Projection principle for constructing functional voxel models

This paper addresses the problem of automated generation of spatial digital models from flat drawings. The relevance of this problem is underscored by the wide range of existing approaches aimed at its solution. A novel aspect of this work is the application of analytical R-functional geometric modeling to these tasks, employing a structural approach for describing complex geometric objects through analytical functions. The principles of computer-aided analytical construction of complex geometric objects using functional voxel modeling (FV-modeling) are discussed. Such modeling ensures the transition from a continuous representation of the domain of analytical functions to a discrete-continuous computer analogue, based on multidimensional graphical image-models that store information about the local function at each point within the discrete domain. The principles of FV-modeling are applied to R-functional modeling functions, which serve as the foundation for analytical constructions of complex geometric object. The study demonstrates how the dimensionality of the argument space can be modified by introducing additional or removing redundant local geometric characteristics, thereby enabling the analysis of their influence on the function’s behavior. The paper explores the principle of increasing the dimensionality of a FV-model of a plane function domain for subsequent application of R-functional modeling methods to a three-dimensional space. By applying V.L. Rvachev’s principle of FV-modeling, the approach allows the computation of local geometric characteristics of a linear function, simplifying the computer representation of the R-functional model. Based on the law of planar rotation around an orthogonal axis, a principle for rotating a FV-model is introduced. This principle enables the construction of a spatial FV-model of a surface of revolution derived from a planar FV-model of a projection function. The developed FV-modeling tools can thus serve as an auxiliary means for addressing the core problem of generating three-dimensional models from two-dimensional projections (drawings).