geometryprocessing

Geometry processing is a field at the intersection of computer graphics and geometric modeling that studies algorithms and techniques for the analysis, editing, and reconstruction of digital geometric data. It deals with shapes represented as polygonal meshes, point clouds, or implicit surfaces, and seeks to improve quality, extract information, or enable further processing and visualization.

Core tasks include smoothing and denoising to remove noise while preserving features; simplification and decimation to reduce data size; remeshing and parameterization to obtain desirable sampling and texture coordinates; and surface reconstruction from sparse, noisy, or incomplete data. Registration and correspondence align disparate shapes and enable shape averaging and morphing. Additional areas cover segmentation, feature detection, shape matching, geometry editing, and compression.

Common techniques combine local differential operators (for example Laplacian-based smoothing and curvature estimation), global optimization, spectral methods, and variational formulations such as Poisson surface reconstruction and Taubin smoothing.

Applications span computer-aided design, reverse engineering, 3D scanning and printing, character animation and virtual reality, medical imaging, and cultural heritage digitization.

Data representations include triangular and polygonal meshes, quadrilateral meshes, point clouds, and implicit surfaces, as well as hybrid approaches that fuse multiple forms.

Key challenges include dealing with measurement noise, holes and missing data, non-manifold geometry, preserving sharp features, topological changes, and computational efficiency for large models.

Geometry processing has roots in the late 1980s and 1990s, growing into a mature multidisciplinary area that combines techniques from graphics, geometry processing, and computation.