Frenet-Serret Formulas: Curvature and Torsion

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Delves into the geometric principles of Gothic architecture, focusing on surface curvature and stereotomy techniques.

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

Explores curves, isometries, Bezier curves, and the Frenet coordinate system.

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

Explores the concept of envelope of curves within families of lines, including implicit equations, super-ellipses, and curvature.

Explores the concepts of curvature, oriented curvature, and inflection points in regular curves.

Explores the geometry of parametric curves, covering tangent vectors, curvature, and curve smoothing techniques.

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

Explores the theory of finite strain and rotation in Kirchhoff rods, covering inextensible strains, finite rotations, and equilibrium.

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