Neural point field based unstructured mesh volume rendering method and device

Abstract

The application provides a non-structure grid volume rendering method and device based on a neural point field, and relates to the technical field of data processing, which comprises the following steps: extracting an outer surface grid of a physical field from original non-structure grid data; performing adaptive sampling on a physical field space gradient module to obtain a training data set containing the coordinates of sampling points and corresponding physical field values; training a pre-built neural point field model by adopting a strategy containing multi-scale Fourier feature coding; generating a projection light ray for each pixel of an image plane, determining the sampling range of the projection light ray in the physical field domain by using the outer surface grid, and generating a space sampling point in the sampling range; inputting the space sampling point into the neural point field model to generate a predicted field value, and generating a corresponding pixel color. The application provides an efficient solution for real-time and high-precision visual analysis of large-scale non-structure grid physical fields.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and more specifically, to a method and apparatus for drawing unstructured mesh volumes based on neural point fields. Background Technology

[0002] Volume rendering is a core technology in scientific computing for revealing the internal structure of three-dimensional physical fields. Traditional volume rendering methods based on unstructured meshes face two major bottlenecks. First, data storage and memory consumption are enormous; processing high-precision simulation data with hundreds of millions of cells often requires tens to hundreds of gigabytes of memory, easily exceeding hardware limitations. Second, computational efficiency is low; each ray needs to undergo complex intersection tests and interpolation calculations with massive numbers of mesh cells. Even with spatial indexing acceleration methods such as octrees and KD-trees, the construction and traversal overhead still makes it difficult to meet the rendering speed requirements for real-time interactive analysis. Therefore, these bottlenecks severely restrict the real-time visualization and analysis of large-scale simulation data. Summary of the Invention

[0003] The purpose of this invention is to provide a method and apparatus for rendering unstructured mesh volumes based on neural point fields, thereby improving the aforementioned problems. To achieve the above objective, the technical solution adopted by this invention is as follows:

[0004] Firstly, this application provides a method for rendering unstructured mesh volumes based on neural point fields, including:

[0005] Obtain the original unstructured mesh, and extract the outer surface mesh of the physical field from the original unstructured mesh data;

[0006] Calculate the physical field spatial gradient of all nodes in the original unstructured mesh, and perform adaptive sampling based on the magnitude of the physical field spatial gradient to obtain a training dataset containing the coordinates of the sampling points and the corresponding physical field values.

[0007] Based on the training dataset, a strategy including multi-scale Fourier feature encoding is used to train the pre-built neural point field model to obtain the trained neural point field model.

[0008] For each pixel of the image plane, a projection ray is generated. The sampling range of the projection ray in the physical field is determined by the outer surface grid, and spatial sampling points are generated within the sampling range.

[0009] Spatial sampling points are input into the neural point field model to generate predicted field values. Based on the predicted field values, corresponding pixel colors are generated, and the image is drawn using a composite.

[0010] Secondly, this application also provides an unstructured mesh volume rendering device based on neural point fields, comprising:

[0011] The mesh extraction module is used to extract the outer surface mesh of the physical field from the raw unstructured mesh data.

[0012] The dataset construction module is used to calculate the physical field spatial gradient of all nodes in the original unstructured mesh, and to perform adaptive sampling based on the magnitude of the physical field spatial gradient to obtain a training dataset containing the coordinates of the sampling points and the corresponding physical field values.

[0013] The model training module is used to train the pre-built neural point field model based on the training dataset using a strategy that includes multi-scale Fourier feature encoding, so as to obtain the trained neural point field model.

[0014] The sampling point generation module is used to generate a projection ray for each pixel of the image plane, determine the sampling range of the projection ray in the physical field using the outer surface grid, and generate spatial sampling points within the sampling range.

[0015] The image synthesis module is used to input spatial sampling points into the neural point field model to generate predicted field values, generate corresponding pixel colors based on the predicted field values, and draw images using the synthesized volume.

[0016] Thirdly, this application also provides an unstructured mesh volume rendering device based on neural point fields, comprising:

[0017] Memory, used to store computer programs;

[0018] A processor is used to implement the steps of the neural point field-based unstructured mesh volume rendering method when executing the computer program.

[0019] Fourthly, this application also provides a readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described method for drawing unstructured mesh volumes based on neural point fields.

