CN102270356A - Construction method of control cage based on comparison method - Google Patents

Abstract

The embodiment of the invention discloses a construction method of a control cage based on a comparison method, comprising the steps of: (1) inputting a three-dimension gridding model; (2) calculating Q matrices of all the peaks in the three-dimension gridding model; (3) selecting all the edges to form peak pairs; (4) calculating the folding peaks and errors of the peak pairs based on the comparison method; (5) placing the peak pairs in a pile according to the size of the errors, wherein the smallest error is in the top; (6) removing the peak pair with the smallest error; (7) updating the peak pairs adjacent to the new peak, and returning to the step (4); and (8) generating a final model. According to the embodiment of the invention, the construction method which realizes the deformation by use of the control cage has the main advantages of simpleness in control and high calculating speed.

Description

A kind of building method of the control cage based on the method for unrealistically comparing

Technical field

The present invention relates to the Computer Processing technical field, relate in particular to a kind of building method of the control cage based on the method for unrealistically comparing.

Background technology

At present, in computer graphics, many computer graphics application are all used complicated, and the model with high degree of detail information reaches a kind of sense of reality.Therefore the structure of this model often needs a very high resolution.Yet, to manipulate intensive model directly and relate to tediously long operation, computing cost is very big.An existing space-like deformation method is controlled the distortion of master mould by a simplified model (being called the control cage) that encases master mould.

The target of control cage arrangement is triangle grid model of input, exports a grid that encases master mould of having simplified.Shortcut calculation before many can satisfy some demands aspect simplification, but in the requirement that encases, not fully up to expectations.

In recent years, the problem of curved surface simplification and multiresolution modeling more and more is subjected to people's attention, and some different shortcut calculations are suggested, and these algorithms can be classified as following three classes:

The first kind: summit extraction method

This method is to select a summit to simplify iteratively, removes all of its neighbor face on this summit, then the result to obtaining, trigonometric ratio again.

Second class: summit aggregation method

This method can be handled polygon model input arbitrarily, constructs a bounding box around master pattern, and is separated into grid.In each grid the inside, all summits that grid comprises are converged into a summit, and the dough sheet of model also changes accordingly.This process is very fast, and still, the size of grid has embodied the error boundary of a geometry, and the mass ratio of output is lower, and, because the number of dough sheet is determined that by concrete grid granularity also very difficulty is constructed the approximate model with concrete dough sheet number.

The 3rd class: the edge contraction method of iteration

The edge contraction method of many algorithms by iteration, simplification that can implementation model, the difference of these algorithm essence is, selects which bar limit to reject, and rejects by continuous execution limit, can simplify the data of grid.

More than these three class methods in efficient with above the quality, all can not satisfy control cage arrangement demand fully.The summit extraction method has strict requirement to the topological sum geometry of model; Summit aggregation method, speed are very fast, but the effect quality after simplifying is very low; The edge contraction method can not be supported to assemble.These methods are the similarity of concern and master mould usually, need encase and ignored.

Summary of the invention

Method of the present invention is to set up a simple more structure, and this structure has summit still less, operates original intensive model by operating this simple structure then.So-called control cage, the structure that can be surrounded original intensive model is used for realizing distortion exactly.

For reaching above-mentioned purpose, the technical solution used in the present invention is: a kind of control cage arrangement method based on the method for unrealistically comparing, and this method comprises with the lower part:

The structure of control cage mainly comprises following step:

(1) input three-dimensional grid model;

(2) calculate the Q matrix on all summits;

(3) it is right to select all limits to constitute the summit;

(4) summit is folded summit and error to calculating based on the method for unrealistically comparing;

(5) according to error size the summit to being placed in the heap least error top set.

(6) it is right to remove the summit of least error;

(7) renewal is right with the summit of new summit adjacency, forwards (4) to;

(8) generate final mask.

The Q matrix on all summits in the described calculating three-dimensional grid model comprises:

$Q=\underset{p\∈\mathrm{planes}\left(v\right)}{\mathrm{\Σ}}{k}_p$

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

P=[a wherein, b, c, d] ^TBe the face adjacent, by ac+by+cz+d=0 and a with vertex v ²+ b ²+ c ²=1 determines, uses Q _iRepresent and vertex v _iCorresponding Q matrix.

