JP4151332B2 - 3D model editing apparatus and computer program - Google Patents

Description

【００３３】
図４に示すように、処理対象である頂点ｉの一次近傍は、頂点ｉを共有するポリゴン群である。つまり、頂点群Ｎi は、頂点ｉを共有するポリゴンの他の頂点の集合である。
【００３４】
上の（１）式は、処理対象の頂点ｉが、ポリラインＰＬＴを構成する頂点群Ｌに含まれない場合、つまり、頂点ｉがポリラインＰＬＴ上の点でない場合に適用される。（１）式において、頂点ｉの座標値Ｐi は、その一次近傍の頂点群Ｎi に含まれる頂点ｊの座標値Ｐj と、それら２つの頂点ｉ，ｊ間の重み係数ｗijとの積の総和によって更新される。重み係数ｗijとして、例えば、２つの頂点ｉ，ｊ間の距離に逆比例し、係数ｗijの総和が１となる値が用いられる。
【００３５】
したがって、この場合には、頂点ｉの一次近傍の頂点群Ｎi に含まれる全ての頂点ｊの座標値Ｐj に基づいて更新される。（１）式による処理が、本発明の第２の平滑化手段に相当する。
【００３６】
これに対して、上の（２）式は、頂点ｉが頂点群Ｌに含まれる場合、つまり、頂点ｉがポリラインＰＬＴ上の点である場合に適用される。（２）式において、頂点ｉの座標値Ｐi は、その一次近傍の頂点群Ｎi に含まれ且つ頂点群Ｌに含まれる各頂点ｊの座標値Ｐj と、それら２つの頂点ｉ，ｊ間の重み係数ｗijとの積の総和によって更新される。
【００３７】
したがって、この場合には、頂点ｉの一次近傍の頂点群Ｎi のうち、頂点群Ｌに含まれる頂点ｊのみが用いられ、頂点群Ｌに含まれない頂点ｊは用いられない。（２）式による処理が、本発明の第１の平滑化手段に相当する。これによって、処理対象の頂点ｉは、常に頂点群Ｌに沿って移動する。頂点群Ｌは設定されたポリラインＰＬＴであるので、処理を行った後もポリラインＰＬＴが維持される。なお、頂点ｉが頂点群Ｌに含まれるか否か、つまり（２）式または（１）式のいずれを適用するかは、モデリングプログラムＰＭが自動的に判断して選択する。
〔２Ｄライン拘束平滑化処理〕
図５および図６は２Ｄライン拘束平滑化処理を説明するための図である。
【００３８】
２Ｄライン拘束平滑化処理では、次の（３）（４）式によって、各頂点の座標値が更新される。
【００３９】
【数２】

【００４０】
ここで、Ｐにハットを付した座標値Ｐi が、２Ｄライン拘束平滑化処理で求められる新しい座標値である。
上の（３）式は、処理対象の頂点ｉが、ポリラインＰＬＴを構成する頂点群Ｌに含まれない場合を示し、この場合には、上の（１）式と同じ値となる。つまり、処理対象の頂点ｉが頂点群Ｌに含まれない場合には、ノーマル平滑化処理と同じ処理が行われる。
【００４１】
上の（４）式は、頂点ｉが頂点群Ｌに含まれる場合に適用される。（４）式で示されるように、頂点ｉが頂点群Ｌに含まれる場合には、そうでない場合に対して補正項ｄj （ハット付き）が加えられる。補正項ｄj の演算に際して、画像ＦＴ上に設定された２次元のポリラインＰＬＳが用いられる。設定されたポリラインＰＬＳと、ポリゴンメッシュＰＭ上に設定された３次元のポリラインＰＬＴとの位置関係が、画像ＦＴとポリゴンメッシュＰＭとの関係から求められる。ポリラインＰＬＴ上の頂点ｉが２次元のポリラインＰＬＳ上に投影されるような拘束を与えた状態で、平滑化の処理が行われる。２次元のポリラインＰＬＳとして、実際にはそのうちの頂点ｉの近傍に存在するセグメント（線分）Ｅi が用いられる。
【００４２】
すなわち、図５および図６に示すように、複数の画像ＦＴ１，２上にそれぞれ設定されたポリラインＰＬＳのうち、処理対象である頂点ｉを投影したときの画像上の距離ｂが設定された閾値ｔよりも小さい位置にあるセグメントＥｉ が用いられる。そのようなセグメントＥｉ をそれぞれ含み、且つ各画像ＦＴ１，ＦＴ２の視点位置Ｏ０ ，Ｏ１ を含む平面Ｓ０ ，Ｓ１ が定義される。頂点ｉの位置から各平面Ｓ０ ，Ｓ１ までの距離ｄ１ ，ｄ２ （ハット付き），を求め、それらのベクトルを座標値Ｐｉ に加算する。
【００４３】
これによって、頂点ｉの位置が、関連するポリラインＰＬＳ上の各平面Ｓ上に強制的に乗るように補正される。結果として、各画像ＦＴに設定されたポリラインＰＬＳによる拘束条件を満たす点Ｐs に収束する。
【００４４】
上の（４）式による処理が、本発明の第１の平滑化手段に相当し、且つ請求項２に記載の処理に相当する。これによって、ノーマル平滑化処理の場合と同様、処理対象の頂点ｉが常に頂点群Ｌに沿って移動し、処理を行った後もポリラインＰＬＴが維持される。
〔直線化平滑化処理〕
図７は直線化平滑化処理を説明するための図である。
【００４５】
直線化平滑化処理では、次の（５）（６）式によって、各頂点の座標値が更新される。
【００４６】
【数３】

【００４７】
ここで、Ｐにチルダを付した座標値Ｐi が、直線化平滑化処理で求められる新しい座標値である。
