Locally refined spline surfaces for terrain and sea bed data: tailored approximation, export and analysis tools

TL;DR

This paper introduces Locally Refined B-spline surfaces as an efficient, smooth, and adaptable method for representing terrain and seabed data, offering advantages over traditional raster and triangulated models.

Contribution

It presents the LR B-spline surface format tailored for compact, locally adaptive modeling of terrain and seabed data, with tools for approximation, export, and analysis.

Findings

Provides a compact, smooth representation of terrain data

Allows local detail modeling with limited data growth

Enables export to standard formats like STEP

Abstract

The novel Locally Refined B-spline (LR B-spline) surface format is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline surface has an overall smooth behaviour and allows the modelling of local details with only a limited growth in data volume. In regions where many data points belong to the same smooth area LR B-splines allow a very lean representation of the shape by locally adapting the resolution of the spline space to the size and local shape variations of the region. The surfaces generated approximate the smooth component of a cloud of data points within user specified tolerances. The method can be modified to improve the accuracy in particular domains and selected data points. The resulting surfaces are well suited for analysis and computing secondary information such as contour curves and minimum and maximum points. The surfaces can be translated into a raster or a tessellated surface of desired quality or exported as collections of tensor product spline surfaces. Data transfer can also be performed using Part 42 of ISO 10303 (the STEP standard) where LR B-splines were published in 2018.