keyword
surface fitting
Surface fitting is a computational technique in geometric modeling, computer graphics, and computer vision that constructs a continuous or discrete mathematical surface to approximate or interpolate a given set of spatial data points. The process typically transforms unorganized three-dimensional coordinate measurements, such as point clouds captured by range scanners or photogrammetry, into coherent geometric representations like polygonal meshes, implicit surfaces, or spline patches. In addition to minimizing distance errors between the constructed surface and the input data, surface fitting methods commonly optimize for desirable geometric properties, including surface smoothness, appropriate topology, and conciseness of representation. This approach is widely applied across reverse engineering, computer-aided design, medical imaging, and scientific visualization to convert raw point samples into structured and usable digital three-dimensional models.
2 items
Mesh optimization
Hugues Hoppe, T. DeRose, T. Duchamp, J. McDonald, W. Stuetzle
Why you should read this
Develops an energy-minimization framework that jointly optimizes mesh connectivity and vertex positions to accurately fit 3D point sets while reducing geometric complexity, recovering sharp features for both surface reconstruction and mesh simplification.
We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0, that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles).
Added
2026-09-24
Surface reconstruction from unorganized points
Hugues Hoppe, Tony DeRose, Tom Duchamp, John McDonald, Werner Stuetzle
Why you should read this
Presents a foundational method for reconstructing 3D surfaces of arbitrary topology and boundary configurations from unorganized point clouds by estimating a signed distance function through consistently oriented local tangent planes and extracting the resulting zero-set mesh.
We describe and demonstrate an algorithm that takes as input an unorganized set of points {x1, . . . , xn} ⊂ IR3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be known in advance — all are inferred automatically from the data. This problem naturally arises in a variety of practical situations such as range scanning an object from multiple view points, recovery of biological shapes from two-dimensional slices, and interactive surface sketching.
Added
2026-09-11