in the accompanying drawings:

Fig. 1 shows the Visual calculation principle process of digital plant;

Fig. 2 shows angle ^α _ij, β _ijthe location drawing;

Fig. 3 shows graticule model simplification Optimizing Flow figure of the present invention.

Embodiment

Below in conjunction with accompanying drawing to implementation example explanation of the present invention.

First, be calculated as the Visual calculation principle of the digital plant of example explanation with SIMULATION OF RADIATION DISTRIBUTION IN MAIZE CANOPY.For maize canopy, the ground grid that only calculates of paramount importance organ blade and canopy to participating in the distribution of canopy light is optimized.Flow process as shown in Figure 1.

S1, the grid model M0 of plant population of input corn;

S2, by maize population grid model taking the organ component netlist lattice model M single as unit is split as _i;

S3, also optimizes after each organ parts grid model is simplified, and back part model M is optimized _i';

S4, will optimize back part model M _i' reconsolidate and become the new grid model M0 ' of plant population;

S5, utilizes the model M 0 ' after optimizing to carry out SIMULATION OF RADIATION DISTRIBUTION IN MAIZE CANOPY calculating.

The embodiment of the present invention mainly elaborates the simplification optimization method to each organ parts grid model in above-mentioned steps S3.

First, adopt the lattice simplified method based on Quadric Error Metrics to simplify to single partial model M, flow process as shown in Figure 3, specifically comprises:

S31, input triangular mesh model M;

S32, calculates each vertex v _ideflation error degree matrix Q _i, note vertex v _ihomogeneous coordinates be [v _xv _yv _z1] ^t, definition v _ito it in abutting connection with triangle set P (v _i) Euclidean distance quadratic sum be Δ (v _i), computing formula is as follows:

$\mathrm{\Δ}\left(v_i\right)=\underset{p\∈P\left(v_i\right)}{\mathrm{\Σ}}{\left(p^T{v}_i\right)}^2={v_i}^T\left(\underset{p\∈P\left(v_i\right)}{\mathrm{\Σ}}{\mathrm{pp}}^T\right)v_i$

P=[a b c d] ^trepresent by the defined plane of equation ax+by+cz+d=0, wherein a ²+ b ²+ c ²=1, and definition Δ (v)=v ^tqv, therefore vertex v _ideflation error degree matrix

S33, to every limit (v _i, v _j), calculate the target location of shrinking summit computing formula is as follows:

${\stackrel{\‾}{v}}_{\mathrm{ij}}{\left[\begin{array}{cccc}{q}_{11}& q_{12}& q_{13}& q_{14}\\ q_{12}& q_{22}& q_{23}& q_{24}\\ q_{13}& q_{23}& q_{33}& q_{34}\\ 0& 0& 0& 1\end{array}\right]}^{-1}\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]$

Wherein q _mntake from matrix (Q _i+ Q _j) (m, n) position, Q _i, Q _jfor vertex v _i, v _jcorresponding degree of error matrix, if above formula right-hand member square formation is irreversible, get the mid point on this limit, for border vertices, increase weights to keep border by penalty factor;

S34, with error as limit (v _i, v _j) contraction weights, and above-mentioned weights are arranged in heaps, minimum weights are set to heap top;

S35, deletes minimum weights limit, heap top, and shrinking this limit is summit renewal comprises vertex v _i, v _jentitlement value information;

S36, repeats above-mentioned steps S32 to step S35, till being met default number of vertex object simplified model M '.

Secondly, adopt Laplacian method operator to carry out fairing operation to the internal vertex of simplifying grid model M ', definition vertex v _iposition after optimizing formula is as follows:

Wherein, the in-degree that n is vertex v, v _ijfor v _ione ring summit, ω i _jfor lax weight coefficient, meet in fairing process, border vertices and given unique point are not carried out loose operations.

About lax weight coefficient ω i _jobtaining value method has multiple, at this we adopt below two kinds of obtaining value methods:

1. even weights: ω i _j=1/n, n is vertex v _iin-degree;

2. discrete mediation weights: wherein λ _ij=(cot α _ij+ cot β _ij)/2, α _ij, β _ijbe respectively and simplify in Vee formation shape grid model M ' with limit (v _i, v _j) as two leg-of-mutton drift angles on base.As shown in Figure 2.