[0020] The beneficial effects of this invention are as follows:

[0021] This invention achieves seamless rendering of various hybrid meshes by replacing the original mesh with neural point fields as a unified and continuous representation of the physical field and integrating gradient-driven sampling and multi-scale training strategies. It can also reconstruct physical field details with high fidelity and significantly improve image quality. At the same time, the rendering process is simplified to efficient neural network forward computation and rule sampling, achieving a leap in rendering speed from minutes to milliseconds. Thus, it provides an efficient solution for real-time, high-precision visualization and analysis of large-scale unstructured mesh physical fields.

[0022] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0023] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a schematic diagram of the unstructured mesh drawing method based on neural point fields described in this embodiment of the invention;

[0025] Figure 2 This is an example of an unstructured mesh based on neural point fields as described in this embodiment of the invention.

[0026] Figure 3 This is a schematic diagram of the physical field distribution described in an embodiment of the present invention;

[0027] Figure 4 This is a schematic diagram of the gradient modulus described in an embodiment of the present invention;

[0028] Figure 5 This refers to the adaptive sampling map described in this embodiment of the invention;

[0029] Figure 6 This is a diagram of the neural point field model architecture described in this embodiment of the invention;

[0030] Figure 7 This is a graph showing the comparison of drawing speeds as described in an embodiment of the present invention;

[0031] Figure 8 This is a schematic diagram of the structure of the unstructured mesh rendering device based on neural point fields described in this embodiment of the invention.

[0032] Figure 9 This is a schematic diagram of the structure of the unstructured mesh rendering device based on neural point fields described in this embodiment of the invention.

[0033] Marked in the image:

[0034] 800. Unstructured mesh rendering device based on neural point fields; 801. Processor; 802. Memory; 803. Multimedia component; 804. I / O interface; 805. Communication component. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0036] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0037] Example 1:

[0038] This embodiment provides a method for drawing unstructured mesh volumes based on neural point fields.

[0039] See Figure 1 The figure shows that this method includes:

[0040] S1. Obtain the original unstructured mesh, and extract the outer surface mesh of the physical field from the original unstructured mesh data; in this field, the outer surface is the interface between the physical field and the external space, and the unstructured mesh consists of nodes and elements. Please refer to [link to relevant documentation]. Figure 2 The figure shows three different non-network structures: (a), (b), and (c).

[0041] Specifically, step S1 includes:

[0042] S11. Extract the topological connectivity of the original unstructured mesh and identify all boundary cells and boundary surfaces that constitute the outer boundary of the physical field.

[0043] In this embodiment, boundary surfaces are identified by analyzing the connection relationships of the units. Specifically, all large source surfaces of all units are traversed, and the number of times each unit surface appears is counted. If a unit surface appears only once, it is the boundary surface of the physical field, i.e., the boundary unit.

[0044] S12. Based on the boundary elements and boundary surfaces, extract the complete outer surface mesh using a boundary tracing algorithm;

[0045] Specifically, an arbitrary boundary face is selected as the starting seed face. Using the three edges of the starting seed face as clues, other adjacent boundary faces sharing the same edge are searched, and the newly found adjacent boundary faces are added to the boundary face set. Finally, all the collected boundary faces form a complete triangular patch mesh, that is, the outer surface mesh.

[0046] S13. Determine the spatial range of the physical field based on the extracted outer surface mesh;

[0047] Specifically, iterate through the coordinates of all vertices of the outer surface mesh and find the minimum values ​​of these vertices along the X, Y, and Z coordinate axes. , , and maximum value , , Therefore, the spatial extent of the physical field is:

[0048] ;

[0049] In the formula, Represents the spatial extent of a physical field, such as Figure 3 As shown in the figure, the original physical field is illustrated. The distribution along the X-axis. The curves of different colors in the figure represent the field value profiles at different Y and Z coordinates, collectively presenting the overall characteristic structure of the physical field.

[0050] Based on the above embodiments, this method further includes:

[0051] S2. Calculate the physical field spatial gradient of all nodes in the original unstructured mesh, and perform adaptive sampling based on the magnitude of the physical field spatial gradient to obtain a training dataset containing the coordinates of the sampling points and the corresponding physical field values.

[0052] In this embodiment, the sampling is guided by the gradient of the intensity of change in the physical field, ensuring that key feature regions obtain more training samples, thereby improving the overall accuracy of the model with a limited amount of data.

