CN103632395A - Method for simplifying three-dimensional geometric graphics on basis of triangle contraction - Google Patents

Abstract

The invention discloses a method for simplifying three-dimensional geometric graphics on the basis of triangle contraction. The method includes firstly, setting conditions for judging triangles and only allowing contraction operation to be carried out on triangles which meet the conditions; secondly, folding and contracting the triangles; thirdly, determining the vertexes V<i> of contraction points with the maximum distances d<i>, using average planes M as planes adjacent to points V<i> and solving the contraction points by a secondary error process. The maximum distances d<i> of the contraction points are equal to computation factors a. The folding and contraction priority of each triangle is represented by a weight L=aXb, the triangles corresponding to small weights L are contracted at first, each factor b represents the area of the corresponding triangle, each average plane M of a triangle plate S<i> of the corresponding triangle T is computed, normal vectors of the average planes M are acquired in such a manner the maximum distances d<i> from the various points V<i> to the triangle plates S<i> are used as the factors a, in other words, each d<i> is equal to an absolute value of nX(V<i>-x), each factor a is the maximum value of the corresponding distances d1, d2 and d3, and the distances d<i> are used for solving the triangles T. The method for simplifying the three-dimensional geometric graphics on the basis of triangle contraction has the advantages that conditional judgment is carried out on the triangles, the triangles are folded and contracted according to priority levels of the triangles, accordingly, simplifying procedures can be optimized, the precision is high, and the original graphics can be effectively preserved.

Description

Three-dimensional geometric shapes short-cut method based on triangle contraction

Technical field

The present invention relates to technical field of image processing, be specifically related to a kind of three-dimensional geometric shapes short-cut method based on triangle contraction.

Background technology

The simplification technical purpose of 3-D geometric model is to reduce the data volume of model, and simplification technology, from geometric angle, guaranteeing, under the prerequisite that mode shape is substantially constant, to reduce the segmentation precision of model surface, reduces the polygon number that it is cut apart as far as possible.The research direction of three-dimensional polygon surface model simplification technology mainly comprises the following aspects: the short-cut method of model, and research could reduce the polygon number of model surface by which type of method or operation; The control method of model simplification time error, research adopts the model after which type of means guarantee is simplified similar in shape to master pattern; The building method of multiresolution series model, how research constructs a series of approximate model, and its level of detail reduces gradually, wherein the level of detail of master pattern is the highest, the meticulousst, and the level of detail of last approximate model is minimum, is the most coarse simplified model; Wherein, the short-cut method of model and error control method are the substances in model simplification technology, in conjunction with the method for these two aspects, just can generate an approximate model of master pattern, be referred to as single resolution simplified model, its building method is the basis of multiresolution simplified model building method.

The external Model Simplification Method that oneself proposes roughly can be divided into following four large classes at present: the short-cut method of repartitioning based on surface, the short-cut method based on Vertex Clustering, short-cut method and the short-cut method based on wavelet theory based on geometric graphic element operation; Domestic correlative study direction comprises: point deletion operation, triangle deletion action, limit shrinkage operation and triangle contraction operation.Wherein, triangle contraction operation is the expansion of limit shrinkage operation, and the contraction object of choosing in each cycling is not a limit, but a triangle surface.Leg-of-mutton three summits are moved to same position, this triangle just shrinks and becomes a point, and originally incided the line segment on this Atria summit or be all connected on the point after merging by the line segment of these three summit outgoing, its triangle surface around also changes thereupon.Existing triangle contraction has various ways, topmost problem is that a kind of effective triangle collapse algorithm that the relative importance value that how to determine triangle contraction: Hamann proposes is curvature and three the interior angle angles according to an Atria summit, determine leg-of-mutton weights, the triangle that weights are minimum is folded into a new point at first; The method also having is that the new point of selection is weights to the maximal value of the distance of each triangle place plane in the relevant triangle set of folded triangle, determines leg-of-mutton fold sequence; Other methods that also have are if Isler is according to leg-of-mutton normal direction difference around leg-of-mutton area and summit, determine summit and leg-of-mutton vision importance degree, its short-cut method decides the type (edge contraction or triangle collapse) of folding operation with the vision importance degree on summit, and determine leg-of-mutton fold sequence with leg-of-mutton vision importance degree, but it is folding point that the method is selected the summit in former grid simply, easily produce larger geometric error.

To sum up, still there are a lot of places that need improvement in existing three-dimensional geometric shapes short-cut method, and urgently a kind of three-dimensional geometric shapes short-cut method based on triangle contraction is optimized.

Summary of the invention

The object of this invention is to provide a kind of more excellent simplelyr, and can at utmost preserve the three-dimensional geometric shapes short-cut method based on triangle contraction of original figure.

