Lecture

Developable Surfaces and Parametrization

Related lectures (29)

Explores stereographic projection and metric tensors on hyperbolic planes, emphasizing isometry and conforming models.

Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.

Explores implicit surface parametrizations and the use of metric tensors in surface parameterization.

Explains the parametric equations of surfaces of revolution generated by curves in space.

Covers linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Covers thin pressure vessels, differential geometry of surfaces, and plate buckling theories.

Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Explores the second fundamental tensor and its role in calculating normal curvature on surfaces.

Covers the intersection of manifolds in exercise 8.2 and fiscal year 8.8.

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

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

Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.

Covers the calculation of angles between curves on regular surfaces and the concept of curvilinear abscissa.

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

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

Covers conforming configurations in veneering, focusing on the pseudosphere example.