Adaptive determination method of mesh simplification rate for multi-resolution rendering

Abstract

The present invention discloses a method for adaptively determining mesh simplification rates for multi-resolution rendering, comprising: S1, gradually simplifying an original mesh model to obtain a set #imgabs0# consisting of simplification rate-cumulative folding loss; S2, normalizing the element points in set #imgabs1# to obtain set #imgabs2#; S3, calculating the vertical distance from each element point in set #imgabs3# to the line #imgabs4#=#imgabs5# to obtain a distance set #imgabs6#; S4, selecting the largest vertical distance in distance set #imgabs7# and using the corresponding element point in set #imgabs8# as a transition point B; S5, calculating an adaptive parameter #imgabs9# based on transition point B to further determine a low simplification rate point A and a high simplification rate point C; and S6, finding the simplification rate of the corresponding element point from set #imgabs10# based on the low simplification rate point A, transition point B, and high simplification rate point C. This method not only balances visual quality and reduces rendering load, but also enhances the system's universality and robustness.

Description

Technical Field

[0001] The present invention relates to the fields of computer graphics and computer vision, and in particular to a method for adaptively determining a mesh simplification rate for multi-resolution rendering. Background Art

[0002] In the field of computer graphics, mesh models are widely used for the digital representation of three-dimensional objects. Large three-dimensional scenes often contain a large number of models at the same time. If all of them are loaded in high-precision or original modeling versions, it will place a huge computing and storage burden on the computer, virtual reality (VR) or mobile device, seriously affecting rendering performance and user experience. To improve the efficiency of scene rendering and the smoothness of interaction, a multi-resolution or multi-level of detail (LOD) model display strategy is usually adopted. That is, when the viewpoint is far away, a highly simplified low-resolution model is loaded. As the viewpoint gradually approaches, it is gradually replaced with a higher-precision model until the original model is returned.

[0003] To obtain models of different resolutions, mesh simplification algorithms such as edge collapse are often used to simplify the original model to varying degrees. A key issue is how to properly set the mesh simplification rate for each resolution level.

[0004] Existing methods for determining the simplification rate of multi-resolution models mainly include the empirical ratio method and the fixed threshold method. The empirical ratio method usually uses a fixed simplification ratio (such as 30%, 60%, and 90%) to gradually reduce the number of triangles in the model. However, this method does not consider the nonlinear relationship between the degree of simplification and visual quality. As a result, although the number of facets between some simplification ratios (such as 30% and 60%) is significantly different, the actual visual effect is not significantly different. Figure 1 As shown in the figure, from left to right are the original model, the model with 30% simplified facets, and the model with 60% simplified facets. As can be seen from the figure, although the facets are quite different, the visual effects are slightly different, which will result in a waste of rendering performance. In addition, when a higher simplification rate (such as 90%) is used to represent a model far from the viewpoint, although the model's projected volume is small in the visual sense and is suitable for significant simplification, the visual quality of the model often decreases rapidly as the simplification rate increases further, as shown in the figure. Figure 2 As shown in the figure, at different high simplification rates of 88%, 90%, 92%, and 94%, the web members of the steel trusses gradually disappear, and the visual quality of the model rapidly decreases with increasing simplification rates. Therefore, the high simplification rate set by the empirical proportional method is difficult to achieve an effective balance between visual effect and performance for different models. The fixed threshold method, on the other hand, typically relies on setting a uniform geometric error threshold to determine the simplification rate. Therefore, it is difficult for this method to provide a universal and effective threshold determination strategy for models of different scales and spatial distribution characteristics. Summary of the Invention

[0005] To solve the problems existing in the prior art, the present invention provides a method for adaptively determining the mesh simplification rate for multi-resolution rendering, which can adaptively determine the degree of simplification of the multi-resolution model according to the characteristics of different original mesh models and actual visual needs, thereby achieving an effective balance between visual quality and rendering performance.

