Ry, ry modeling and ry

The ry model represents an object by forming a semi-space formed by the edge interface of the ry. All attributes inside an object are the same. The so-called semi-space of a plane or surface is a space plane or surface that divides the space into two parts. If one part is located inside the object, the other part is located outside the object.

The development of the theory of ry modeling can be traced back to the 1970s S. Initially, the constructive solid geometry CSG (constructive solid geometry) method was used to roughly describe the created entities, then, the entity is converted to the boundary notation to represent the created model. The entity shape is mainly used to define the nominal geometric shape of the product. It emphasizes the universality and integrity of the model.AlgorithmThe problem of representation of any geometric shape is solved.

An object is a three-dimensional object with a single internal attribute. Entity modeling is the process of generating a closed entity through various methods and operations. Methods such as edge interface representation, implicit function representation, and the constructor ry described below can generate an object.

The CSG method is also called to construct the ry. A complex entity is generated by regular Boolean operations between simple entities. A binary tree structure is used to represent related entities and related parallel, cross, and differential Boolean operations. The leaf node represents the entity involved in the Boolean operation, and the intermediate operation result is used. The root node of the binary tree represents the final operation result. The CSG tree only reflects the construction process and method of the object, and does not reflect the geometric information of the surface, edge, vertex, and the relationship between them. Therefore, this representation is also called an implicit model or process model of an object.

For the basic body in the representation method, we need to give the relevant parameters of the body, and then the system will give the surface equation of the Body element. When performing the intersection operation, we will obtain the intersection through the surface equation. The intermediate results of the Boolean set operation are difficult to be expressed by a simple algebraic equation. Therefore, they cannot be involved in subsequent Boolean geometric operations. This method is inconvenient for the output of the final shape. Therefore, the CSG method is difficult to represent the intermediate ry. One method to solve this problem is to convert an object into a boundary representation during definition and perform Boolean ry operations. This is a common method in the entity modeling system.