How do STL files represent the complex, smooth surfaces of CAD models?

STL files represent the complex, smooth surfaces of CAD models using a series of interconnected triangles. This triangulation approach is essential because it simplifies the representation of 3D geometry for additive manufacturing processes. Each triangle consists of three vertices, and by combining many of these triangles, intricate shapes and smooth surfaces can be approximated.

The use of triangles is particularly advantageous in 3D printing because it allows for a uniform representation regardless of the complexity of the surface being modeled. Each triangle can be defined using just its vertex positions, making the file format relatively straightforward and compatible with various 3D printing software.

In contrast, options such as a collection of curves or a grid of surfaces are not typical representations in STL files. Curves would imply a different approach to modeling that STL does not support, while a grid of surfaces could be more complex and less efficient for 3D printing. A mesh of points also does not capture the surface information needed for additive manufacturing effectively. Thus, the connectivity and simplicity of interconnected triangles make them the ideal choice for representing the geometry in STL files, enabling accurate and efficient translation from digital models to physical parts.