[0006] To this end, the present invention adopts the following technical solutions:

[0007] A method for adaptively determining a mesh simplification rate for multi-resolution rendering comprises the following steps:

[0008] S1, using the QEM mesh simplification algorithm, at a given simplification rate The original mesh model is gradually simplified to obtain Group element point ( , ) ,in, For the simplification rate, is the cumulative fold loss, (1~ );

[0009] S2, for the set The element points in are normalized to obtain Element points after group normalization , forming a set ,in is the normalized simplification rate, is the normalized cumulative fold loss;

[0010] S3, traverse the collection sequentially Element points in, calculate the distance from each element point to the straight line = Vertical distance , forming a distance set ;

[0011] S4, select distance set The maximum vertical distance is , will be collected Zhongyu The corresponding element point is used as transition point B;

[0012] S5, calculate the adaptive parameters according to the transition point B , filter out the distance set All greater than or equal to The vertical distance from The vertical distance with the minimum value is , The vertical distance with the maximum value is ; The collection In 、 The corresponding element points are used as low simplification rate point A and high simplification rate point C;

[0013] S6, according to the vertical distances corresponding to the low simplification rate point A, transition point B, and high simplification rate point C, in the distance set The subscript in , from the set Find the element point corresponding to the subscript in , and use the simplification rate of the found element point as the simplification rate 、 and , used to generate simplified mesh models with high, medium and low precision.

[0014] In the above step S5, the adaptive parameter is calculated by the following formula :

[0015] ,

[0016] Where:

[0017] , indicating the transition point B and the coordinate point The inclination of the line between them relative to the X-axis, is the coordinate of transition point B;

[0018] , indicating the transition point B and the coordinate point The inclination of the line between them relative to the Y axis;

[0019] is the shape factor;

[0020] Nether , upper bound , , and Used to limit adaptive parameters The value range of Too extreme a value will affect the resolution of multiple simplifications, ensuring clear distinction and practicality between each LOD level.

[0021] In the above step S1, the set The method to obtain is as follows:

[0022] Using QEM mesh simplification algorithm at a given simplification rate Next, simplify the original mesh model and get a new vertex each time you fold an edge;

[0023] For the New vertices, calculate the sum of the squares of the distances from the first new vertex to all triangles in the neighborhood of the two endpoints of the corresponding folded edge, and use the sum of the squares as the cumulative folding loss , calculate the simplification rate of the current original mesh model ;

[0024] when When, for the new vertices, calculate the The sum of the squares of the distances from the new vertex to all triangles in the neighborhood of the two endpoints of the corresponding folded edge is added to the cumulative folding loss. Accumulate and get the accumulated value as the cumulative fold loss , calculate the simplification rate of the current original mesh model , repeat the process of obtaining new vertices until the simplification rate of the current mesh model reaches the set simplification rate , and its cumulative fold loss is , will get The group simplification rate-cumulative fold loss is sorted from small to large according to the simplification rate to obtain the set .

[0025] Preferably, the simplification rate in step S1 is The value range is 90% to 99%.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] 1. The mesh simplification rate adaptive determination method of the present invention is based on the cumulative folding loss curve. It dynamically determines the simplification rate threshold according to the geometric complexity and simplification sensitivity of different original mesh models, and adaptively determines the positions of low simplification rate point A, transition point B, and high simplification rate point C, thereby automatically selecting the simplification rate. This not only balances visual quality and reduces rendering load, but also enhances the universality and robustness of the system.

[0028] 2. The grid simplification rate adaptive determination method of the present invention sets a lower limit and upper limit , effectively preventing the extreme situations where the low simplification rate point A, transition point B, and high simplification rate point C are too concentrated or too dispersed on the cumulative folding loss curve, ensuring that the generated multi-resolution model has practical rendering switching significance and avoiding the LOD level aggregation or sparse distribution problem.

[0029] 3. The low simplification rate point A, transition point B, and high simplification rate point C determined by the adaptive mesh simplification rate determination method of the present invention all have clear curve basis and visual significance. This avoids the problems of strong subjectivity and over-reliance on experience in level setting in traditional methods, realizes the reasonable division of different precision LOD levels in multi-resolution models, improves the scientificity and practicality of model LOD management, and has important engineering application value and broad promotion prospects.

