4.1 System requirement analysis
The purpose of this research is to develop a more general interactive art visualization system, which can support various common interactions with multimedia data of input devices such as voice, graphics, video, etc., and also support some virtual reality devices and provide different types of output representations. The following describes the research background of node based visual programming model from the perspective of interaction technology and visualization technology.
Interaction technology is a broad field. It uses a variety of technical methods to interact with the computer, which is characterized by high threshold. Art designers usually can only design ideas and concepts without much programming ability. The simple and friendly human-computer interaction is the basis of the platform design system, which can improve the design ability of art designers and reduce the complexity of design work.
In the system operation interface layer, the user's operation behavior can be summarized as follows: select the appropriate node type in the system operation interface: input node, output node or processing node; Get all the node objects required by the scene; Specify the data association between nodes by connecting them.
4.3 System visualization model
In this paper, K-Means clustering algorithm is selected to achieve clustering analysis of data. This algorithm can cluster disordered and chaotic data. First, select a point as the initial center, and then perform data calculation to analyze the distance between adjacent points. If the distance is relatively close, it can be defined as a high approximation class, and then replace the cluster points to continuously cycle the calculation, and finally end the calculation when the number of clusters reaches the threshold.
In K-Means clustering algorithm, it is very important to calculate the distance between each data point. Distance directly determines the classification of clustering. The Euclidean distance is used here to calculate the distance between these samples. Suppose the sample data xi={xi1, xi2,..., xim}, xj={xj1, xj2,..., xjm}, then the distance between xi and xj is:
$$\text{d}\text{i}\text{s}\text{t}\left({\text{x}}_{\text{i}},{\text{x}}_{\text{j}}\right)={\left(\sum _{\text{k}=1}^{\text{n}} {\left|{\text{x}}_{\text{i}\text{k}}-{\text{x}}_{\text{j}\text{k}}\right|}^{2}\right)}^{\frac{1}{2}}$$
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In this paper, we assume that the sample set is D={x1, x2,..., xm}, the final cluster obtained by K-Means algorithm is C={c1, c2,..., ck}, and the least squares error formula is:
$$\text{E}=\sum _{\text{i}=1}^{\text{k}} \sum _{{\text{x}}^{\text{ϵ}}{\mathcal{C}}_{\text{i}}} {∥\text{x}-{\text{u}}_{\text{i}}∥}_{2}^{2}$$
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Where, ui is the clustering mean vector ci, \({∥\text{x}-{\text{u}}_{\text{i}}∥}_{2}^{2}\) is the Euclidean distance from the cluster sampling point to the cluster center.
$${\text{u}}_{\text{i}}=\frac{1}{\left|{\mathcal{c}}_{\text{i}}\right|}\sum _{{ }^{\text{x}}\in {\mathcal{C}}_{\text{i}}} \text{x}$$
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If the amount of data connected to each point in the region we are processing is M, there are N such data points in the current region, and the bandwidth at this time is B, then if the calculation method used in processing is based on CPU, the required processing time is Tcpu, and when GPU is used for processing, the time is TGPU, where β 1 and β 2 is the number of iterations when CPU and GPU operations are used, respectively, β 2 > β 1.
$${\text{T}}_{\text{c}\text{P}\text{U}}=\text{M}\text{N}\text{B}{{\beta }}_{1}$$
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$${\text{T}}_{\text{G}\text{P}\text{U}}=\text{B}{{\beta }}_{2}$$
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The basic principle of direct volume translation is to capture the effect of light passing through translucent materials. A common translation integral can be expressed as follows:
$${\text{I}}_{{\lambda }}(\text{x},\text{r})={\int }_{0}^{\text{L}} {\text{C}}_{{\lambda }}\left(\text{s}\right){\mu }\left(\text{s}\right){\text{e}}^{-{\int }_{0}^{1} {\mu }\left(\text{t}\right)\text{d}\text{t}}\text{d}\text{s}$$
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Generally speaking, there is no analytic solution for the above integrals. Using Taylor expansion, approximate discrete results are obtained:
$${\text{I}}_{{\lambda }}(\text{x},\text{r})=\sum _{\text{i}=0}^{\text{L}/{\Delta }\text{s}} {\text{C}}_{{\lambda }}\left({\text{s}}_{\text{i}}\right){\alpha }\left({\text{s}}_{\text{i}}\right)\prod _{\text{j}=0}^{\text{i}-1} \left(1-{\alpha }\left({\text{s}}_{\text{j}}\right)\right)$$
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The above equation can be described by the following iterative operators:
$${\tilde{\text{C}}}_{\text{o}\text{u}\text{t}}^{{\prime }}={{\alpha }}_{\text{i}\text{n}}{\text{C}}_{\text{i}\text{n}}+\left(1-{{\alpha }}_{\text{i}\text{n}}\right){\tilde{\text{C}}}_{\text{o}\text{u}\text{t}}$$
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$${{\alpha }}_{\text{out }}^{{\prime }}={{\alpha }}_{\text{in }}+\left(1-{{\alpha }}_{\text{in }}\right){{\alpha }}_{\text{out }}$$
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It should be noted that the color here is divided into natural color and presentation color. The so-called natural color refers to the material itself multiplied by its opacity value α Previous color; The so-called color expression refers to multiplying by α The color after the value can be understood as the color observed by human beings. The relationship between expressive color and essential color can be described by the following formula:
$${\tilde{\text{C}}}_{\text{i}}={{\alpha }}_{\text{i}}{\text{C}}_{\text{i}}$$
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An important characteristic of over operator is that it satisfies the associative law, namely:
$$\left(\text{A}\text{ over }\text{B}\right)\text{ over }\text{C}=\text{A}\text{ over }\left(\text{B}\text{ over }\text{C}\right)$$
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The over part operator is very meaningful for parallel volume rendering, because the correct results of parallel volume rendering based on object space segmentation can only be obtained by satisfying the association law, which is the theoretical basis of object space parallelism in parallel volume rendering.