[0053] Specifically, step S2 includes:

[0054] S21. At each node of the original unstructured mesh, the spatial gradient vector of the physical field is calculated using the Green-Gaussian gradient reconstruction method;

[0055] For unstructured meshes, the gradient at a node cannot be directly obtained through differencing and needs to be reconstructed based on information from surrounding elements. Therefore, this embodiment uses the Green-Gauss method from computational fluid dynamics to calculate the physical field spatial gradient at each node. The specific implementation process is as follows:

[0056] S211. For node Find all nodes that contain the given node. The grid cells are then divided and all grid cells are stored in the cell set. ;

[0057] S212. Set of Computational Units The physical field values ​​and cell volume of each grid cell;

[0058] S213. Calculate the nodes based on the physical field values ​​and element volumes. Physical field spatial gradient :

[0059] ;

[0060] In the formula, Represents a node The control volume is one-third of the sum of the volumes of all mesh cells. The area vector of the opposite faces. Represents the physical field value.

[0061] S22. Calculate the magnitude of the spatial gradient vector at each node, and use it as the gradient magnitude of each node. The specific calculation method is as follows:

[0062] ;

[0063] In the formula, Gradient vectors Components in the x, y, and z directions, For the Euclidean norm, Represents a node gradient magnitude, The larger the value, the stronger the physical field at the node. The more dramatic the changes in the vicinity, the more key features it contains, such as Figure 4 As shown in the figure, the distribution of gradient magnitude in the X direction is illustrated.

[0064] S23. The ratio of the gradient magnitude of each node to the sum of the gradient magnitudes of all nodes is taken as the sampling probability of the corresponding node:

[0065] ;

[0066] In the formula, Indicates the use of probability. This represents the sum of the gradient magnitudes of all nodes.

[0067] S24. For example Figure 5As shown, sampling points in the training dataset are generated by sampling from all nodes according to the sampling probability of all nodes.

[0068] Specifically, set the total number of target sampling points M, based on the sampling probability. M sampling points are selected from the original node set using random sampling with replacement to generate the training dataset. The training dataset It contains M samples, each sample consisting of three-dimensional coordinates. and the corresponding physical field values constitute.

[0069] Based on the above embodiments, this method further includes:

[0070] S3. Based on the training dataset, a strategy including multi-scale Fourier feature encoding is used to train the pre-built neural point field model to obtain the trained neural point field model.

[0071] In this embodiment, a multilayer perceptron is constructed as a neural point field model, such as... Figure 6 As shown, the neural point field model comprises an input layer, four fully connected hidden layers, and an output layer. Each hidden layer is followed by a nonlinear activation function. The input layer receives three-dimensional coordinates. Mapped to the corresponding physical field values Then it is output from the output layer.

[0072] Specifically, step S3 includes:

[0073] S31. Configure a set of standard deviation values ​​to control the frequency of Fourier feature encoding. ,in, , The standard deviation is the total number of scales, and it is used to control the frequency distribution of the encoded features. The larger the value, the higher the frequency of the generated features.

[0074] S32. Iteratively execute the following steps according to the standard deviation values ​​in ascending order:

[0075] S33. Using the standard deviation value corresponding to the current iteration, perform Fourier feature encoding on the coordinates of the sampling points in the training dataset;

[0076] Specifically, based on the standard deviation of the current scale Generate a random Gaussian matrix ,in Each element is independently sampled from a mean of 0 and a standard deviation of . Gaussian distribution Subsequently, the training dataset was... Each coordinate in Applying Fourier feature coding :

[0077] ;

[0078] In the formula, This is a transpose.

[0079] S34. Based on the model parameters or initial parameters obtained from the previous iteration of training, train the neural point field model using the currently encoded data to generate model parameters.

[0080] Using the encoded dataset The model is trained, and the weighted mean squared error loss is calculated. An adaptive optimizer is used to take the model parameters from the previous scale training convergence as the initial parameters for the current scale training. During training, strategies such as cosine annealing are used to dynamically adjust the learning rate.

[0081] S35. After completing all iterations, the trained neural point field model is obtained based on the generated model parameters.

