Parametric or Non-parametric? Understanding the Inherent Trade-offs between Forms of Object Representation

The need for efficient computing in construction modelling and analysis workflows often requires making tradeoffs between the inherent advantages and disadvantages of different datatypes being generated and managed. This is notably observed in geometry reconstruction (e.g., scan-to-BIM, reverse engineering, etc.), where a tradeoff often occurs between computational efficiency and the choice between increased semantic enrichment or increased representational accuracy (often both cannot be achieved simultaneously). This dichotomy can be generalized as a choice or tradeoff between parametric and non-parametric object representation forms. This paper presents a simple conceptual model for characterizing the datatypes used for representing and defining construction geometry to understand key tradeoffs that exist. First, we survey existing literature across multiple domains to identify and distill key attributes used in characterization according to the terms parametric and non-parametric. Then, we develop and illustrate a conceptual model using an analogy to mathematical expressions vs. discrete digital approximations employed in computer vision (e.g., Gaussian kernel, Hough Transform, and Scale Invariant Feature Transform (SIFT) algorithm). Finally, we outline future research opportunities for improving the state of object representation.