上の（５）式は、処理対象の頂点ｉが、ポリラインＰＬＴを構成する頂点群Ｌに含まれない場合を示し、この場合にはノーマル平滑化処理と同じ処理が行われ、上の（１）式と同じ値となる。
【００４８】
上の（６）式は、頂点ｉが頂点群Ｌに含まれる場合に適用される。（６）式で示されるように、頂点ｉが頂点群Ｌに含まれる場合には、そうでない場合に対して補正項ｄj （チルダ付き）が加えられる。補正項ｄj の演算に際して、図７に示すように、３次元のポリラインＰＬＴ上の頂点群Ｌに対してフィッティングされた直線Ｌ’が用いられる。頂点群Ｌに対して直線をフィッティングさせる処理として、公知の方法を用いることができ、自動的に行うことが可能である。フィッティングによって、頂点群Ｌを近似した仮想の直線Ｌ’が得られる。
【００４９】
各頂点ｉは、直線Ｌ’上に射影して乗せられる。すなわち、３次元のポリライン（エッジ部）ＰＬＴに属する頂点ｉが、ポリラインＰＬＴ上の頂点群Ｌに近似する直線Ｌ’上に配置されるような拘束を与えた状態で、各頂点ｉの平滑化が行われる。これにより、エッジ部に属する頂点ｉが直線化され、適切な位置の直線Ｌ’として得られる。
【００５０】
なお、直線化平滑化処理を１回行うことにより、頂点ｉは直線Ｌ’上に乗ることとなるので、２回目以降は直線Ｌ’上を移動するだけとなる。図７に示すように、補正項ｄj （チルダ付き）は、頂点ｉから直線Ｌ’に向かう最短の距離ベクトルである。
【００５１】
上の（６）式による処理が、本発明の第１の平滑化手段に相当し、且つ請求項３に記載の処理に相当する。これによって、処理対象の頂点ｉが常に頂点群Ｌに沿って移動し、処理を行った後もポリラインＰＬＴが維持される。
〔アンチ収縮処理〕
図８は頂点ｉがエッジ部に属する場合のアンチ収縮処理を説明するための図、図９は頂点ｉがエッジ部に属しない場合のアンチ収縮処理を説明するための図、図１０はアンチ収縮処理による重心位置ベクトルまたは中点の移動を説明する図である。
【００５２】
アンチ収縮処理がオンになっている場合には、以下に説明するアンチ収縮処理が実行される。アンチ収縮処理は、各平滑化処理が１回行われるごと、つまり頂点ｉの座標値Ｐが更新されるごとに実行される。
【００５３】
アンチ収縮処理では、次の（７）（８）（９）式によって、各頂点の座標値が更新される。
【００５４】
【数４】

【００５５】
ここで、Ｐにバーを付した座標値Ｐi が、アンチ収縮処理で求められる新しい座標値である。新しい座標値Ｐi は、元の座標値に対して、補正項ｄi （バー付き）が加えられる。補正項ｄi は、処理対象の頂点ｉがポリラインＰＬＴを構成する頂点群Ｌに含まれる場合には（８）式で計算され、含まれない場合には（９）式で計算される。
【００５６】
すなわち、処理対象の頂点ｉが頂点群Ｌに含まれる場合には、（８）式、図８、および図１０に示されるように、頂点ｉの一次近傍を構成する全てのポリゴンＰＧの位置変化に関連して、頂点ｉが移動する。この場合の頂点ｉの移動量は、各ポリゴンＰＧの面積の重心ｇの法線方向の移動量の平均に相当する量となる。つまり、平滑化処理によって移動した一次近傍のポリゴンＰＧの重心位置を元に戻すような処理が行われる。これによって、平滑化処理によって収縮した分が戻され、元の体積が保存される。
【００５７】
処理対象の頂点ｉが頂点群Ｌに含まれない場合には、（９）式、図９、および図１０に示されるように、頂点ｉの一次近傍を構成するポリゴンＰＧの頂点のうち、頂点群Ｌに含まれる頂点のみを用いて、頂点ｉの移動量および移動方向が求められる。この場合の頂点ｉの移動量は、各ポリゴンＰＧの重心によるのではなく、頂点群Ｌに含まれるポリゴンＰＧの頂点の中点ｈの法線方向の移動量の平均に相当する量となる。つまり、平滑化処理によって移動したポリラインＰＬＴ上のポリゴンＰＧの頂点の中点位置を元に戻すような処理が行われる。これは、平滑化処理の際に、周囲の全ての頂点を用いずに頂点群Ｌ上の頂点のみを用いて平滑化処理を行っているのであるから、アンチ収縮処理により戻す際にも、頂点群Ｌ上の頂点のみを用いて戻すのが望ましいからである。
【００５８】
これによって、平滑化処理により収縮した分が戻され、元の体積が保存される。しかも、エッジ部に属する頂点ｉに対して行われた平滑化処理に対しては、エッジ部に属する頂点のみを用いてアンチ収縮処理が行われることとなり、アンチ収縮処理による歪みが生じ難い。因みに、従来のアンチ収縮処理では局部的な歪みが生じ易い。
【００５９】
また、アンチ収縮処理が平滑化処理によって収縮した分に対して、元の方向に戻るのではなく、法線方向に戻るので、ポリゴンメッシュＰＭの各ポリゴンＰＧの大きさが揃う方向にポリゴンＰＧが移動することとなる。その結果、ポリゴンＰＧとポリゴンＰＧとのなす角度が浅くなっていき、平滑化処理による効果がより一層発揮されることとなる。
【００６０】