[0030] 4. The mesh simplification rate adaptive determination method of the present invention is based on the curve morphology index ( and ) The adaptive parameters calculated It effectively adapts to different types of original grid models and improves the applicability and versatility of various structures and density models in actual engineering. The curve morphology index is used to characterize the "L-shaped" or "linear" trend of the simplified curve.

[0031] 5. The mesh simplification rate adaptive determination method of the present invention performs loss recording and analysis based on the existing QEM mesh simplification algorithm. It does not require additional high-dimensional feature construction or complex training. It is easy to implement and simple, and can be directly applied to the simplification project of the original mesh model. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a visual comparison of the original model, the model with 30% simplified triangles, and the model with 60% simplified triangles when using the existing empirical proportional method;

[0033] Figure 2 This is a comparison of the effects of simplification using the existing empirical ratio method. The simplification rates of (a) to (d) are 88%, 90%, 92%, and 94%, respectively.

[0034] Figure 3 This is a schematic diagram of the principle of the mesh simplification algorithm used in Example 1 of the present invention;

[0035] Figure 4 is a cumulative folding loss curve diagram in Example 1 of the present invention;

[0036] Figure 5 Schematic diagram of the position of transition point B in Example 1 of the present invention;

[0037] Figure 6 Schematic diagram of the positions of the low simplification rate point A and the high simplification rate point C in Example 1 of the present invention;

[0038] Figure 7 Schematic diagram of the steel truss model in Example 2 of the present invention;

[0039] Figure 8is a cumulative folding loss curve diagram in Example 2 of the present invention;

[0040] Figure 9 Figure 2 is a comparison of the simplification effects in Example 2 of the present invention, where (a) is the original model, (b) is a model with a simplification rate of 63.2%, (c) is a model with a simplification rate of 85.1%, and (d) is a model with a simplification rate of 90.4%.

[0041] Figure 10 for Figure 9 Partially enlarged views of Figures (a) to (d);

[0042] Figure 11 Schematic diagram of the original model of the power transformer in Example 3 of the present invention;

[0043] Figure 12 This is a cumulative folding loss curve diagram in Example 3 of the present invention;

[0044] Figure 13 The simplified effect diagram of Example 3 of the present invention, (a) is the original model, and the simplification rates of (b) to (d) are 59.3%, 82.2%, and 90.8%, respectively;

[0045] Figure 14 for Figure 13 Partially enlarged views of Figures (a) to (d). DETAILED DESCRIPTION

[0046] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0047] Example 1

[0048] A method for adaptively determining a mesh simplification rate for multi-resolution rendering comprises the following steps:

[0049] S1, get the cumulative fold loss curve:

[0050] Using the QEM (Quadric Error Metrics) mesh simplification algorithm, at a given simplification rate The original mesh model is gradually simplified, and a new vertex is obtained each time an edge is folded. The process of folding an edge e and changing two vertices p and q into a new vertex v is as follows: Figure 3 shown.

[0051] For the New vertices, calculate the sum of the squares of the distances from the first new vertex to all triangles in the neighborhood of the two endpoints of the corresponding folded edge, and use the sum of the squares as the cumulative folding loss , calculate the simplification rate of the current original mesh model ;

[0052] when When, for the new vertices, calculate the The sum of the squares of the distances from the new vertex to all triangles in the neighborhood of the two endpoints of the corresponding folded edge is added to the cumulative folding loss. Accumulate and get the accumulated value as the cumulative fold loss , calculate the simplification rate of the current mesh model , and obtain a set of simplified rates - Cumulative fold loss , repeat the process of obtaining new vertices until the simplification rate of the current mesh model reaches the set simplification rate , the simplified rate is The cumulative fold loss is , will get The group simplification rate-cumulative fold loss is sorted from small to large according to the simplification rate to obtain the set , according to the set The cumulative fold loss curve is obtained, and the cumulative fold loss curve is simplified at a rate of Axis, with cumulative fold loss as Axis, such as Figure 4 shown.

