Implicit surfaces are mathematical representations of shapes defined by a function that describes the points in space. Instead of using traditional polygons or meshes, an implicit surface is defined by an equation, such as f(x, y, z) = 0, where the surface consists of all points (x, y, z) that satisfy this equation. This allows for smooth and continuous shapes, making it easier to represent complex geometries. One common application of implicit surfaces is in computer graphics, where they are used to create realistic models and animations. They can also be found in 3D modeling software and simulations, providing advantages in rendering and collision detection due to their mathematical properties.