3D Shape Modeling Using Perturbation Functions

The paper describes mathematical methods for setting free forms based on perturbation functions. Basic primitives in the form of quadrics are considered. Complex forms are created using quadrics and perturbation functions using set-theoretic operations (Boolean functions). These three-dimensional objects undergo geometric transformations such as scaling, moving, and rotating, and can be deformed, positioned, and oriented anywhere in three-dimensional space. Solid modeling and 3D modeling for 3D printing are briefly considered.