Visualization of Geometric Models of Faceted Solids in Point Calculus

Abstract

The paper considers the case of faceted solids and discusses visualisation of geometric solids in the form of a three-parameter set of points which belongs to a three-dimensional space. To visualize geometric solids, taking advantage of the modern GPU hardware acceleration, the Ray marching method is used. The implementation considers the definition of a signed distance function, which is reduced to the task of determining the set of intersection points of the projection rays with the rendered geometric solid. After that, for each pixel of the screen, its color is determined in accordance with whether the ray passes through the geometric solid or not. The analytical description of geometric solids and the solution of their intersection problem with projecting rays are solved within the framework of the point calculus mathematical apparatus. As a result, it was concluded that the proposed approach justifies itself, providing high rendering performance and the complete absence of visual artifacts when rendering faceted solids.