なお、アンチ収縮処理を行うタイミングとして、平滑化処理を１回行うごとに実行してもよいが、平滑化処理をｎ回行うごとに、それまでの収縮分を戻すためのアンチ収縮処理を１回でまとめて行うようにしてもよい。
【００６１】
上の（８）（９）式による演算は、平滑化処理の前後における３次元モデル（３次元データ）の各部の局所体積の変化を評価する処理に相当する。また、（７）式による演算は、平滑化処理の前後における３次元モデルの各部の局所体積の変化が少なくなるように平滑化処理後のポリゴンＰＧの各頂点の座標値Ｐｉ を補正する処理に相当する。これらは請求項４に記載の処理に相当する。
【００６２】
上述の実施形態によると、エッジ部として特定された頂点とそうでない頂点とを区別して平滑化処理が行われ、その結果、３次元モデルのエッジが維持され、しかも滑らかな３次元形状を得ることができる。
【００６３】
上の実施形態において、対象物の種類、編集装置１の全体または各部の構成、形状、個数、処理の内容および順序などは、本発明の趣旨に沿って適宜変更することができる。
【００６４】
【発明の効果】
本発明によると、３次元モデルのエッジが維持され、しかも滑らかな３次元形状を得ることができる。
【図面の簡単な説明】
【図１】本発明の実施形態に係る３次元モデルの編集装置のブロック図である。
【図２】ポリラインを説明するための図である。
【図３】平滑化処理の種類を選択するための画面の例を示す図である。
【図４】ノーマル平滑化処理を説明するための図である。
【図５】２Ｄライン拘束平滑化処理を説明するための図である。
【図６】２Ｄライン拘束平滑化処理を説明するための図である。
【図７】直線化平滑化処理を説明するための図である。
【図８】頂点がエッジ部に属する場合のアンチ収縮処理を説明するための図である。
【図９】 頂点がエッジ部に属しない場合のアンチ収縮処理を説明するための図である。
【図１０】アンチ収縮処理による重心位置ベクトルの移動を説明する図である。
【符号の説明】
１ 編集装置
１０ 装置本体（エッジ部を指定する手段、第１の平滑化手段、第２の平滑化手段、選択手段、エッジラインを指定する手段、関連付ける手段、評価する手段、座標値を補正する手段）
ＭＬ ３次元モデル
ＤＴ ３次元データ（３次元モデル）
ＦＴ 画像
ＰＬＴ ３次元のポリライン（エッジ部）
ＰＬＳ ２次元のポリライン（エッジライン）
ＰＧ ポリゴン
ｉ 頂点[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a three-dimensional model editing apparatus and a computer program, and in particular, is used to perform smoothing so that edges of a three-dimensional model are maintained in a clear state.
[0002]
[Prior art]
Conventionally, in the field of CG (Computer Graphics) or industrial design, a three-dimensional shape input device that optically three-dimensionally measures an object that is an object is often used. The three-dimensional shape input device irradiates a target object with a laser or pattern light and captures the reflected light on the surface of the object with a sensor to accurately sample and input the three-dimensional shape of the object. As a result, three-dimensional data consisting of a three-dimensional point group is obtained on the surface of the object, and based on this, three-dimensional data (three-dimensional model) consisting of a polygon mesh is generated.
[0003]
[Problems to be solved by the invention]
However, when rendering display of the three-dimensional data obtained as described above is performed, there is a problem that the edge portion becomes unclear.
