Spatial Curves: Intersections and Singularities

Related lectures (30)

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

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

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

Examines geometric singularities in architectural design through the analysis of spatial intersections.

Explores spatial curves, singularities, and mechanisms, analyzing their geometric properties and applications.

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Covers the geometric properties of hyperbolic paraboloids and hyperboloids, focusing on their construction and curvature characteristics.

Explores surfaces with variable curvature, constant curvature, and gothic surfaces, as well as singularities and the inversion of normals.

Covers the calculation of integrals over unclosed curves, focusing on essential singularities and residue calculation.

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