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Course Recap and Asymptotic Grid Shells
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Related lectures (31)
Weingarten Application of Regular Surfaces
Covers the application of the Weingarten map on regular surfaces and the shape operator.
Hyperbolic Geometry
Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
Minimal Surfaces and Discrete Differential Geometry
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Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.
Differential Geometry: Parametric Curves & Surfaces
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Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.
Differential Geometry: Surfaces
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Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.
Principal Curvatures: Gaussian Curvature
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Explores principal curvatures and Gaussian curvature in the context of minimal surfaces, demonstrating their real-world applications.
Differential Geometry of Surfaces
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Covers the fundamentals of differential geometry of surfaces, including the equilibrium of shells, pressure vessels, and the curvature of surfaces.
Minimal Surfaces: Analytic Examples
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Explores minimal surfaces, their properties, history, classification based on curvature, and examples from the Minimal Surfaces Gallery.
Shells I
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Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.
Curve Tracing: Minimal Surfaces
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Explores minimal surfaces and asymptotic lines on curved surfaces.
Mean and Gaussian Curvature
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Explores mean and Gaussian curvature, emphasizing their calculation for different bases and surfaces.
Discrete Differential Geometry
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Covers topics in discrete differential geometry, including differential operators, Laplace-Beltrami operator, functions on triangle meshes, and discrete curvatures.
Differential Geometry of Surfaces
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Covers linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.
Geometric Surfaces: Paraboloids and Hyperboloids in Architecture
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Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.
Shells I: Mechanics of Slender Structures
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Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.
Computing Minimal Surfaces
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Explores the computation of minimal surfaces, Laplacian, Gauss curvature, numerical solutions, and mesh processing.
Shells I: Mechanics of Slender Structure
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Covers thin pressure vessels, differential geometry of surfaces, and plate buckling theories.
Surfaces and Curvature in Geometry
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Explores surfaces, curvature, ruled surfaces, and practical applications in geometry.
Surfaces with Variable Curvature
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Explores surfaces with variable curvature, discussing their construction and properties.
Gaussian Curvature in Plates
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Explores Gaussian curvature, principal curvatures, and nonlinear strain in thin elastic plates.
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