GaussMap

GaussMap is a computational tool designed to analyze and visualize the geometry of surfaces using Gaussian curvature. Developed primarily for mathematical and computational geometry research, it provides a means to study the intrinsic properties of surfaces embedded in three-dimensional space. The software is particularly useful in fields such as differential geometry, computer graphics, and computational biology, where understanding surface curvature is essential.

The tool operates by taking a triangulated surface mesh as input, which is a common representation of 3D shapes in digital form. GaussMap computes the Gaussian curvature at each vertex of the mesh, a measure that describes how the surface deviates from being flat at a given point. The software then generates visualizations, such as curvature heatmaps or 3D plots, to help users interpret the curvature distribution across the surface. Additionally, it can produce a Gauss map, a stereographic projection of the surface onto a sphere, which provides a compact representation of the surface’s curvature properties.

GaussMap is often used in conjunction with other geometric processing tools to perform tasks like surface simplification, shape analysis, or feature extraction. Its output can aid in identifying key geometric features, such as saddle points, peaks, or valleys, which are critical in applications like medical imaging, material science, and digital fabrication. The software is typically implemented in programming environments like MATLAB or Python, making it accessible to researchers and engineers with computational backgrounds.

While not a standalone commercial product, GaussMap is often integrated into academic research projects or open-source toolkits. Its simplicity and effectiveness make it a valuable resource for those working with complex surface geometries, bridging the gap between theoretical mathematics and practical applications.