The invention provides a kind of three-dimensional geometric shapes short-cut method based on triangle contraction, comprise the following steps: first, the diabolo that imposes a condition judges, the triangle T only satisfying condition is just carried out shrinkage operation; Secondly, diabolo carries out folding shrinking; Wherein, the priority that triangle collapse shrinks represents by weights L=ab, and L is less, more first shrinks this triangle, and factor b is leg-of-mutton area, and each leg-of-mutton normal vector of establishing in triangular plate Si is n _k, center is x _k, area is A _k, so, the mean level of the sea M that the plane that the normal vector n of definition and center x construct is defined as triangular plate Si is: N=(∑ A _kn _k)/∑ A _k, n=N/|N|, x=(∑ x _ka _k)/∑ A _k; Factor a: diabolo T, ask relevant leg-of-mutton triangular plate Si, then calculate the mean level of the sea M of Si, its normal vector is the each point V that asks T _idistance d to Si _iget maximum as a, that is: d _i=| n (V _i-x) |, a=max (d ₁, d ₂, d ₃); Determine that constriction point is taken at the d obtaining in calculated factor a _imaximum summit V _i, using mean level of the sea M as with V _iadjacent plane, utilizes second order error method to obtain constriction point.

Preferably, the condition in described determining step comprises: only having at most a summit is border vertices; Associated triangle ring C is aperiodic; Each adjacent triangle T _niin, by the valence mumber on the shared summit of T, be not equal to 4.

Compared with prior art, the three-dimensional geometric shapes short-cut method diabolo based on triangle contraction of the present invention carries out condition judgment, and carries out folding shrinking according to priority level, has optimized simplification process, and has had higher precision, preserves better original figure.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, to the accompanying drawing of required use in embodiment or description of the Prior Art be briefly described below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skills, do not paying under the prerequisite of creative work, can also obtain according to these accompanying drawings other accompanying drawing.

Fig. 1 is the process flow diagram that the present invention is based on the three-dimensional geometric shapes short-cut method of triangle contraction.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is clearly and completely described, obviously, described embodiment is only the present invention's part embodiment, rather than whole embodiment.Embodiment based in the present invention, those of ordinary skills, not making all other embodiment that obtain under creative work prerequisite, belong to the scope of protection of the invention.

With reference to figure 1, a kind of three-dimensional geometric shapes short-cut method based on triangle contraction that the embodiment of the present invention provides, comprises the following steps:

Step S001: the diabolo that imposes a condition judges, the triangle T only satisfying condition is just carried out shrinkage operation;

Step S002: diabolo carries out folding shrinking; Wherein, the priority that triangle collapse shrinks represents by weights L=ab, and L is less, more first shrinks this triangle, and factor b is leg-of-mutton area, and each leg-of-mutton normal vector of establishing in triangular plate Si is n _k, center is x _k, area is A _k, so, the mean level of the sea M that the plane that the normal vector n of definition and center x construct is defined as triangular plate Si is: N=(∑ A _kn _k)/∑ A _k, n=N/|N|, x=(∑ x _ka _k)/∑ A _k; Factor a: diabolo T, ask relevant leg-of-mutton triangular plate Si, then calculate the mean level of the sea M of Si, its normal vector is the each point V that asks T _idistance d to Si _iget maximum as a, that is: d _i=| n (V _i-x) |, a=max (d ₁, d ₂, d ₃); Determine that constriction point is taken at the d obtaining in calculated factor a _imaximum summit V _i, using mean level of the sea M as with V _iadjacent plane, utilizes second order error method to obtain constriction point.

Preferably, the condition in described step S001 comprises: only having at most a summit is border vertices; Associated triangle ring C is aperiodic; Each adjacent triangle T _niin, by the valence mumber on the shared summit of T, be not equal to 4.

In step S002, by second order error method, obtain constriction point and specifically adopt second order error matrix method, first, for each point in master pattern surface mesh arranges a symmetrical 4X4 error matrix, be designated as:

$Q=\left[\begin{array}{cccc}q11& q12& q13& q14\\ q12& q22& q23& q24\\ q13& q23& q33& q34\\ q14& q24& q34& q44\end{array}\right]$

