Geodesics and Map Projections

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Related lectures (34)

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

Hyperbolic Geometry

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

Conformal Maps and Hyperbolic Geometry

Explores conformal maps, hyperbolic geometry, and isometric properties of disks.

Curvature and Inflection Points

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

Helical Curves: Theory and Applications

Explores the theory and applications of helical curves, focusing on circular helices with various parameters.

Projections: Types and Applications MOOC: Elements of Geomatics

Explores different types of map projections and their practical applications in geomatics, emphasizing the importance of preserving angles and choosing the right projection for accurate representation.

Rigidity in Negative Curvature

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Beams: Forces, Stresses, and Deformations

Analyzes beams, forces, stresses, deformations, curvature, deflection, and rigidity.

Altitude Models: Derivative Variables

Covers global relief indicators, altitude models, slope, orientation, curvature, and morphological indices for terrain description.

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture Log in to Mediaspace to watch this video

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

Differential Geometry: Parametric Curves & Surfaces Log in to Mediaspace to watch this video

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

Surfaces with Variable Curvature Log in to Mediaspace to watch this video

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

Shells I: Mechanics of Slender Structures Log in to Mediaspace to watch this video

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

Surfaces with Constant Curvature Log in to Mediaspace to watch this video

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

Geometric Principles in Architecture: Hyperboloids and Paraboloids Log in to Mediaspace to watch this video

Discusses geometric principles in architecture, focusing on hyperboloids and paraboloids and their applications in design and structural engineering.

Sphere Geometry: Properties and Projections Log in to Mediaspace to watch this video

Explores sphere properties, projections, and symmetry, including apparent contours and missing projections of points.

Plates II: Mechanics of Slender Structures Log in to Mediaspace to watch this video

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

Surfaces and Curvature in Geometry Log in to Mediaspace to watch this video

Explores surfaces with constant null curvature and their development, as well as the construction of networks of curves in hyperbolic paraboloids.

Curvature and Osculating Circle Log in to Mediaspace to watch this video

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

Minimal Surfaces and Discrete Differential Geometry Log in to Mediaspace to watch this video

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

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