Differential Geometry of Curves and Surfaces

By Kristopher Tapp. 1952

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

PCPNet Learning Local Shape Properties from Raw Point Clouds (2017, background): “In the context of continuous surfaces, local surface properties such as normals and curvature are classical differential geometric notions [dC76] and are known to uniquely characterize local geometry up to rigid transformations.”
Gravitational bending angle of light for finite distance and the Gauss-Bonnet theorem (2016, methodology): “Then, the Gauss-Bonnet theorem can be expressed as [34]”
A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes (2015, background): “While details on this map can be found in the literature [12, 13], it is sufficient for our purpose to quickly recall its definition.”
The Fundamental Theorem of Surface Theory for Surfaces with Little Regularity (2003, methodology): “For the local version of this result, we refer the reader to [5, 17–20].”
Novel computer program for fast exact calculation of accessible and molecular surface areas and average surface curvature (2002, methodology): “The matrix of external-internal relationship between each pair of cycles A and B is determined, using the stereographic projection.(11,12) 2.”
Surface modelling of soil pH (2009, background): “According to fundamental theorem of curves (Okubo, 1987; Toponogov, 2006), curvature, slope and intercept uniquely define a curve, and a surface is uniquely defined by the first and the second fundamental coefficients.”
3D quantitative shape analysis on form, roundness, and compactness with μCT (2016, background): “According to Do Carmo [49], all curves lying on S and having the same tangent vector T at p have the same normal curvature at this point.”
A signal processing approach to fair surface design (1995, background): “It is known that, for a curvature continuous surface, if the curve is let to shrink to to the point vi, the integral converges to the mean curvature (vi) of the surface at the point vi times the normal vector Ni at the same point [7]”
Designing Responsive Buckled Surfaces by Halftone Gel Lithography (2012, methodology): “Written in terms of the coordinates on the flat, unswelled gel sheet, the target curvature at a material point r is set by the swelling factor Ω(r) according to Gauss’s theorema egregium, K = −∇(2) lnΩ/(2Ω) (25).”
Affordance detection of tool parts from geometric features (2015, background): “3) Principle curvatures (PCurv): The principle curvatures [8] are an extrinsic invariant of the local patch geometry, and are independent of viewpoint.”
Fundamentals of spherical parameterization for 3D meshes (2003, methodology): “The theory of mappings between various Riemann surfaces is well understood in the continuous case using classical differential geometry [7].”
Continuous Mesh Framework Part I: Well-Posed Continuous Interpolation Error (2011, background): “We refer to [2, 3, 12] for a complete review on Riemannian metric spaces.”
A review of numerical methods for nonlinear partial differential equations (2012, methodology): “Finite-diﬀerence methods consist of a discrete grid, Ω Δ := { x j } , and a gridfunction, W Δ := { W j } .”