Concept

Parametric surface

Related lectures (32)

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

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

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

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

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

Covers the concept of parametric surfaces and the importance of orientation.

Explores surface integrals over parameterized orientable surfaces and their applications in flux and work evaluation.

Explores developable surfaces, parametrization, equations verification, and conformally flat surfaces.

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

Explores Green's Theorem applied to surface integrals, emphasizing regular surfaces and coordinate transformations.

Explores regular surfaces and painting with normal vectors, integral calculations, symmetries, and surface orientation.

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

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

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

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

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

Explains the surface integral for vector fields and demonstrates its calculation process through examples.

Covers the calculation of areas using integrals for geometric regions defined by curves and parametric equations.

Covers the concept of bounding the Poisson bracket invariant on surfaces, exploring joint work with A. Logunov and S. Tanny.

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.