Differential geometry of curves and surfaces

By V. Toponogov, V. Rovenski. 2006

352 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/8619f0495b516b9e9cefbd00875dc1d936620244

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In Biomedical Engineering

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Automatically parcellating the human cerebral cortex. (2004, background): “The first of these is the average convexity as defined in Fischl et al. (1999a), while the second is the mean curvature of the surface (do Carmo, 1976).”
Stress focusing in elastic sheets (2007, background): “DiDonna et al. (2002). Shown are two cross sections of the sheet.”
Predicting the soil moisture retention curve, from soil particle size distribution and bulk density data using a packing density scaling factor (2014, methodology): “We also fitted a cubic polynomial function to the overall predicted data and calculated the area between the fitted polynomial and the 1 : 1 line from the difference of the numerical integrals of these two functions (do Carmo, 1976).”
An Introduction to Differential Geometry with Applications to Elasticity (2006, background): “, do Carmo [1976]. This result is another special case of the fundamental theorem of Riemannian geometry alluded to in Section 1.”
From Golden Spirals to Constant Slope Surfaces (2009, background): “These curves are also known as rhumb lines (see [2]).”
SAL: Sign Agnostic Learning of Shapes From Raw Data (2019, background): “Plane reproduction is important for surface approximation since surfaces, by definition, have an approximate tangent plane almost everywhere [16].”
High-accuracy surface modelling and its application to DEM generation (2010, background): “The first fundamental coefficients are used to express how the surface inherits the natural inner product of R3, in which R3 is the set of triples (x, y, z) of real numbers (Carmo 2006).”
Concepts and techniques of optimization on the sphere (2014, background): “They can be found in many introductory books on Riemannian and differential Geometry, for example in [4], [5] and [22].”
Surface modelling of soil properties based on land use information (2011, methodology): “High accuracy surface modelling (HASM) was then developed in terms of fundamental theorem of surfaces (Okubo, 1987; Toponogov, 2006) by Yue et al.”