CN111047684A - Model simplification method based on three-dimensional model characteristics - Google Patents
Model simplification method based on three-dimensional model characteristics Download PDFInfo
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Abstract
The invention discloses a model simplification method based on three-dimensional model characteristics, and belongs to the technical field of computer graphics. The method specifically comprises the following steps: inputting vertex data and triangular patch data of a three-dimensional model, obtaining 2D projection data of the three-dimensional model in front view, side view and top view directions, extracting a fitting curve of three-dimensional model contour data in the projection, calculating a feature vector difference value or a collapse edge weight value for two end points of a selected edge according to the fitting curve of the obtained 2D projection data, namely a feature point data set, and a feature vector of each feature point, and selecting an effective collapse edge and an effective collapse direction; then collapsing the edge, updating the vertex data set, and increasing the error value in the error accumulator; and judging whether the collapse error reaches a set threshold value, if not, continuing simplification, if so, ending simplification, combining simplified data and generating a simplified model. The method can quickly and efficiently obtain an ideal simplified model and improve the working efficiency.
Description
Technical Field
The invention belongs to the technical field of computer graphics, and particularly relates to a model simplification method based on three-dimensional model characteristics.
Background
Three-dimensional models are currently used in a wide variety of different fields. They are used in the medical industry to make accurate models of organs; the film industry uses them for moving characters, objects, and real films; the video game industry uses them as a resource in computers and video games; the engineering community uses them for designing new equipment, vehicles, structures, and other application areas, among others.
A three-dimensional model generally refers to a three-dimensional polygonal mesh model, that is, a collection of polygons or "faces" that together form the surface of a three-dimensional object. Any polygon can be divided into a plurality of triangles, and any polygon mesh can be converted into a triangle mesh. Therefore, in particular, a polygonal mesh composed entirely of triangles is called a triangular mesh.
With the progress of scientific technology, models constructed and used in various fields are more and more refined and complex, and the complex models bring huge pressure to computer processing, drawing systems and network transmission. Therefore, model simplification becomes a very important research topic. Model simplification means that the number of the surface, the number of the vertex and the number of the edges of the model are reduced by adopting a proper algorithm on the premise of keeping the shape of the original model set basically unchanged. How to rapidly and efficiently realize model simplification is also a popular research direction in the field.
Disclosure of Invention
In view of the foregoing problems in the prior art, an object of the present invention is to provide a model simplification method based on three-dimensional model features, so as to obtain an ideal simplified model quickly and efficiently.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a model simplification method based on three-dimensional model features comprises the following steps:
s1: inputting three-dimensional model vertex data and triangular patch data;
s2: obtaining 2D projection data of the three-dimensional model in three directions of front view, side view and overlook;
s3: preprocessing the 2D projection data, extracting a fitting curve of the three-dimensional model contour data in the projection, and calculating a characteristic vector;
s4: randomly selecting collapse edges, and selecting effective collapse edges and effective collapse directions according to a fitting curve of the 2D projection data obtained in the step S3, namely a feature point data set and a feature vector of each feature point;
s5: collapsing the effective collapse edge according to the effective collapse direction, updating the vertex data set, and increasing the error value in the error accumulator;
s6: judging whether the collapse error reaches a set threshold value, repeating the steps S4 and S5 if the collapse error does not reach the set threshold value, and entering the next step if the collapse error reaches the set threshold value;
s7: and combining the simplified data to generate a simplified model.
Preferably, step S3 includes the steps of:
s3-1: multiplying 2D projection data by a transformation matrix, Pi＝pi×MTWherein M isTRepresenting a transformation matrix, piRepresenting input projection data, PiRepresenting the transformed projection data, thereby transforming the 2D projection data into space coordinates with the center of gravity of the model as the origin of the coordinate system;
s3-2: a sector segmentation method is adopted, a minimum enclosing circle containing projection data is segmented, in each sector segmentation area, a point with the maximum distance value from the circle center of the minimum enclosing circle is calculated and selected as a characteristic point of the area, the distance value is a characteristic value, a vertex point on a three-dimensional model corresponding to the characteristic point is a characteristic vertex point in the sector area of the projection data, and a set of the characteristic points forms a fitting curve of the three-dimensional model contour data in the projection;
s3-3: and calculating the characteristic vector of the characteristic point according to the fitted curve.
