In the digital age, the importance of access to cultural heritage through virtual environments is increasing. One of the key aspects of creating a high-quality digital representation of museum exhibits is modeling their physical attributes with a high degree of detail. This work describes the development of a method for the virtual representation of museum exhibits by creating three-dimensional models based on algorithms for the intersection of various geometric shapes. We have classified the typical geometric shapes of the exhibits and developed algorithms to accurately simulate their interactions. This allows for more accurate and realistic visualization of exhibits in virtual space, thereby improving user interaction with cultural heritage through digital technologies. The application of this approach helps to expand access to museum collections and opens up new opportunities for education and research.