[0004]
One of the reasons why this problem occurs is that unnatural unevenness around the edge blurs the edge due to the local noise included in the three-dimensional data. Therefore, to reduce local noise, as in L. Kobbelt, S. Campagna, J. Vorsatz, and H. Seidel, "Interactive Mu1ti-Resolution Modeling on Arbitrary Meshes," Proc. SIGGRAPH '98, 1998, Generally, a smoothing method is used in which vertex coordinates are iteratively replaced with a weighted average of neighboring vertex coordinates.
[0005]
However, according to such a smoothing technique, the curvature is diffused, so that the edge is rounded. That is, since the edge information has a high frequency, the edge is scraped off along with the smoothing. In addition, if the repetition is repeated to increase the degree of smoothing, the volume shrinks. A method for preventing volume shrinkage is proposed in US Pat. No. 5,506,947. However, in this case, since the local volume is not evaluated, the degree of correction needs to be set by the user.
[0006]
Another reason is that the three-dimensional shape of the object is measured discretely. Since the measurement points are determined by the relative positional relationship between the object and the three-dimensional shape input device, the measurement points are not arranged along the edges, and the edges are scraped off.
[0007]
SUMMARY An advantage of some aspects of the invention is that it provides a three-dimensional model editing apparatus and a computer program capable of obtaining a smooth three-dimensional shape while maintaining edges as much as possible.
[0008]
Editing apparatus according to the present invention is a editing apparatus of a three-dimensional model composed of polygon mesh, and means for designating the edge portion on the three-dimensional model, the edge portion designated polygons of said three-dimensional model It belongs each vertex is processed, the coordinate values of the apexes of the processed, performs an operation using only the vertices belonging to the edge portion a and and the specified vertices near the apex of the processed, each processed The first smoothing means for performing smoothing by moving the vertices and updating the coordinate values thereof, and processing each of the vertices of the polygon of the three-dimensional model, and the coordinate values of the vertices of each processing target The second smoothing means for performing smoothing by performing calculations different from those of the first smoothing means, moving the vertices of the respective processing targets and updating the coordinate values thereof, and If belonging to an edge portion with vertices specified by selecting the first smoothing unit, if not belonging to the edge portion and a selection means for selecting the second smoothing means.
[0009]
Further, a two-dimensional image in which the correspondence between the coordinate values of each vertex of the polygon of the three-dimensional model and the coordinates of each pixel on the two-dimensional image is known, and means for designating an edge line on such a two-dimensional image And a means for associating the edge line specified on the two-dimensional image with the edge portion specified on the three-dimensional model, wherein the first smoothing means the calculation for giving restraint as vertices are projected onto the edge line coordinate value of the apex may be configured such intends row belong.
[0010]
Further, the first smoothing means is configured to perform smoothing by giving a constraint that a vertex belonging to the edge portion is arranged on a straight line that approximates the edge portion, and the vertex to be smoothed May be configured to select the first smoothing means when it belongs to the designated edge portion, and to select the second smoothing means when it does not belong to the edge portion.
[0011]
Further, means for evaluating a change in local volume of each part of the three-dimensional model before and after smoothing by the first smoothing means or the second smoothing means, and the three-dimensional model before and after smoothing Means for correcting the coordinate value of each vertex of the smoothed polygon so as to reduce the change in the local volume of each part may be provided.
[0012]
DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 is a block diagram of a three-dimensional model editing apparatus 1 according to an embodiment of the present invention.
[0013]
In FIG. 1, an editing apparatus 1 includes an apparatus main body 10, a magnetic disk device 11, a medium drive device 12, a display device 13, a keyboard 14, a mouse 15, and the like.
[0014]
The apparatus body 10 includes a CPU, a RAM, a ROM, a video RAM, an input / output port, various controllers, various interfaces, and the like. Various functions described below are realized by the CPU executing programs stored in the RAM and ROM.
[0015]
The magnetic disk device 11 includes an OS (Operating System), a modeling program (three-dimensional editing program) PR for generating a three-dimensional model (three-dimensional shape model) ML or performing texture mapping, a program for inputting data, Other programs, input or generated three-dimensional data (three-dimensional shape data) DT, image (two-dimensional image data) FT, generated three-dimensional model ML, other data, and the like are stored. These programs and data are loaded into the RAM of the apparatus main body 10 at appropriate times.
[0016]
The modeling program PR includes initialization processing, edge designation processing, normal smoothing processing, 2D line constraint smoothing processing, linearization smoothing processing, selection processing, anti-shrinkage processing, mapping processing, and other processing. The program is included.
[0017]
The medium drive device 12 accesses a semiconductor memory HM such as a CD-ROM (CD), a floppy disk FD, a magneto-optical disk, a compact flash (registered trademark), and other recording media, and reads / writes data or programs. An appropriate drive device is used according to the type of the recording medium. The modeling program PR described above can also be installed from these recording media. The three-dimensional data DT and the image FT can also be input via a recording medium.
[0018]
The display surface HG of the display device 13 displays the various data described above, the three-dimensional data DT, the image FT, the image of the processing process by the modeling program PR, the generated three-dimensional model ML, and other images or data. Is done.