Preferably, the calculating the feature vector of the feature point in step S3-3 specifically includes: calculating formula D according to the eigenvectori＝di×ki(i ═ 1, 2, Λ, 360) the feature vector of the feature points of each sector area is calculated, where d isiCharacteristic value, k, representing the i-th sectoriThe characteristic point representing the ith sector area is projectedAnd (d) combining the curvatures on the curves, wherein Di is a feature vector of the feature point.
Preferably, the specific steps of selecting the effective collapse edge and the effective collapse direction in step S4 are as follows:
s4-1, if two end point data u and v contained in the collapse edge are in a three-dimensional model vertex set corresponding to the obtained feature point data set, calculating a feature vector difference value of u and v, namely fitting a feature vector difference value of feature points corresponding to u and v on a curve, judging whether the feature vector difference value of u and v is smaller than a threshold value β, if the feature vector difference value of u and v is smaller than β, performing collapse as the collapse edge, otherwise, setting the threshold value β by a user, wherein the size of β represents the significance of regional feature change, the larger the significance of the regional feature change β is, the smaller the significance of the regional feature change is β, and the method for determining the UV collapse direction of the collapse edge comprises the steps of selecting the feature point with the smaller feature vector of the two feature points of u and v as the collapse feature point, and keeping the feature point with the larger feature vector value as the collapse direction.
S4-2: if the two end point data of the collapse edge do not belong to the feature point data set at the same time, calculating the collapse edge weight with the collapse direction from u to v according to a collapse edge weight calculation formula, wherein the formula is as follows:
wherein u and v represent the two end points of the edge,
f, n are triangular faces,
normal is the normal vector of the face,
tu is the set of all faces containing the u point,
tuv is a set of all surfaces including u point and v point, and the edge with the weight value not greater than the threshold set by the user is an effective collapse edge.
Preferably, in step S5, the error value is calculated by: the two ends of the collapse edge are u and v points, the effective collapse direction is u to v, a point p2 which is not connected with v before the collapse edge collapses but connected with v after the collapse edge collapses is selected, and an error value is calculated by a collapse edge weight formula:
the formula for calculating the side collapse weight is as follows:
if there are a plurality of points P2 that satisfy the condition, one of the points is randomly selected for calculation.
Has the advantages that: compared with the prior art, the invention has the advantages that:
according to the model simplification method based on the three-dimensional model characteristics, the automatic and rapid simplification of the model grid data is realized according to the self characteristics of the three-dimensional model data and the automatic constraint simplification ending mark. The model can be represented by minimum vertex data and triangle patch data on the basis of ensuring the model fineness, namely the model detail information, to be required by a user.
Drawings
FIG. 1 is a schematic view of collapsed side and top.
Detailed Description
The invention is further described with reference to specific examples. In the present application, a three-dimensional model refers to a triangular mesh model.
Example 1: model simplification method based on three-dimensional model characteristics
Firstly, inputting three-dimensional model vertex data and triangular patch data, and obtaining 2D projection data of the three-dimensional model vertex data in three directions of front view, side view and overlook. Carrying out data transformation on the 2D projection data of the three-dimensional model in the front view direction, the side view direction and the overlook direction for the first time, and transforming the 2D projection data into space coordinates with the center of gravity of the model as the origin of a coordinate system, so that the data of the three directions of the front view direction, the overlook direction and the overlook direction of the model are in the same relative coordinate system, and the data calculation is facilitated; meanwhile, all the 2D projection data have the same reference center point, so that the comparability and the referential of the data are ensured, and the specific transformation method comprises the following steps: multiplying 2D projection data by a transformation matrix, i.e. Pi＝pi×MTWherein M isTRepresenting a transformation matrix, piRepresenting input 2D projection data, PiRepresenting transformed projection data.
The method for calculating the feature points calculates the feature points in all the sector areas in the 2D projection data, the set of the feature points forms a fitting curve of the three-dimensional model contour data in the projection, the curvature value of the feature points on the fitting curve is calculated according to the fitting curve and the curvature calculation formula, and the formula D is calculated according to the feature vectori＝di×ki(i ═ 1, 2, ^, 360) where diCharacteristic value, k, representing the i-th sectoriThe curvature of the characteristic point representing the ith sector area on the 2D projection fitting curve, Di is the characteristic vector of the characteristic point, and the characteristic vector of each sector area is calculated.