[0053] S2, for the set Normalize the element points in :

[0054] The Min-Max normalization method is used to normalize the set Element points in Perform normalization and obtain Element points after group normalization , forming a set ,in is the normalized simplification rate, is the normalized cumulative fold loss, , and then obtain the normalized cumulative fold loss curve.

[0055] Among them, the target interval in the Min-Max normalization method is .

[0056] S3, compute collection From the element point to the line = Vertical distance:

[0057] Traverse the collection sequentially , calculate each element point To the straight line = Vertical distance , forming a distance set , where x , .

[0058] S4, based on distance collection Determine transition point B:

[0059] Select distance set The maximum vertical distance is , the set obtained by S2 Zhongyu The corresponding coordinate point is used as transition point B, such as Figure 5 As shown. The coordinates of transition point B are expressed as .

[0060] Transition point B is the inflection point of the normalized cumulative fold loss curve. Transition point B is used to separate the normalized cumulative fold loss curve into the "slowly growing cumulative loss" interval and the "rapidly growing cumulative loss" interval.

[0061] S5, based on distance collection Determine the low simplification rate point A and the high simplification rate point C. The specific steps are as follows:

[0062] First, the adaptive parameters are determined according to the transition point B ,have:

[0063] ,

[0064] Where, , indicating the transition point B and the coordinate point The inclination of the line between them relative to the X-axis; , indicating the transition point B and the coordinate point The inclination of the line between them relative to the Y axis; is the shape factor; , , where the lower bound and upper bound Used to limit adaptive parameters The value range of If the value is too extreme, it will affect the resolution effect during the subsequent multi-level simplification, ensuring that each LOD level has clear distinction and practicality.

[0065] Then according to the distance collection and adaptive parameters Determine the low simplification rate point A and the high simplification rate point C:

[0066] Traverse the distance set , filter out all values ​​greater than or equal to The vertical distance of , select the distance set middle The vertical distance with the minimum value is , will be collected Zhongyu The corresponding point is point A, and the coordinates of point A are expressed as ; Select distance set middle The vertical distance with the maximum value is , will be collected Zhongyu The corresponding coordinate point is point C, and the coordinates of point C are expressed as ,like Figure 6 shown.

[0067] When the normalized cumulative fold loss curve approaches an L-shape (i.e., a substantial increase in the simplification rate of the original mesh model only results in a slight increase in the cumulative fold loss), the transition point B determined by the method of the present invention is close to the coordinate point , the calculated adaptive parameters The closer the value is to , based on adaptive parameters The closer the determined low simplification rate point A and high simplification rate point C are to the transition point B, the higher the degree of compression of the original mesh model can be achieved without affecting the visual quality; when the normalized cumulative folding loss curve approaches a straight line (i.e., a small increase in the simplification rate of the original mesh model causes a significant increase in the cumulative folding loss), the transition point B determined by the method of the present invention is close to the coordinate point , the calculated adaptive parameters The closer the value is to , based on adaptive parameters The further away the determined points A and C are from the transition point B, the accuracy of the original mesh model in close-range usage scenarios is guaranteed and the distribution of the simplification rate range is enhanced.

[0068] S6, obtaining the actual simplification rates corresponding to the low simplification rate point A, the transition point B, and the high simplification rate point C:

[0069] According to the vertical distances corresponding to the low simplification rate point A, transition point B, and high simplification rate point C in the distance set The subscript in , from the set Find the element point corresponding to the subscript in , and use the simplification rate of the found element point as the simplification rate 、 and , used to generate simplified mesh models with high, medium and low precision. For example, if the vertical distance of point A with low simplification rate is The corresponding set The vertical distance , since its subscript is 20, then from the set Find the element point with subscript 20 in ( , ), the simplification rate of this element point Simplification rate .

[0070] When using the method of the present invention to simplify the grid, first set the simplification rate to 、 and , respectively, use the QEM mesh simplification algorithm to simplify the original mesh model, and the simplified rate is The corresponding high-precision simplified mesh model and the simplified rate are The corresponding medium-precision simplified mesh model and simplified rate are The corresponding low-precision simplified mesh model is used, and the high-, medium- and low-precision simplified mesh models are applied to the near, medium and far viewing distance ranges to achieve LOD switching rendering, effectively improving the system rendering performance while ensuring the visual effect.