[0019]
The keyboard 14 and the mouse 15 are used for the user to make various designations for the image FT and the three-dimensional data DT displayed on the display device 13, and input various data or commands to the apparatus main body 10. Used to give
[0020]
The apparatus main body 10 is connected to a digital camera DC for photographing an object from various viewpoints and inputting an image FT. In addition, a three-dimensional measuring device TC is connected for photographing the object and inputting the three-dimensional data DT. The three-dimensional measuring device TC measures the three-dimensional data DT of the object in a non-contact manner by, for example, a light cutting method. The three-dimensional measuring apparatus TC measures an object placed on a turntable (not shown) and inputs three-dimensional data DT to the apparatus main body 10. The three-dimensional data DT is described in relative coordinates from the reference position of the three-dimensional measuring device TC.
[0021]
In addition, instead of the three-dimensional data DT, data that is the basis for generating the three-dimensional data DT may be output from the three-dimensional measuring device TC, and the three-dimensional data DT may be obtained by calculation by the apparatus body 10. . The digital camera DC and the three-dimensional measuring device TC are provided with position and orientation sensors that detect the position and orientation and output position and orientation information. The positional relationship between the digital camera DC, the three-dimensional measuring device TC, and the turntable is calibrated in advance based on the position and orientation information, stored in the magnetic disk device 11, and on the image FT acquired by photographing or measurement. The correspondence between the coordinates of each pixel and the position information of each vertex of the polygon mesh PM based on the three-dimensional data DT is known.
[0022]
It is also possible to acquire the three-dimensional data DT and the image FT by the three-dimensional measuring device TC itself. In that case, the positional relationship between the three-dimensional data DT and the image FT is defined by the internal parameters of the three-dimensional measuring apparatus TC, or a projection matrix is generated.
[0023]
Next, functions of the editing apparatus 1 will be described.
FIG. 2 is a diagram for explaining the polylines PLS and PLT.
First, a data input program is started, and position and orientation information that has been calibrated in advance is read from the magnetic disk device 11 into the memory of the device body 10. Then, the three-dimensional measuring device TC, the digital camera DC, and the turntable are controlled, and an object is photographed or measured from various angles, and the three-dimensional data DT (three-dimensional model ML) and the image FT are stored in the apparatus main body 10. Enter and store in memory.
[0024]
The input three-dimensional data DT is converted into a coordinate system based on a predetermined position based on the rotation angle of the turntable at the time of shooting, and stored in the magnetic disk device 11. Further, the image FT is stored in the magnetic disk device 11 together with the optical parameter data. Each point of the three-dimensional data DT can be identified on the image FT by projecting it onto the image FT based on the position and orientation information attached to each image FT and the optical parameter data.
[0025]
The modeling program is activated, and the converted three-dimensional data DT, the corresponding image FT, and optical parameter data are read from the magnetic disk device 11 into the memory. On the three-dimensional data DT, a curve (polyline PLT) for specifying a portion to be handled as an edge portion is set. The curve is set by first setting a two-dimensional edge line (polyline PLS) on the image FT as shown in FIG. The polygon mesh PM of the three-dimensional data DT is projected on the image FT on which the polyline PLS is set. By connecting the vertices of the polygon PG projected in the vicinity of the polyline PLS of the image FT, mesh edges (edge portions) connected along the edges of the polygon PG are obtained. The obtained mesh edge is a three-dimensional polyline PLT.
[0026]
Further, the polygon PG is divided by the polyline PLS with respect to the polygon mesh PM projected on the image FT, and the edge of the divided polygon PG, that is, the line corresponding to the polyline PLS is set as the three-dimensional polyline PLT. May be. Further, instead of dividing the polygon PG, the three-dimensional polyline PLT may be set by moving the vertex of the polygon PG so as to coincide with the polyline PLS.
[0027]
As another method for setting the polyline PLT, a method for setting a wireline three-dimensional display image at an arbitrary viewpoint or a texture-mapped three-dimensional display image in the same way as setting the polyline PLS on the image FT But you can.
[0028]
A three-dimensional smoothing process is performed on the three-dimensional data DT in which the polyline PLT (edge portion) is set. The three-dimensional smoothing process is executed after selecting functions for two types of options, an option for the smoothing process and an option for the anti-shrinkage process. FIG. 3 shows an example of the screen HG1 for selection.
[0029]
As described above, there are three types of smoothing processing: normal smoothing processing, 2D line constrained smoothing processing, and linearization smoothing processing. In each smoothing process, the processing contents differ depending on whether or not the vertex to be processed is a point on the polyline (edge portion) PLT. When the vertex to be processed is a point on the polyline PLT, different processes are performed in each of the three types of smoothing processes. If the vertex to be processed is not a point on the polyline PLT, the same processing is performed in three types of smoothing processing.
[0030]
Select ON or OFF for the anti-shrink processing option. Therefore, any process is performed by a combination of the process selected from the three types of smoothing processes and the on / off of the option of the anti-shrink process. Next, each process will be described in detail.
