Research On Track Blocks Coding System With Rotational Invariance

The proportion of track building block game in toy market is increasing gradually,so the problem of building and optimizing building blocks is worth studying.When building blocks,we need to query and identify them firstly,and coding can improve the efficiency of recognizing and querying blocks,so it is necessary to establish an effective classification and coding system.Due to the benefit of enterprises,it needs to be adjusted because of the differences in coding objects and emphasis.The research object of this paper is n prism track blocks,with the characteristics of surface and body tracks.There are many kinds of building blocks formed by different arrangement and combination of tracks,and the internal spatial structure is complex.The internal spatial structure can't be represented by the existing coding schemes.In this paper,a method of representing the track block by two-dimensional function under polar coordinates is proposed.Firstly,the surface of the building blocks containing the track information is expanded,the problems in the three-dimensional space are transformed into the two-dimensional plane problems;the track height is transformed into the polar diameter independent of the physical length;the function value of the block function under the polar coordinates is the sum of the number of the track entrances and exits and the number of the center points.Secondly,due to the rotational invariance of the track block,the representation of the track block is not unique,so we have to specify a normal representation as the functional coding of the building block.On the contrary,we can get the building blocks from the two-dimensional discrete function or determine that there is no building block under this function.On the basis of the two-dimensional function under the polar coordinates,according to the basic tracks and relative position of building blocks,the building blocks are classified and encoded,and a compression form of coding is obtained.Experiments of three prism and six prism blocks by above steps show that this method has better expression of internal spatial structure and is more extendable than the traditional coding methods.When the two-dimensional discrete function representation of track blocks under polar coordinates is written in the form of a matrix,it can be regarded as a gray image with constant width and varying length,and the building block recognition is transformed into an image matching problem.In addition,the rotation problem that needs to be considered in building blocks is reflected in the translation of Y-axis in the rigidity transformation.Therefore,the phase correlation algorithm is used in this paper to judge the similarity between the two blocks.The results of matching the gray value images of the four orbital blocks show that the similarity between the blocks and the similarity between the two using the maximum value in the phase correlation to match the theory are consistent.So the solution of the coding problem and the matching problem in this paper is more adaptable for the problem of building and optimizing track blocks.