[0071] The high-, medium-, and low-precision simplified mesh models are used to support multi-resolution loading based on viewpoint distance, and are combined with the original model to form four LOD levels. Under the premise that visual errors can be ignored, the simplification rate is increased as much as possible. The high-precision simplified mesh model corresponding to the low-simplification rate point A is a model with maximum compression and almost no perceptual loss, suitable for loading scenarios close to the viewpoint; the high-simplification rate point C is the landmark point where significant visual errors begin to appear, and its corresponding low-precision simplified mesh model is suitable for loading scenarios far from the viewpoint; the transition point B is located between the low-simplification rate point A and the high-simplification rate point C, which is a compromise point with high cost-effectiveness. The medium-precision simplified mesh model corresponding to the transition point B takes into account both visual quality and simplification rate, and is suitable for model loading at medium viewing distances.

[0072] Example 2

[0073] The grid simplification rate adaptive determination method of the present invention is used to determine the following Figure 7 Simplification ratio of the steel truss model shown.

[0074] First, set the simplification rate is 95%, and we get Figure 8 The cumulative fold loss curve shown sets the lower bound Set upper bound , calculate the adaptive parameters The simplification rates corresponding to the low simplification rate point A, transition point B, and high simplification rate point C are determined to be 63.2%, 85.1%, and 90.4%, respectively. The high-precision simplified steel truss model with a simplification rate of 63.2%, the medium-precision simplified steel truss model with a simplification rate of 85.1%, and the low-precision simplified steel truss model with a simplification rate of 90.4% are used at different viewpoint distances. The visual effects of the original model and the high-, medium-, and low-precision simplified steel truss models at the same viewpoint distance are shown in the figure below. Figure 9 The corresponding partial enlarged diagram is shown in Figure 10 shown.

[0075] Depend on Figure 9 and Figure 10 It can be seen that the simplification rate of the high-precision simplified steel truss determined by the mesh simplification rate adaptive determination method of the present invention has reached 63.2%, but there is almost no obvious difference in visual effect between it and the original steel truss model, showing a high fidelity. The simplification rate of the medium-precision simplified steel structure truss model is 85.1%. Figure 10 Although some detail is lost, the overall visual quality remains good. The low-precision simplified steel truss model with a 90.4% simplification rate shows significant simplification of some detailed areas (such as the web members). However, since the low-precision simplified steel truss model is only loaded at a long viewpoint distance, this simplification is barely noticeable visually.

[0076] Example 3

[0077] The grid simplification rate adaptive determination method of the present invention is used to determine the following Figure 11 Simplification ratio of the power transformer model shown.

[0078] First, set the simplification rate is 95%, and we get Figure 12 The cumulative fold loss curve shown sets the lower bound Set upper bound , calculate the adaptive parameters The simplification rates corresponding to the low simplification rate point A, transition point B, and high simplification rate point C are determined to be 59.3%, 82.2%, and 90.8%, respectively. The high-precision simplified power transformer model with a simplification rate of 59.3%, the medium-precision simplified power transformer model with a simplification rate of 82.2%, and the low-precision simplified power transformer model with a simplification rate of 90.8% are used at different viewpoint distances. The visual effects of the original model and the high-, medium-, and low-precision simplified power transformer models at the same viewpoint distance are shown in the figure below. Figure 13 The corresponding partial enlarged diagram is shown in Figure 14 shown.

[0079] Compared with the steel truss model in Example 2, the dimension of the cumulative geometric loss of the power transformer model is about two orders of magnitude higher, but the grid simplification rate adaptive determination method of the present invention can still effectively extract the actual simplification rates of the representative low simplification rate point A, transition point B, and high simplification rate point C, indicating that the grid simplification rate adaptive determination method of the present invention has good robustness and wide adaptability.