[Normal smoothing processing]
FIG. 4 is a diagram for explaining normal smoothing processing.
[0031]
In the normal smoothing process, new coordinate values of each vertex are obtained and updated by the following equations (1) and (2). The number of updates k is performed as many times as specified by the user.
[0032]
[Expression 1]

[0033]
As shown in FIG. 4, the primary neighborhood of the vertex i to be processed is a polygon group sharing the vertex i. That is, the vertex group Ni is a set of other vertices of the polygon sharing the vertex i.
[0034]
The above equation (1) is applied when the vertex i to be processed is not included in the vertex group L constituting the polyline PLT, that is, when the vertex i is not a point on the polyline PLT. In equation (1), the coordinate value Pi of the vertex i is the sum of the products of the coordinate value Pj of the vertex j included in the vertex group Ni of the primary neighborhood and the weighting coefficient wij between the two vertices i and j. Updated. As the weighting coefficient wij, for example, a value that is inversely proportional to the distance between the two vertices i and j and the sum of the coefficients wij is 1 is used.
[0035]
Accordingly, in this case, updating is performed based on the coordinate values Pj of all the vertices j included in the vertex group Ni in the vicinity of the vertex i. The processing according to equation (1) corresponds to the second smoothing means of the present invention.
[0036]
On the other hand, the above equation (2) is applied when the vertex i is included in the vertex group L, that is, when the vertex i is a point on the polyline PLT. In the equation (2), the coordinate value Pi of the vertex i is included in the vertex group Ni of the primary neighborhood and the coordinate value Pj of each vertex j included in the vertex group L, and the weight between the two vertices i and j. It is updated by the sum of products with the coefficients wij.
[0037]
Therefore, in this case, only the vertex j included in the vertex group L among the vertex groups Ni in the primary neighborhood of the vertex i is used, and the vertex j not included in the vertex group L is not used. The processing according to equation (2) corresponds to the first smoothing means of the present invention. As a result, the vertex i to be processed always moves along the vertex group L. Since the vertex group L is the set polyline PLT, the polyline PLT is maintained even after processing. Whether or not the vertex i is included in the vertex group L, that is, whether the equation (2) or (1) is applied is automatically determined and selected by the modeling program PM.
[2D line constraint smoothing]
5 and 6 are diagrams for explaining the 2D line constrained smoothing process.
[0038]
In the 2D line constraint smoothing process, the coordinate values of the vertices are updated by the following equations (3) and (4).
[0039]
[Expression 2]

[0040]
Here, the coordinate value Pi obtained by adding a hat to P is a new coordinate value obtained by the 2D line constraint smoothing process.
The above equation (3) shows a case where the vertex i to be processed is not included in the vertex group L constituting the polyline PLT. In this case, the value is the same as the equation (1) above. That is, when the processing target vertex i is not included in the vertex group L, the same processing as the normal smoothing processing is performed.
[0041]
The above equation (4) is applied when the vertex i is included in the vertex group L. As shown by the equation (4), when the vertex i is included in the vertex group L, a correction term dj (with a hat) is added to the case where the vertex i is not. In calculating the correction term dj, a two-dimensional polyline PLS set on the image FT is used. The positional relationship between the set polyline PLS and the three-dimensional polyline PLT set on the polygon mesh PM is obtained from the relationship between the image FT and the polygon mesh PM. The smoothing process is performed in a state where the vertex i on the polyline PLT is constrained to be projected onto the two-dimensional polyline PLS. As the two-dimensional polyline PLS, a segment (line segment) Ei existing in the vicinity of the vertex i is actually used.
[0042]
That is, as shown in FIGS. 5 and 6, among the polylines PLS set on the plurality of images FT1 and FT2, respectively, the threshold value on which the distance b on the image when the vertex i to be processed is projected is set. A segment Ei located at a position smaller than t is used. Wherein such segments Ei respectively, and the plane S0, S1 including the point of view O0, O 1 of each image FT1, FT2 is defined. The distances d1 and d2 (with a hat) from the position of the vertex i to the planes S0 and S1 are obtained, and these vectors are added to the coordinate value Pi.
[0043]
As a result, the position of the vertex i is corrected so as to be forced on each plane S on the related polyline PLS. As a result, it converges to a point Ps that satisfies the constraint condition by the polyline PLS set in each image FT.
[0044]
The processing according to the above equation (4) corresponds to the first smoothing means of the present invention and corresponds to the processing according to claim 2. As a result, as in the case of the normal smoothing process, the vertex i to be processed always moves along the vertex group L, and the polyline PLT is maintained even after the process is performed.
[Linear smoothing]
FIG. 7 is a diagram for explaining the linearization smoothing process.
[0045]
In the straightening smoothing process, the coordinate values of the vertices are updated by the following equations (5) and (6).
[0046]
[Equation 3]

[0047]
Here, a coordinate value Pi obtained by adding a tilde to P is a new coordinate value obtained by the linearization smoothing process.