[0082] Based on the above embodiments, this method further includes:

[0083] S4. Generate a projection ray for each pixel of the image plane, determine the sampling range of the projection ray in the physical field using the outer surface grid, and generate spatial sampling points within the sampling range;

[0084] In this embodiment, a ray path is determined for each pixel in the image, passing through a three-dimensional physical field, and spatial points for field value sampling are generated along the ray path.

[0085] Specifically, step S4 includes:

[0086] S41. Calculate the intersection point of the projected ray and the outer surface mesh;

[0087] Specifically, the resolution of the image plane is For each pixel on the image plane Generate a principal ray originating from the virtual camera. In the standard perspective projection model, this projected ray R can be expressed by the parametric equation:

[0088] ;

[0089] in, As the origin of the light, It is the direction vector of light, passing through pixels. The position is calculated on the image plane. It indicates the distance along the direction of the light ray.

[0090] Subsequently, each triangular facet in the outer surface mesh is traversed sequentially, and the intersection points are calculated. .

[0091] Preferably, a spatial acceleration structure, such as a bounding box hierarchy, is constructed for the outer surface mesh. The BVH can quickly eliminate a large number of faces that cannot intersect with light rays, and only perform intersection calculations on a few potentially intersecting faces, thereby reducing computational complexity.

[0092] S42. Take the first intersection point entering the physical field along the direction of the light rays as the sampling start point, and the last intersection point leaving the physical field as the sampling end point;

[0093] Since the outer surface mesh is closed, a ray intersecting the physical field will typically have two intersection points: an entry point and an exit point. All calculated intersection point parameters are sorted by size. The smallest intersection point corresponds to the sampling start point where the ray enters the physical field, and the largest intersection point corresponds to the sampling end point where the ray leaves the physical field. If a ray has no intersection point with the outer surface mesh or only one intersection point, it is considered that the ray of that pixel has not traversed the effective field and can be skipped or assigned the background color.

[0094] S43. Determine the sampling range based on the sampling start point and sampling end point:

[0095] ;

[0096] In the formula, This represents the effective sampling line segment through which light passes through the physical field. Indicates the sampling termination point. Indicates the sampling start point.

[0097] Spatial sampling points are generated within the sampling range:

[0098] Along the effective sampling line segment, according to the preset spatial sampling step size Generate a series of uniformly distributed spatial sampling points The sampling points Used to query neural point field models.

[0099] Based on the above embodiments, this method further includes:

[0100] S5. Input the spatial sampling points into the neural point field model to generate predicted field values, generate corresponding pixel colors based on the predicted field values, and draw the image using a composite.

[0101] Specifically, step S5 includes:

[0102] S51. Based on the preset transfer function, map the predicted field value of each spatial sampling point to the corresponding color value and transparency value;

[0103] First, for each spatial sampling point of the same ray R Encode using Fourier features that are consistent with the highest frequency scale during the training phase. ,Will Convert to feature vector Then, the feature vectors The input is used in the neural point field model. The model performs forward propagation on the encoded features and outputs... Predicted physical field values ;

[0104] Finally, the predicted physical field values ​​are obtained using a pre-defined transfer function. Mapped to visualized optical properties. The transfer function includes color mapping. and transparency mapping The mapping process is represented as follows:

[0105] ;

[0106] in, A three-dimensional vector representing RGB colors;

[0107] ;

[0108] in, It is a scalar with a value range of [0,1], where 0 represents complete transparency and 1 represents complete opacity.

[0109] S52. Obtain all spatial sampling points located on the same projected ray;

[0110] S53. Following the order from the sampling start point to the sampling end point, update the current cumulative color and cumulative transparency of the current projected ray based on the color value and transparency value of each spatial sampling point on the current projected ray;

[0111] Preferably, a front-to-back synthesis algorithm is used to simulate the light absorption and emission model. The cumulative color of the light is initialized as follows: The cumulative transparency is 0. Then, sampling points are acquired in order from the sampling start point to the sampling end point, and the contribution weight of the current sampling point to the final color is calculated. :

[0112] ;

[0113] In the formula, Indicates the cumulative opacity of light;

[0114] Based on the contribution weight Update color and opacity :

[0115] ;

[0116] In the formula, The value gradually increases as the number of sampling points increases, indicating that light becomes less transparent after passing through more material.