Meanwhile, also for each some v, define the tolerance of a displacement error:

v ^TQv=q ₁₁x ²+2q ₁₂xy+2q ₁₃xz+2q ₁₄x+q ₂₂y ²+2q ₂₃yz+2q ₂₄y+q ₃₃z ²+2q ₃₄z+q ₄₄

If some v moves to v ', v ' has had certain distance with the adjacent surface of mobile front some v, supposes that p is a plane ax+by+cz+d=0 adjacent with v, note p=[a, b, c, d] ^t, v ' is p to the distance of p ^tv '.Adopt the quadratic sum ∑ (p of these distances ^tv ') ², as error criterion, when v does not move, v=v ', has

v ^TQv=∑(p ^Tv′) ²=∑(v′ ^Tp)(p ^Tv′)=v′ ^T(∑pp ^T)v′

∴ Q=∑ pp ^t, wherein ${\mathrm{pp}}^T=\left[\begin{array}{cccc}{a}^2& \mathrm{ab}& \mathrm{ac}& \mathrm{ad}\\ \mathrm{ab}& b^2& \mathrm{bc}& \mathrm{bd}\\ \mathrm{ac}& \mathrm{bc}& c^2& \mathrm{cd}\\ \mathrm{ad}& \mathrm{bd}& \mathrm{cd}& d^2\end{array}\right]$

Visible, the initial error matrix Q of each point is determined by the plane at its adjacent triangle place.By the Q of each point, just can calculate its deflation error for each limit.Suppose limit (v1, the v2) → v ' that will shrink, the error matrix that defines simply v ' is Q '=Q1+Q2, and the error (contraction cost) that its shrinkage operation produces is ε (v ')=v ' ^tq ' v ', wherein makes the v of error minimum, is exactly the optimum position that this edge is shrunk to new point.According to least square method, error is asked to local derviation, make it equal 0:

$\left[\begin{array}{cccc}q11& q12& q13& q14\\ q12& q22& q23& q24\\ q13& q23& q33& q34\\ 0& 0& 0& 1\end{array}\right]v^{\&prime;}=\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]$

If this equation has solution, i.e. first matrix's reversibility, the position of v ' is:

$v^{\&prime;}={\left[\begin{array}{cccc}q11& q12& q13& q14\\ q12& q22& q23& q24\\ q13& q23& q33& q34\\ 0& 0& 0& 1\end{array}\right]}^{-1}\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]$

If without solution, from v1, v2, or select a point that makes deflation error minimum between the mid point of v1, v2 line.

Visible, utilize second order error matrix, can, for each cost that can carry out the limit calculating shrinkage operation of shrinkage operation, obtain the optimum position that this edge shrinks.If all choose that limit of Least-cost at every turn, shrink, the model causing changes minimum, has reached the object that has kept master pattern profile.

Compared with prior art, the three-dimensional geometric shapes short-cut method diabolo based on triangle contraction of the present invention carries out condition judgment, and carries out folding shrinking according to priority level, has optimized simplification process, and has had higher precision, preserves better original figure.

The three-dimensional geometric shapes short-cut method based on the triangle contraction above embodiment of the present invention being provided, be described in detail, in the present invention, applied specific case principle of the present invention and embodiment are set forth, the explanation of above embodiment is just for helping to understand method of the present invention and core concept thereof; , for one of ordinary skill in the art, according to thought of the present invention, all will change in specific embodiments and applications, in sum, this description should not be construed as limitation of the present invention meanwhile.

Claims (2)

1. the three-dimensional geometric shapes short-cut method based on triangle contraction, is characterized in that, comprises the following steps: first, the diabolo that imposes a condition judges, the triangle T only satisfying condition is just carried out shrinkage operation; Secondly, diabolo carries out folding shrinking; Wherein, the priority that triangle collapse shrinks represents by weights L=ab, and L is less, more first shrinks this triangle, and factor b is leg-of-mutton area, and each leg-of-mutton normal vector of establishing in triangular plate Si is n _k, center is x _k, area is A _k, so, the mean level of the sea M that the plane that the normal vector n of definition and center x construct is defined as triangular plate Si is:

N=(∑A _kn _k)/∑A _k，n=N/|N|，x=(∑x _kA _k)/∑A _k；

Factor a: diabolo T, ask relevant leg-of-mutton triangular plate Si, then calculate the mean level of the sea M of Si, its normal vector is the each point V that asks T _idistance d to Si _iget maximum as a, that is: d _i=| n (V _i-x) |, a=max (d ₁, d ₂, d ₃);

Determine that constriction point is taken at the d obtaining in calculated factor a _imaximum summit V _i, using mean level of the sea M as with V _iadjacent plane, utilizes second order error method to obtain constriction point.

2. the three-dimensional geometric shapes short-cut method based on triangle contraction as claimed in claim 1, is characterized in that, the condition in described determining step comprises: only having at most a summit is border vertices; Associated triangle ring C is aperiodic; Each adjacent triangle T _niin, by the valence mumber on the shared summit of T, be not equal to 4.

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