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Generalized Distance Metric and Its Application of Worley Noise Function Implementation
조청운 (사)한국컴퓨터게임학회 2024 한국컴퓨터게임학회논문지 Vol.37 No.1
In this paper, a Manhattan distance measurement method is generalized and added by taking an absolute value in each axis direction, and a distance measurement method for two and three dimensions is presented. It is also used to apply it to the Worley noise function and implement it. Existing methods can only calculate for two dimensions, but in the proposed method, it can be applied to both two and three dimensions. In addition, with the newly proposed method, a wider range of pattern changes can be made when applied to the Worley noise function using Manhattan distance. In addition, since the concept of distance is a basic concept used in a wide variety of fields, generalizing it can be said to have a very important meaning. Focusing on the fact that the existing Manhattan distance appears in the form of a rhombus for two dimensions and an octahedron for three dimensions, we intend to expand it. The proposed method presents a generalized concept of distance by extending the existing Euclidean distance and Manhattan distance concepts for two and three dimensions using a very simple method. By applying this extended distance concept to the Worley noise function, richer and more diverse forms can be obtained, and procedural texture patterns based on the Worley noise can also produce more diverse results. In this study, the usefulness of the proposed distance calculation method can be confirmed by experimenting with patterns that can be obtained using the newly proposed method and showing examples of extended results of patterns that can be obtained from existing distance concepts.
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A Novel Two-Dimensional Distance Metric to Generalize Manhattan Distance
조청운 (사)한국컴퓨터게임학회 2023 한국컴퓨터게임학회논문지 Vol.36 No.3
Distance is a fundamental definition in fields such as geometry, mathematics, and physics. Because it is a very fundamental metric, it is not easy to create a new definition. In this study, we analyze existing distance definition and propose to generalize Euclidean distance and Manhattan distance, which are mainly used distance metric in existing distance definition. We analyze the definition of Minkowski distance, which is previously used as a concept of generalization along with Chebyshev distance, and the disadvantages of using this distance metric. By introducing a new perspective that interprets the existing Manhattan distance as a distance measured in four axes rather than simply adding the distances in each axis direction, this research introduces a new distance metric in two dimensions. This is a metric that generalizes the Euclidean distance and the Manhattan distance, and the proposed distance metric is derived from a geometrical aspect and an algorithm for calculating it is presented. We applied the existing distance definition and compared the differences through the results of generating a Voronoi area by the shortest distance from randomly distributed points in two dimensions. It is expected that the proposed method can be applied and expanded to the field of various graphics algorithms that use the distance metric.
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