Surfaces with Variable Curvature

Related lectures (29)

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Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Explores surfaces with variable curvature, discussing their construction and properties.

Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Explores Gaussian curvature, principal curvatures, and nonlinear strain in thin elastic plates.

Explores surfaces with constant curvature, emphasizing the significance of minimal oriented radius and the properties of pseudo-spheres.

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Explores the mechanics of slender structures, discussing plate evaluation, bending energy, and curvature tensors.