Described the summit is comprised calculate folding summit and error based on the method for unrealistically comparing:

Every limit (v to master mould _i, v _j), if be folded into a bit The following calculating of corresponding error that causes:

$E\left(\stackrel{\‾}{v}\right)={\stackrel{\‾}{v}}^t(Q_i+Q_j)\stackrel{\‾}{v}$

As limit (v _i, v _j) be folded into point

Just directly use

The Q matrix of representing new point; Originally and v _iOr v _jThe point that links to each other, become and

Link to each other, and remove the coincidence limit.

In embodiments of the present invention, use the control cage to realize that the major advantage of distortion is that control is simple, fast operation.The model of a sealing of operation, for example, triangle gridding needs quite little computing cost, only to need the element of calculation control cage be the linear combination of weight to calculate good parameter coordinate in advance because change these summits.Because these advantages, many distortion select to use the control cage, although it is very complicated to control cage sometimes.

Description of drawings

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

Fig. 1 is the process flow diagram based on the control cage arrangement method of the method for unrealistically comparing in the embodiment of the invention;

Fig. 2 is the folding synoptic diagram based on the control cage arrangement method of the method for unrealistically comparing in the embodiment of the invention;

Fig. 3 is the experiment effect figure based on the control cage arrangement method of the method for unrealistically comparing in the embodiment of the invention.

Embodiment

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

Fig. 1 shows the process flow diagram of a kind of control cage arrangement method based on the method for unrealistically comparing in the embodiment of the invention, comprises as follows:

S101: input three-dimensional grid model;

S102: the Q matrix that calculates all summits in the three-dimensional grid model;

S103: it is right to select all limits to constitute the summit;

S104: the summit is folded summit and error to calculating based on the method for unrealistically comparing;

S105: according to error size the summit to being placed in the heap least error top set;

S106: the summit that removes least error is right;

S107: it is right to upgrade with the summit of new summit adjacency, forwards S104 to;

S108: generate final mask.

At first import three-dimensional grid model, calculate the Q matrix on all summits then, the computing method that Q is ordered are as follows:

a ²+ b ²+ c ²=1 determines.

Use Q _iRepresent and vertex v _iCorresponding Q matrix.So to every limit (v of master mould _i, v _j), if be folded into a bit

The corresponding error that causes can followingly be calculated:

$E\left(\stackrel{\‾}{v}\right)={\stackrel{\‾}{v}}^t(Q_i+Q_j)\stackrel{\‾}{v}---\left(2\right)$

As limit (v _i, v _j) be folded into point

Just directly use

The Q matrix of representing new point.Originally and v _iOr v _jThe point that links to each other, become and

Link to each other, and remove the coincidence limit.With this limit of constantly reducing error minimum in the model, simplify.

In order to construct the control cage that encases master mould, how need to think better of selected point

Here adopt the method for unrealistically comparing to seek, to certain bar limit (v _s, v _e), it is as follows to seek flow process:

{ initialization error emin is infinitely great, and vmin is empty.

To all with v _sLimit (v for the summit _s, v _i)

To all with v _eFace (v for the summit _e, v _j, v _k)

Vtmp=limit (v _s, v _i) and face (v _e, v _j, v _k) intersection point

Etmp=uses formula (2) to calculate vtmp with respect to limit (v _s, v _e) error

If etmp is less than emin{

Whether check vtmp always and limit (v _s, v _e) outside the face that links to each other

If not, continue to look for next face (v _e, v _j, v _k)

If vtmp always and limit (v _s, v _e) face that links to each other outer

Vmin=vtmp is set; Emin=etmp;

To all with v _eLimit (v for the summit _e, v _i)

To all with v _sFace (v for the summit _s, v _j, v _k)

If limit (v _e, v _i) and face (v _s, v _j, v _k) considered that just skipped following step, continue to seek next face (v _s, v _j, v _k).

