Data Density Requirements as Functions of Design Speed Controlling Accuracy of Representation of Horizontal and Vertical Curves in Surface Models for Automated Machine Guidance

When designed, horizontal and vertical highway alignment components are parametrically described geometric objects (e.g., smooth curves and straight lines). However, surface models resulting from highway design and for use in construction by automated machine guidance (AMG) are not geometrically smooth. Rather, they are triangulated irregular networks containing straight line segments that serve as edges of contiguous triangular facets. Designers and construction contractors must decide how frequently to discretize parametric design objects for adequate representation by such line segments in surface models. Higher data frequencies, or densities, result in more accurate representations of design. However, high data densities lead to large file sizes, greater storage and data management requirements, and greater data transfer times. This paper presents mathematical derivations that relate minimum required data densities to error tolerances for horizontal and vertical curves. Geometry, physics, and quantifiable human factors are used to couple expressions of tolerable error with parameters of curves and, more fundamentally, with design speeds. An example is provided in which the method was used to produce interim standards for electronic design AMG for data-sharing pilot projects with the Wisconsin Department of Transportation. The mathematics should be straightforward for incorporation in design software to ensure that individual design objects, groups of objects, or entire corridors are represented to acceptable levels of accuracy, with minimum data requirements, in surface models used for construction by AMG. The scope of this research is limited to control of discrete errors in representations of smooth curves by straight line segments. Uncertainties resulting from measurements are not addressed.