Usually, can restrain by the iteration of 50 left and right for plant organ data acquisition, reach satisfactory result.

The embodiment of the present invention, carries out multiple dimensioned simplification to plant organ, and realizes the optimization of simplifying rear grid model.The embodiment of the present invention can be by the extremely bin of small number of graticule model simplification, simplification rate can be low to moderate below 3%, on this basis, when plant population's grid model is realized to significantly simplification, keep organ morphological feature, ensure mesh quality, and the Visual calculation of utilizing the botanical geometric model after embodiment of the present invention method is simplified to carry out, in ensureing computational accuracy, can significantly improve counting yield.

Although described by reference to the accompanying drawings embodiments of the present invention, but those skilled in the art can make various modifications and variations without departing from the spirit and scope of the present invention, such amendment and modification all fall into by within claims limited range.

Claims (4)

1. towards the lattice simplified method of plant organ of Visual calculation, it is characterized in that: first adopt the lattice simplified method based on Quadric Error Metrics to simplify to the triangular mesh model M of input, be simplified grid model M '; Then adopt Laplacian method operator to carry out fairing operation to the internal vertex of simplifying grid model M '.

2. a kind of lattice simplified method of plant organ towards Visual calculation according to claim 1, is characterized in that, grid model M is simplified to the lattice simplified method based on Quadric Error Metrics adopting and comprise:

S31, input triangular mesh model M;

S32, calculates each vertex v _ideflation error degree matrix Q _i, note vertex v _ihomogeneous coordinates be [v _xv _yv _z1] ^t, definition v _ito it in abutting connection with triangle set P (v _i) Euclidean distance quadratic sum be Δ (v _i), computing formula is as follows:

$\mathrm{\Δ}\left(v_i\right)=\underset{p\∈P\left(v_i\right)}{\mathrm{\Σ}}{\left(p^T{v}_i\right)}^2={v_i}^T\left(\underset{p\∈P\left(v_i\right)}{\mathrm{\Σ}}{\mathrm{pp}}^T\right)v_i$

P=[a b c d] ^trepresent by the defined plane of equation ax+by+cz+d=0, wherein a ²+ b ²+ c ²=1, definition for the deflation error degree matrix of vertex v i;

S33, to every limit (v _i, v _j), calculate the target location of shrinking summit computing formula is as follows:

${\stackrel{\‾}{v}}_{\mathrm{ij}}{\left[\begin{array}{cccc}{q}_{11}& q_{12}& q_{13}& q_{14}\\ q_{12}& q_{22}& q_{23}& q_{24}\\ q_{13}& q_{23}& q_{33}& q_{34}\\ 0& 0& 0& 1\end{array}\right]}^{-1}\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]$

Wherein q _mntake from matrix (Q _i+ Q _j) (m, n) position, Q _i, Q _jfor vertex v _i, v _jcorresponding degree of error matrix, if above formula right-hand member square formation is irreversible, get the mid point on this limit, for border vertices, increase weights to keep border by penalty factor;

S34, with error as limit (v _i, v _j) contraction weights, and above-mentioned weights are arranged in heaps, minimum weights are set to heap top;

S35, deletes minimum weights limit, heap top, and shrinking this limit is summit renewal comprises vertex v _i, v _jentitlement value information;

S36, repeats above-mentioned steps S32 to step S35, till being met default number of vertex object simplified model M '.

3. a kind of lattice simplified method of plant organ towards Visual calculation according to claim 1, is characterized in that: adopt Laplacian method operator to carry out fairing operation to the internal vertex of simplifying grid model M ', definition vertex v _iposition after optimizing formula is as follows:

Wherein, the in-degree that n is vertex v, v _ijfor v _ione ring summit, ω i _jfor lax weight coefficient, meet in fairing process, border vertices and given unique point are not carried out loose operations.

4. a kind of lattice simplified method of plant organ towards Visual calculation according to claim 3, is characterized in that, lax weight coefficient ω i _jobtaining value method is: evenly weights: ω i _j=1/n, n is vertex v _iin-degree; Or, discrete mediation weights: wherein λ i _j=(cot α i _j+ cot β i _j)/2, α _ij, β _ijbe respectively and simplify in Vee formation shape grid model M ' with limit (v _i, v _j) as two leg-of-mutton drift angles on base.