When the three-dimensional model is simplified and collapse edges are randomly selected from vertex data, whether the difference value of the characteristic vectors of u and v (namely the difference value of the characteristic vectors of the characteristic points corresponding to u and v on a fitting curve) in the obtained characteristic point vertex set is smaller than a threshold value β or not is judged, if the difference value is in the characteristic point vertex set, whether the difference value of the characteristic vectors of u and v (namely the difference value of the characteristic vectors of the characteristic points corresponding to u and v on the fitting curve) is smaller than the threshold value β or not is judged, the size of the threshold value β represents the feature change significance of the area collapsed by the collapse of the user, the value β is manually set by the user, the larger the value β of the feature change significance is, the smaller the value β of the feature change significance is judged, if the difference value of the characteristic vectors of u and v is smaller than the threshold value β, the uv collapse edges can be used as collapse edges to perform collapse, if the difference value of the characteristic vectors of u and v is smaller than the threshold value β, the difference value of the characteristic vectors of the two collapse edges can be used as the merged characteristic point information, otherwise, the information of the feature points can be combined, and the characteristic point information of the feature points can be determined.
If the two endpoints u and v of the collapse edge do not belong to the feature point data set at the same time, calculating the collapse edge weight value with the collapse direction from u to v according to a collapse edge weight value calculation formula, wherein the formula specifically comprises the following steps:
where u and v represent the two end points of the edge, f, n are the triangular faces, normal is the normal vector of the face, Tu is the set of all faces containing the u point, and Tuv is the set of all faces containing the u point and the v point. The closer the normal multiplication of the two surfaces is to 1, the more parallel the two surfaces are, and the less influence of the surface elimination is. When the surface is eliminated, the vector of the collapse edge is compared with the characteristic vector of the sector area where the surface is located, when the cross product value of the normal vector of the surface where the collapse edge is located and the characteristic vector of the characteristic area where the collapse edge is located is closer to 0, the fact that the surface where the collapse edge is located is close to vertical to the surface where the characteristic vector is located is indicated to belong to a model characteristic change area, the elimination of the surface patch has a large influence on the model, and the collapse edge is not easy to serve as the collapse edge to simplify data; the special condition that the two end point data of the collapse edge belong to the feature point data set at the same time is eliminated, and when the collapse edge weight value calculated according to the formula is smaller than the threshold value sigma set by the user (the user can set a specific sigma value according to the actual simplification requirement of the model), the importance of the edge is low, and the edge can be eliminated.
After the above judgment, when the randomly selected collapse edge is effective, the edge collapse treatment is carried out according to the effective direction, if two vertexes of the collapse edge are u and v, and if the u-to-v direction is the effective collapse direction, the concrete collapse step is as follows: and moving the vertex u to the vertex v, removing the triangle with the side uv, replacing all the positions which are left to be used for the vertex u with the vertex v, finally removing the vertex u, and updating the vertex data set. And after each collapse, increasing the error value increased by the collapse in the error accumulator, ending model simplification when the accumulated collapse error reaches a threshold value preset by a user, otherwise, continuing the steps of selecting collapse edges, judging whether the collapse edges are effective, performing collapse treatment, updating a vertex data set and other simplified models until the error value reaches the threshold value, ending model simplification, combining simplified data and generating the simplified model. The error value calculation method is to use the absolute value of the difference value of the feature vector values calculated before and after the two feature vertexes of the collapse edge are combined as an error value, and the calculation method is exemplified as follows:
as shown in fig. 1, the side formed by u and v points is a collapsed effective side, and the effective collapse direction is u to v, that is, the u points are merged into v points, as shown in the figure, P0, P1, and P2 connected to u change the previous connection relationship, which only changes the previous non-adjacent relationship between P2 and v into an adjacent relationship, and the collapse error value is calculated by the collapsed edge weight formula as:
if there are a plurality of points P2 that satisfy the condition, one of the points is randomly selected for calculation.
Claims (5)
1. A model simplification method based on three-dimensional model features is characterized by comprising the following steps:
s1: inputting three-dimensional model vertex data and triangular patch data;
s2: obtaining 2D projection data of the three-dimensional model in three directions of front view, side view and overlook;
s3: preprocessing the 2D projection data, extracting a fitting curve of the three-dimensional model contour data in the projection, and calculating a characteristic vector;
s4: randomly selecting collapse edges, and selecting effective collapse edges and effective collapse directions according to a fitting curve of the 2D projection data obtained in the step S3, namely a feature point data set and a feature vector of each feature point;
s5: collapsing the effective collapse edge according to the effective collapse direction, updating the vertex data set, and increasing the error value in the error accumulator;
s6: judging whether the collapse error reaches a set threshold value, repeating the steps S4 and S5 if the collapse error does not reach the set threshold value, and entering the next step if the collapse error reaches the set threshold value;
s7: and combining the simplified data to generate a simplified model.
