The concept of parametric method parameterization technology is rooted in the original and modified graphic structures. This system employs off-line parameterization, which differs from online approaches that typically require real-time user input. Instead, users define constraints directly within the drawing, using auxiliary lines as a foundational element. The system enables users to freely map and manipulate graphics, while internally recognizing both dimensional and geometric topological constraints—explicit or implicit—through these auxiliary lines. As a result, the auxiliary line becomes central to the constraint model, with all graphical entities (like lines and circles) and size entities linked to it. When dimensions change, the corresponding auxiliary lines are updated, triggering cascading updates across related elements, ensuring consistency throughout the design.
One key reason for adopting off-line parameterization is its alignment with traditional engineering drawing practices. Auxiliary lines are widely used in technical drawings to locate critical points, and they are typically simple elements such as dots, lines, or circles. These lines don’t stand alone but serve as guides to establish relationships between other elements. They represent geometric constraints in an intuitive and reliable way, making them ideal for parameterization. Their geometric properties are stable, and their construction and intersection handling are straightforward. Additionally, directionality can be incorporated into auxiliary lines, which is essential for fully expressing constraints. Since auxiliary lines often relate directly to dimensioning, it's efficient to extract and build them from existing dimension marks to define and identify graphic elements.
In CAD parametric design, the idea of parameterization can also be applied through auxiliary lines. Each step in the drawing process is structured, with each auxiliary line depending on at most one variable, resulting in a localized and efficient algorithm. From an engineering drawing perspective, elements are categorized into known and unknown components, just like sizes are divided into known and unknown values. In manual drafting, a strict sequence is followed: first, a reference point is established, then known elements are drawn based on known dimensions. Unknown elements are transformed into known ones by defining new dimensions, allowing the drawing to progress systematically until completion. This order is crucial for computer analysis of drawings.
To support this approach, the system uses an interactive database method. It allows users to define standard part graphics interactively and builds a database linking these graphics to their associated data. Standard parts must be parameterized, and their management is closely tied to the overall parameterization system. We have developed systems for mechanical and standard parts, including couplings (like bolts and nuts), support members (such as bearings), and structural components (like springs).
Two key technologies in the parametric system involve inserting parameter subgraphs into the main graph. This process ensures that the original image remains unaffected, while the parameter map continues to respond correctly to changes in size. The driver parameter diagram assumes that the parameter file drives the parameter map. The standard component parameterization database includes basic data in a specific format, along with a gallery of parametric prototype maps and methods for retrieving both data and graphics efficiently.
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