Expression (5) above shows a case where the vertex i to be processed is not included in the vertex group L constituting the polyline PLT. In this case, the same process as the normal smoothing process is performed, and the above (1 ) The same value as the formula.
[0048]
The above equation (6) is applied when the vertex i is included in the vertex group L. As shown by the equation (6), when the vertex i is included in the vertex group L, a correction term dj (with a tilde) is added to the case where the vertex i is not. In calculating the correction term dj, as shown in FIG. 7, a straight line L ′ fitted to the vertex group L on the three-dimensional polyline PLT is used. As a process of fitting a straight line to the vertex group L, a known method can be used and can be automatically performed. By fitting, a virtual straight line L ′ approximating the vertex group L is obtained.
[0049]
Each vertex i is projected and placed on the straight line L ′. That is, smoothing of each vertex i in a state where the vertex i belonging to the three-dimensional polyline (edge portion) PLT is arranged on the straight line L ′ that approximates the vertex group L on the polyline PLT. Is done. Thereby, the vertex i belonging to the edge portion is linearized and obtained as a straight line L ′ at an appropriate position.
[0050]
Note that, by performing the linearization smoothing process once, the vertex i rides on the straight line L ′, and therefore only moves on the straight line L ′ after the second time. As shown in FIG. 7, the correction term dj (with a tilde) is the shortest distance vector from the vertex i toward the straight line L ′.
[0051]
The processing according to the above equation (6) corresponds to the first smoothing means of the present invention and corresponds to the processing according to claim 3. As a result, the vertex i to be processed always moves along the vertex group L, and the polyline PLT is maintained even after processing.
[Anti-shrink treatment]
8 is a diagram for explaining anti-shrinkage processing when the vertex i belongs to the edge portion, FIG. 9 is a diagram for explaining anti-shrinkage processing when the vertex i does not belong to the edge portion, and FIG. 10 is an anti-shrinkage processing. It is a figure explaining the movement of a gravity center position vector or a middle point by processing.
[0052]
When the anti-shrinkage process is on, the anti-shrink process described below is executed. The anti-shrinkage process is executed every time each smoothing process is performed once, that is, every time the coordinate value P of the vertex i is updated.
[0053]
In the anti-shrinkage process, the coordinate value of each vertex is updated by the following equations (7), (8), and (9).
[0054]
[Expression 4]

[0055]
Here, a coordinate value Pi obtained by adding a bar to P is a new coordinate value obtained by the anti-shrinkage process. The new coordinate value Pi has a correction term di (with a bar) added to the original coordinate value. The correction term di is calculated by the equation (8) when the vertex i to be processed is included in the vertex group L constituting the polyline PLT, and is calculated by the equation (9) when it is not included.
[0056]
That is, when the vertex i to be processed is included in the vertex group L, as shown in the equation (8), FIG. 8, and FIG. In relation to, vertex i moves. In this case, the amount of movement of the vertex i is equivalent to the average of the amounts of movement in the normal direction of the center of gravity g of the area of each polygon PG. That is, processing is performed to restore the center of gravity of the polygon PG near the primary moved by the smoothing processing. As a result, the amount contracted by the smoothing process is restored, and the original volume is preserved.
[0057]
If the vertex i to be processed is not included in the vertex group L, as shown in the equation (9), FIG. 9 and FIG. Using only the vertices included in the group L, the movement amount and movement direction of the vertex i are obtained. In this case, the movement amount of the vertex i is not based on the center of gravity of each polygon PG, but is an amount corresponding to the average movement amount in the normal direction of the midpoint h of the vertex of the polygon PG included in the vertex group L. That is, a process for returning the midpoint position of the vertex of the polygon PG on the polyline PLT moved by the smoothing process is performed. This is because the smoothing process is performed using only the vertices on the vertex group L without using all the surrounding vertices. This is because it is desirable to return using only the vertices on the group L.
[0058]
As a result, the amount contracted by the smoothing process is restored, and the original volume is preserved. Moreover, for the smoothing process performed on the vertex i belonging to the edge part, the anti-shrinkage process is performed using only the vertex belonging to the edge part, and distortion due to the anti-shrinkage process hardly occurs. Incidentally, local distortion tends to occur in the conventional anti-shrinkage process.
[0059]
In addition, since the anti-shrinkage processing is shrunk by the smoothing processing, it does not return to the original direction but returns to the normal direction, so that the polygon PG is aligned in the direction in which the sizes of the polygons PG of the polygon mesh PM are aligned. Will move. As a result, the angle formed between the polygon PG and the polygon PG becomes shallower, and the effect of the smoothing process is further exhibited.
[0060]
Note that the timing of performing the anti-shrinkage process may be executed every time the smoothing process is performed, but every time the smoothing process is performed n times, the anti-shrinkage process for returning the contraction amount until then is 1 You may make it carry out collectively at once.
[0061]
The calculations according to the above equations (8) and (9) correspond to a process for evaluating a change in local volume of each part of the three-dimensional model (three-dimensional data) before and after the smoothing process. In addition, the calculation according to the equation ( 7 ) is a process for correcting the coordinate value Pi of each vertex of the polygon PG after the smoothing process so that the change in the local volume of each part of the three-dimensional model before and after the smoothing process is reduced. Equivalent to. These correspond to the processing described in claim 4.