[0117] S54. When the accumulated transparency reaches the preset termination threshold, stop updating and obtain the final accumulated color of the currently projected light;

[0118] S55. Use the final accumulated color of the currently projected light as the color of the corresponding pixel to synthesize the volume drawing image;

[0119] Specifically, the final accumulated color of each ray R is assigned to the corresponding pixel. Steps S4 and S5 are executed in parallel for all pixels, ultimately generating a complete volume rendering image that reflects the internal structure of the three-dimensional physical field.

[0120] In this embodiment, a pre-trained neural point field model is used to efficiently acquire the physical field values ​​of spatial sampling points, and optical integration is used to synthesize a two-dimensional image with perspective effects, achieving efficient rendering. Figure 7 As shown, it can be seen that the performance advantage of the present invention increases by orders of magnitude as the data scale increases.

[0121] Example 2:

[0122] like Figure 8 As shown, this embodiment provides an unstructured mesh volume rendering device based on neural point fields, the device comprising:

[0123] The mesh extraction module is used to extract the outer surface mesh of the physical field from the raw unstructured mesh data.

[0124] The dataset construction module is used to calculate the physical field spatial gradient of all nodes in the original unstructured mesh, and to perform adaptive sampling based on the magnitude of the physical field spatial gradient to obtain a training dataset containing the coordinates of the sampling points and the corresponding physical field values.

[0125] The model training module is used to train the pre-built neural point field model based on the training dataset using a strategy that includes multi-scale Fourier feature encoding, so as to obtain the trained neural point field model.

[0126] The sampling point generation module is used to generate a projection ray for each pixel of the image plane, determine the sampling range of the projection ray in the physical field using the outer surface grid, and generate spatial sampling points within the sampling range.

[0127] The image synthesis module is used to input spatial sampling points into the neural point field model to generate predicted field values, generate corresponding pixel colors based on the predicted field values, and draw images using the synthesized volume.

[0128] Based on the above embodiments, the mesh extraction module includes:

[0129] The topology extraction unit is used to extract the topological connection relationships of the original unstructured mesh and identify all boundary cells and boundary surfaces that constitute the outer boundary of the physical field.

[0130] Surface mesh building units are used to extract the complete outer surface mesh based on the boundary units and boundary surfaces using a boundary tracing algorithm;

[0131] The spatial extent determination unit is used to determine the spatial extent of the physical field based on the extracted outer surface mesh.

[0132] Based on the above embodiments, the dataset construction module includes:

[0133] The gradient calculation unit is used to calculate the spatial gradient vector of the physical field at each node of the original unstructured mesh using the Green-Gaussian gradient reconstruction method.

[0134] The modulus calculation unit is used to calculate the modulus of the spatial gradient vector at each node, and use it as the gradient modulus of each node.

[0135] The probability allocation unit is used to take the ratio of the gradient magnitude of each node to the sum of the gradient magnitudes of all nodes as the sampling probability of the corresponding node.

[0136] The sampling execution unit is used to sample from all nodes according to the sampling probability of all nodes to generate sampling points in the training dataset.

[0137] Based on the above embodiments, the model training module includes:

[0138] The parameter configuration unit is used to configure a set of standard deviation values ​​for controlling the frequency of Fourier feature encoding;

[0139] An iterative training control unit is used to iteratively execute training operations in ascending order of the standard deviation values. The training operations include: using the standard deviation value corresponding to the current iteration to perform Fourier feature encoding on the coordinates of the sampling points in the training dataset; and using the currently encoded data to perform one round of training on the neural point field model based on the model parameters or initial parameters obtained from the previous round of iterative training.

[0140] The model generation unit is used to obtain the trained neural point field model based on the model parameters generated during training after all iterations are completed.

[0141] Based on the above embodiments, the sampling point generation module includes:

[0142] An intersection calculation unit is used to calculate the intersection point of the projected ray and the outer surface mesh;

[0143] The key point determination unit is used to take the first intersection point entering the physical field along the direction of the light as the sampling start point and the last intersection point leaving the physical field as the sampling end point.

[0144] The range definition unit is used to determine the sampling range based on the sampling start point and the sampling end point.

[0145] It should be noted that the specific manner in which each module performs its operation in the apparatus described in the above embodiments has been described in detail in the embodiments of the method, and will not be elaborated here.

[0146] Example 3:

[0147] Corresponding to the above method embodiments, this embodiment also provides an unstructured mesh rendering device based on neural point fields. The unstructured mesh rendering device based on neural point fields described below and the unstructured mesh rendering method based on neural point fields described above can be referred to each other.