[0080] In addition, since the overall shape of the cumulative loss curve of the power transformer model is closer to linear than that of the steel truss model, the positions of the determined low simplification rate point A, transition point B, and high simplification rate point C are also relatively far apart, which is in line with the design principle of the adaptability of the simplification rate distribution of the present invention.

[0081] Compared with the traditional method of fixed simplification ratio (such as 30%, 60%, and 90%), the grid simplification rate adaptive determination method of the present invention adaptively determines the simplification rate at each LOD level by analyzing the simplification rate-cumulative loss curve, effectively taking into account both visual quality and simplification efficiency. While ensuring the visual effect of the model, a higher simplification rate is achieved, and a reasonable, explainable and adaptively optimized balance is achieved between model quality and rendering performance based on the characteristics of different models.

[0082] In the present invention, the simplification rate The lower limit of is usually set to 90%. In the simplification process, The value of is related to the number of triangles in the simplified original mesh model. The more triangles in the original mesh model, The larger the value of When the simplification rate When the simplification rate exceeds 99%, the original mesh model may be severely degraded, resulting in a significant increase in its cumulative folding loss, thereby affecting the overall shape of the cumulative folding loss curve. The setting range is 90% to 99%.

Claims

1. A method for adaptively determining mesh simplification rate for multi-resolution rendering, characterized in that: The following steps are involved: S1, using the QEM mesh simplification algorithm, at a given simplification rate The original mesh model is gradually simplified to obtain Group element point ( , ) ,in, For the simplification rate, is the cumulative fold loss, (1~ ); S2, for the set The element points in are normalized to obtain Element points after group normalization , forming a set ,in is the normalized simplification rate, is the normalized cumulative fold loss; S3, traverse the collection sequentially Element points in, calculate the distance from each element point to the straight line = Vertical distance , forming a distance set ; S4, select distance set The maximum vertical distance is , will be collected Zhongyu The corresponding element point is used as transition point B; S5, calculate the adaptive parameters according to the transition point B , filter out the distance set All greater than or equal to The vertical distance from The vertical distance with the minimum value is , The vertical distance with the maximum value is ; The collection In 、 The corresponding element points are used as low simplification rate point A and high simplification rate point C; S6, according to the vertical distances corresponding to the low simplification rate point A, transition point B, and high simplification rate point C, in the distance set The subscript in , from the set Find the element point corresponding to the subscript in , and use the simplification rate of the found element point as the simplification rate 、 and , used to generate simplified mesh models with high, medium and low precision.

2. The method for adaptively determining mesh simplification rate for multi-resolution rendering according to claim 1, wherein: In step S5, the adaptive parameter is calculated by the following formula : ， Where: , indicating the transition point B and the coordinate point The inclination of the line between them relative to the X-axis, is the coordinate of transition point B; , indicating the transition point B and the coordinate point The inclination of the line between them relative to the Y axis; is the shape factor; Nether , upper bound , , and Used to limit adaptive parameters The value range of .

3. The method for adaptively determining mesh simplification rate for multi-resolution rendering according to claim 1, wherein: S1 collection The method to obtain is as follows: Using QEM mesh simplification algorithm at a given simplification rate Next, simplify the original mesh model and get a new vertex each time you fold an edge; For the New vertices, calculate the sum of the squares of the distances from the first new vertex to all triangles in the neighborhood of the two endpoints of the corresponding folded edge, and use the sum of the squares as the cumulative folding loss , calculate the simplification rate of the current original mesh model ; when When, for the new vertices, calculate the The sum of the squares of the distances from the new vertex to all triangles in the neighborhood of the two endpoints of the corresponding folded edge is added to the cumulative folding loss. Accumulate and get the accumulated value as the cumulative fold loss , calculate the simplification rate of the current original mesh model , repeat the process of obtaining new vertices until the simplification rate of the current mesh model reaches the set simplification rate , and its cumulative fold loss is , will get The group simplification rate-cumulative fold loss is sorted from small to large according to the simplification rate to obtain the set .

4. The method for adaptively determining mesh simplification rate for multi-resolution rendering according to claim 1, wherein: In step S1, the simplification rate The value range is 90% to 99%.

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