2. The method for model simplification based on three-dimensional model features according to claim 1, wherein step S3 comprises the following steps:
s3-1: multiplying 2D projection data by a transformation matrix, Pi＝pi×MTWherein M isTRepresenting a transformation matrix, piRepresenting input projection data, PiRepresenting the transformed projection data, thereby transforming the 2D projection data into space coordinates with the center of gravity of the model as the origin of the coordinate system;
s3-2: a sector segmentation method is adopted, a minimum enclosing circle containing projection data is segmented, in each sector segmentation area, a point with the maximum distance value from the circle center of the minimum enclosing circle is calculated and selected as a characteristic point of the area, the distance value is a characteristic value, a vertex point on a three-dimensional model corresponding to the characteristic point is a characteristic vertex point in the sector area of the projection data, and a set of the characteristic points forms a fitting curve of the three-dimensional model contour data in the projection;
s3-3: and calculating the characteristic vector of the characteristic point according to the fitted curve.
3. The method for model simplification based on three-dimensional model features according to claim 2, wherein the feature vectors of the feature points are calculated in step S3-3, specifically: calculating formula D according to the eigenvectori＝di×ki(i ═ 1, 2, Λ, 360) the feature vector of the feature points of each sector area is calculated, where d isiCharacteristic value, k, representing the i-th sectoriRepresents the firstThe curvature of the characteristic points of the i fan-shaped areas on the projection fitting curve is shown, and Di is the characteristic vector of the characteristic points.
4. The method of model simplification based on three-dimensional model features according to claim 1,
the specific steps of selecting the effective collapse edge and the effective collapse direction in the step S4 are as follows:
s4-1, if two endpoint data u and v contained by the collapse edge are in a three-dimensional model vertex set corresponding to the obtained feature point data set, calculating a feature vector difference value of u and v, namely fitting the feature vector difference value of feature points corresponding to u and v on a curve, and judging whether the feature vector difference value of u and v is smaller than a threshold value β, if the feature vector difference value of u and v is smaller than β, the collapse edge can be used for collapsing, otherwise, the threshold value β is set by a user, the size of β represents the significance of the change of the feature of the region, the greater the significance of the change of the feature of the region β is, the smaller the significance of the change of the feature of the region β is;
s4-2: if the two end point data of the collapse edge do not belong to the feature point data set at the same time, calculating the collapse edge weight with the collapse direction from u to v according to a collapse edge weight calculation formula, wherein the formula is as follows:
wherein u and v represent the two end points of the edge,
f, n are triangular faces,
normal is the normal vector of the face,
tu is the set of all faces containing the u point,
tuv is a set of all surfaces including u point and v point, and the edge with the weight value not greater than the threshold set by the user is an effective collapse edge.
5. The method for model simplification based on three-dimensional model features according to claim 1, wherein in step S5, the error value is calculated by: the two ends of the collapse edge are points u and v, the effective collapse direction is u to v, and the collapse is selectedAnd calculating an error value by a collapse edge weight formula at a point p2 which is not connected with v before collapse but connected with v after collapse:
the formula for calculating the side collapse weight is as follows:
if there are a plurality of points P2 that satisfy the condition, one of the points is randomly selected for calculation.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112446940A (en) * | 2020-12-04 | 2021-03-05 | 北京爱奇艺科技有限公司 | Simplification method and device for 3D model, electronic equipment and storage medium |
| CN117473655A (en) * | 2023-12-27 | 2024-01-30 | 中国人民解放军国防科技大学 | Aircraft simulation driving design method and device based on edge collapse grid optimization |
| CN112446940B (en) * | 2020-12-04 | 2024-04-19 | 北京爱奇艺科技有限公司 | Simplifying method and device for 3D model, electronic equipment and storage medium |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112446940A (en) * | 2020-12-04 | 2021-03-05 | 北京爱奇艺科技有限公司 | Simplification method and device for 3D model, electronic equipment and storage medium |
| CN112446940B (en) * | 2020-12-04 | 2024-04-19 | 北京爱奇艺科技有限公司 | Simplifying method and device for 3D model, electronic equipment and storage medium |
| CN117473655A (en) * | 2023-12-27 | 2024-01-30 | 中国人民解放军国防科技大学 | Aircraft simulation driving design method and device based on edge collapse grid optimization |
| CN117473655B (en) * | 2023-12-27 | 2024-03-15 | 中国人民解放军国防科技大学 | Aircraft simulation driving design method and device based on edge collapse grid optimization |
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Application publication date: 20200421 |