[0062]
According to the above-described embodiment, the smoothing process is performed by distinguishing the vertex specified as the edge portion from the vertex that is not, and as a result, the edge of the three-dimensional model is maintained, and a smooth three-dimensional shape is obtained. Can do.
[0063]
In the above embodiment, the type of the object, the configuration of the whole or each part of the editing apparatus 1, the shape, the number, the content and order of the processing, and the like can be appropriately changed in accordance with the spirit of the present invention.
[0064]
【The invention's effect】
According to the present invention, the edge of the three-dimensional model is maintained, and a smooth three-dimensional shape can be obtained.
[Brief description of the drawings]
FIG. 1 is a block diagram of a three-dimensional model editing apparatus according to an embodiment of the present invention.
FIG. 2 is a diagram for explaining a polyline.
FIG. 3 is a diagram illustrating an example of a screen for selecting a type of smoothing processing.
FIG. 4 is a diagram for explaining normal smoothing processing;
FIG. 5 is a diagram for explaining 2D line constraint smoothing processing;
FIG. 6 is a diagram for explaining 2D line constrained smoothing processing;
FIG. 7 is a diagram for explaining linearization smoothing processing;
FIG. 8 is a diagram for explaining anti-shrinkage processing when a vertex belongs to an edge portion.
FIG. 9 is a diagram for explaining anti-shrinkage processing when a vertex does not belong to an edge portion.
FIG. 10 is a diagram for explaining the movement of the center-of-gravity position vector by anti-shrinkage processing.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Editing apparatus 10 Apparatus main body (The means which designates an edge part, 1st smoothing means, 2nd smoothing means, selection means, means which designates an edge line, an association means, an evaluation means, A coordinate value is corrected means)
ML 3D model DT 3D data (3D model)
FT image PLT 3D polyline (edge)
PLS 2D polyline (edge line)
PG polygon i vertex

Claims (5)

An editing device for a 3D model composed of polygon meshes,
Means for designating an edge portion on the three-dimensional model;
Wherein each vertex is processed belonging to the edge portion designated polygon of the three-dimensional model, the coordinate values of the vertices of each processed, the edge portion A with and specified vertices near the apex of the processed First smoothing means for performing smoothing by performing calculation using only the vertices belonging to, moving the vertices of each processing target and updating the coordinate values;
Each vertex of the polygon of the three-dimensional model is set as a processing target, a calculation different from that of the first smoothing unit is performed on the coordinate value of each processing target vertex, and the coordinate value of each processing target is moved. A second smoothing means for performing smoothing by updating
A selecting means for selecting the first smoothing means when the vertex to be smoothed belongs to the designated edge portion, and selecting the second smoothing means when not belonging to the edge portion;
A three-dimensional model editing apparatus characterized by comprising: A two-dimensional image in which the correspondence between the coordinate value of each vertex of the polygon of the three-dimensional model and the coordinates of each pixel on the two-dimensional image is known, means for designating an edge line on such a two-dimensional image,
Means for associating the edge line specified on the two-dimensional image with the edge portion specified on the three-dimensional model;
The first smoothing means performs the calculation on the coordinate value of the vertex by giving a constraint that the vertex belonging to the edge portion is projected onto the edge line.
The three-dimensional model editing apparatus according to claim 1. The first smoothing means performs the calculation on the coordinate value of the vertex by giving a constraint such that the first smoothing unit is arranged on a straight line fitted to the vertex group belonging to the edge portion.
The three-dimensional model editing apparatus according to claim 1. Means for evaluating a change in local volume of each part of the three-dimensional model before and after smoothing by the first smoothing means or the second smoothing means;
Means for correcting the coordinate value of each vertex of the smoothed polygon so that the change in local volume of each part of the three-dimensional model before and after smoothing is reduced ;
The three-dimensional model editing apparatus according to any one of claims 1 to 3. A computer program for editing a three-dimensional model consisting of a polygon mesh, when executed by a computer,
Means for designating an edge portion on the three-dimensional model based on a user's designated input;
Each vertex belonging to the specified edge portion of the polygon of the three-dimensional model is a processing target, and the coordinate value of each processing target vertex is a vertex around the processing target vertex and the specified edge portion First smoothing means for performing smoothing by performing computation using only the vertices belonging to, moving the vertices to be processed and updating the coordinate values thereof,
Each vertex of the polygon of the three-dimensional model is set as a processing target, a calculation different from that of the first smoothing unit is performed on the coordinate value of each processing target vertex, and the coordinate value of each processing target is moved. By updating the second smoothing means for performing smoothing , and
If it belongs to an edge portion with vertices specified to be subjected to smoothing selects said first smoothing means, if not belonging to the edge portion is a selection means for selecting the second smoothing means And
A computer program for causing a computer to function .

Images