Vtmp=limit (v _e, v _i) and face (v _s, v _j, v _k) intersection point

Etmp=uses formula (2) to calculate vtmp with respect to limit (v _s, v _e) error

If etmp is less than emin{

Whether check vtmp always and limit (v _s, v _e) outside the face that links to each other

If not, continue to look for next face (v _s, v _j, v _k)

If vtmp always and limit (v _s, v _e) face that links to each other outer

Vmin=vtmp is set; Emin=etmp;

Check vmin be sky

Return vmin and emin}

Otherwise

Return a far point, and a very big error amount.}

}

Because the process of top searching point is to seek intersection point constantly, and their error of comparison, it is big to give up error, and it is little to get error, so, this method is called the method for unrealistically comparing.

As shown in Figure 2, the summit that straight line connected of dash area is to v _iAnd v _j, be that the summit that will fold is right,

Be the summit that is used for replacing, after folding, the dough sheet of dash area is eliminated, originally with v _iAnd v _jAdjacent dough sheet is also followed again Adjacent.

Upgrade all of its neighbor limit on new summit then, and calculate and to be used for the summit and the consequent error of replacing next time, promptly enter next iteration.So iteration is gone down until producing final model.Fig. 3 specifies three kinds of different top to count respectively to a stick model (palpus of octopus model), uses this method to construct the experimental result of control cage.

Because the method for unrealistically comparing is calculated new point and is depended on dough sheet around the limit, after we eliminate a limit, except new point and error need be calculated in the limit of new generation, the limit that links to each other with new limit owing to its on every side dough sheet change, so also be subjected to influence.

Such problem is also arranged in QEM, and new point produces, and causes that new limit produces, and produces new dough sheet, equally so the limit that links to each other with new limit also is affected.But,, do not mind whether intersecting,, but continue to allow it based on initial Q matrix so it does not recomputate the error on the limit that links to each other with new limit with model because the QEM purpose is to approach master mould.

But in control cage arrangement process, similar except needs with master mould, also need to remain on the model outside.And control cage under the prerequisite that remains on the model outside, and approximate model is good more, and degree of approximation still can be weighed by QEM.Produce as new limit, the dough sheet that links to each other with it will change, and therefore the error on the limit that links to each other with it may also can change, and need recomputate.

More than to what the embodiment of the invention provided, be described in detail, used specific case herein principle of the present invention and embodiment set forth, the explanation of above embodiment just is used for help understanding method of the present invention and core concept thereof; Simultaneously, for one of ordinary skill in the art, according to thought of the present invention, the part that all can change in specific embodiments and applications, in sum, this description should not be construed as limitation of the present invention.

Claims (3)

1. building method based on the control cage of the method for unrealistically comparing is characterized in that described method comprises:

(1) input three-dimensional grid model;

(2) the Q matrix on all summits in the calculating three-dimensional grid model;

(3) it is right to select all limits to constitute the summit;

(4) summit is folded summit and error to calculating based on the method for unrealistically comparing;

(5) according to error size the summit to being placed in the heap least error top set;

(6) it is right to remove the summit of least error;

(7) renewal is right with the summit of new summit adjacency, forwards (4) to;

(8) generate final mask.

2. the method for claim 1 is characterized in that, the Q matrix on all summits in the described calculating three-dimensional grid model comprises:

$Q=\underset{p\∈\mathrm{planes}\left(v\right)}{\mathrm{\Σ}}{k}_p$

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

P=[a wherein, b, c, d] ^TBe the face adjacent, by ac+by+cz+d=0 and a with vertex v ²+ b ²+ c ²=1 determines, uses Q _iRepresent and vertex v _iCorresponding Q matrix.

3. method as claimed in claim 2 is characterized in that, described the summit is comprised calculate folding summit and error based on the method for unrealistically comparing:

Every limit (v to master mould _i, v _j), if be folded into a bit

The following calculating of corresponding error that causes:

$E\left(\stackrel{\‾}{v}\right)={\stackrel{\‾}{v}}^t(Q_i+Q_j)\stackrel{\‾}{v}$

As limit (v _i, v _j) be folded into point

Just directly use

The Q matrix of representing new point; Originally and v _iOr v _jThe point that links to each other, become and

Link to each other, and remove the coincidence limit.

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