1. A computer-implemented method for rendering a computer-aided design model representing a real-world object, the method comprising: constructing a boundary representation data structure of the computer-aided design model, the boundary representation data structure storing topological data comprised of data defining a face; constructing a data structure representing a parameter space of the face; decomposing the parameter space into a plurality of cells; for each cell, indicating a presence of the face in the cell by designating the cell as one of an empty type cell, a full type cell, an edge type cell, and a vertex type cell; encoding the plurality of cells into a texture construct; transmitting the texture construct to a graphics processing unit where further processing renders the face on a computer monitor, wherein the edge type cell and the vertex type cell reference representations of one or more trimming surfaces, wherein the trimming surfaces correspond to neighboring faces of the face; and performing a ray casting process to render the face using data encoded in the texture construct as determined by an intersection of a ray and a surface corresponding to the face.