Mathematical Algorithms for the Texture and Lighting of 3D Surfaces in a Computer

At present, the generation of 3D objects by computer has become a fundamental tool for the development of most sciences. Modeling a three-dimensional surface on a computer whose display is a two-dimensional graphic screen presents some challenges such as simulating the depth on the graphic screen. To overcome this drawback, the authors propose to use Vector Differential Analysis (Differential Geometry), since calculating the normal vector to the Surface eliminates hidden sections and differentiates external faces of internal faces to texturize differently. In the same way, taking advantage of the properties of the Vector Gradient, it is possible to simulate light intensities on the surfaces.