[0148] Figure 9 This is a block diagram illustrating an unstructured mesh rendering device 800 based on a neural point field, according to an exemplary embodiment. Figure 9 As shown, the neural point field-based unstructured mesh rendering device 800 may include a processor 801 and a memory 802. The neural point field-based unstructured mesh rendering device 800 may also include one or more of a multimedia component 803, an I / O interface 804, and a communication component 805.

[0149] The processor 801 controls the overall operation of the neural point field-based unstructured mesh rendering device 800 to complete all or part of the steps in the aforementioned neural point field-based unstructured mesh rendering method. The memory 802 stores various types of data to support the operation of the neural point field-based unstructured mesh rendering device 800. This data may include, for example, instructions for any application or method operating on the neural point field-based unstructured mesh rendering device 800, as well as application-related data such as contact data, sent and received messages, images, audio, video, etc. The memory 802 can be implemented using any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The multimedia component 803 may include a screen and an audio component. The screen may be, for example, a touchscreen, and the audio component is used to output and / or input audio signals. For example, the audio component may include a microphone for receiving external audio signals. The received audio signals may be further stored in the memory 802 or transmitted via the communication component 805. The audio component also includes at least one speaker for outputting audio signals. I / O interface 804 provides an interface between processor 801 and other interface modules, such as keyboards, mice, and buttons. These buttons can be virtual or physical. Communication component 805 is used for wired or wireless communication between the neural point field-based unstructured mesh rendering device 800 and other devices. Wireless communication includes Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G, or 4G, or a combination thereof. Therefore, the corresponding communication component 805 may include a Wi-Fi module, a Bluetooth module, or an NFC module.

[0150] In an exemplary embodiment, the neural point field-based unstructured mesh rendering device 800 may be implemented by one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components to execute the above-described neural point field-based unstructured mesh rendering method.

[0151] In another exemplary embodiment, a computer-readable storage medium including program instructions is also provided, which, when executed by a processor, implement the steps of the above-described unstructured mesh rendering method based on neural point fields. For example, the computer-readable storage medium may be the memory 802 including the program instructions, which may be executed by the processor 801 of the unstructured mesh rendering device 800 based on neural point fields to complete the above-described unstructured mesh rendering method based on neural point fields.

[0152] Example 4:

[0153] Corresponding to the above method embodiments, this embodiment also provides a readable storage medium. The readable storage medium described below can be referred to in conjunction with the above-described method for drawing unstructured mesh volumes based on neural point fields.

[0154] A readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the unstructured mesh volume drawing method based on neural point fields described in the above method embodiments.

[0155] Specifically, the readable storage medium can be a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, or any other readable storage medium capable of storing program code.

[0156] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0157] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for rendering unstructured mesh volumes based on neural point fields, characterized in that, include: Obtain the original unstructured mesh, and extract the outer surface mesh of the physical field from the original unstructured mesh data; Calculate the physical field spatial gradient of all nodes in the original unstructured mesh, and perform adaptive sampling based on the magnitude of the physical field spatial gradient to obtain a training dataset containing the coordinates of the sampled points and their corresponding physical field values, including: At each node of the original unstructured mesh, the spatial gradient vector of the physical field is calculated using the Green-Gaussian gradient reconstruction method; Calculate the magnitude of the spatial gradient vector at each node, and use it as the gradient magnitude of each node; The ratio of the gradient magnitude of each node to the sum of the gradient magnitudes of all nodes is used as the sampling probability of the corresponding node. Sampling points in the training dataset are generated by sampling from all nodes based on the sampling probability of all nodes. Based on the training dataset, a strategy including multi-scale Fourier feature encoding is used to train the pre-built neural point field model, resulting in a trained neural point field model, including: Configure a set of standard deviation values ​​to control the frequency of Fourier feature encoding; The following steps are performed iteratively, following the order of the standard deviation values ​​from smallest to largest: Using the standard deviation value corresponding to the current iteration, perform Fourier feature encoding on the coordinates of the sampling points in the training dataset; Based on the model parameters or initial parameters obtained from the previous iteration of training, the neural point field model is trained once using the currently encoded data to generate model parameters. After all iterations are completed, the trained neural point field model is obtained based on the generated model parameters; For each pixel of the image plane, a projection ray is generated. The sampling range of the projection ray in the physical field is determined by the outer surface grid, and spatial sampling points are generated within the sampling range. Spatial sampling points are input into the neural point field model to generate predicted field values. Based on the predicted field values, corresponding pixel colors are generated, and the image is drawn using a composite.

