Extension of the Dynamic Geometry Software for CeDG Support and Application to the Accurate Flattening of Developable Spatial Surfaces
摘要
CeDG is a computer-based approach to build parametric 3D models of systems based on Descriptive Geometry (GD) procedures. The CeDG version used in previous studies was based on a raw version of GeoGebra (dynamic geometry software), which did not implement new tools, and particularly commands to measure lengths in locus based curves. This limitation prevented the complete implementation of the method to calculate the true flat pattern of oblique conical surfaces, forcing the use of approximation methods. In this study, we have extended GeoGebra with a set of new commands—tools, including several focused to the computation of lengths along locus—based curves. The flat pattern of a generic oblique cone has been computed using these new tools, as a case study to assess the accuracy and computational efficiency of the Geogebra extension for CeDG. Although the system was flattening with minor errors (0.4–1.3%), and the extension of GeoGebra supports the reliability and functionality of the new tools, the computation of locus lengths induced some ripple and loss of smoothness in the dynamic response of the system. Our findings suggest that the GeoGebraScript code and tools—command techniques used in CeDG evolution should be combined with Java/C GeoGebra source additions to reach a better computer efficiency in CeDG.