2. The method for rendering unstructured mesh volumes based on neural point fields according to claim 1, characterized in that, Extracting the outer surface mesh of the physical field from the original unstructured mesh data, including: Extract the topological connectivity of the original unstructured mesh and identify all boundary cells and boundary surfaces that constitute the outer boundary of the physical field. Based on the boundary elements and boundary surfaces, the complete outer surface mesh is extracted using a boundary tracing algorithm; The spatial extent of the physical field is determined based on the extracted outer surface mesh.

3. The method for rendering unstructured mesh volumes based on neural point fields according to claim 1, characterized in that, Determining the sampling range of the projected light within the physical field using the outer surface mesh includes: Calculate the intersection point of the projected ray and the outer surface mesh; The first intersection point entering the physical field along the direction of the light ray is taken as the sampling start point, and the last intersection point leaving the physical field is taken as the sampling end point. The sampling range is determined based on the sampling start point and the sampling end point.

4. A device for drawing unstructured mesh volumes based on neural point fields, characterized in that, include: The mesh extraction module is used to extract the outer surface mesh of the physical field from the raw unstructured mesh data. The dataset construction module is used to calculate the physical field spatial gradient of all nodes in the original unstructured mesh, and to perform adaptive sampling based on the magnitude of the physical field spatial gradient to obtain a training dataset containing the coordinates of the sampling points and the corresponding physical field values, including: The gradient calculation unit is used to calculate the spatial gradient vector of the physical field at each node of the original unstructured mesh using the Green-Gaussian gradient reconstruction method. The modulus calculation unit is used to calculate the modulus of the spatial gradient vector at each node, and use it as the gradient modulus of each node. The probability allocation unit is used to take the ratio of the gradient magnitude of each node to the sum of the gradient magnitudes of all nodes as the sampling probability of the corresponding node. The sampling execution unit is used to sample from all nodes according to the sampling probability of all nodes to generate sampling points in the training dataset; The model training module is used to train the pre-built neural point field model based on the training dataset using a strategy including multi-scale Fourier feature encoding, to obtain the trained neural point field model, including: The parameter configuration unit is used to configure a set of standard deviation values ​​for controlling the frequency of Fourier feature encoding; An iterative training control unit is used to iteratively execute training operations in ascending order of the standard deviation values. The training operations include: using the standard deviation value corresponding to the current iteration to perform Fourier feature encoding on the coordinates of the sampling points in the training dataset; and using the currently encoded data to perform one round of training on the neural point field model based on the model parameters or initial parameters obtained from the previous round of iterative training. The model generation unit is used to obtain the trained neural point field model based on the model parameters generated during training after all iterations are completed. The sampling point generation module is used to generate a projection ray for each pixel of the image plane, determine the sampling range of the projection ray in the physical field using the outer surface grid, and generate spatial sampling points within the sampling range. The image synthesis module is used to input spatial sampling points into the neural point field model to generate predicted field values, generate corresponding pixel colors based on the predicted field values, and draw images using the synthesized volume.

5. The unstructured mesh rendering device based on neural point fields according to claim 4, characterized in that, The mesh extraction module includes: The topology extraction unit is used to extract the topological connection relationships of the original unstructured mesh and identify all boundary cells and boundary surfaces that constitute the outer boundary of the physical field. Surface mesh building units are used to extract the complete outer surface mesh based on the boundary units and boundary surfaces using a boundary tracing algorithm; The spatial extent determination unit is used to determine the spatial extent of the physical field based on the extracted outer surface mesh.

6. The unstructured mesh rendering device based on neural point fields according to claim 4, characterized in that, The sampling point generation module includes: An intersection calculation unit is used to calculate the intersection point of the projected ray and the outer surface mesh; The key point determination unit is used to take the first intersection point entering the physical field along the direction of the light as the sampling start point and the last intersection point leaving the physical field as the sampling end point. The range definition unit is used to determine the sampling range based on the sampling start point and the sampling end point.

Images