Concept

Parametrization (geometry)

Related lectures (31)

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Parametrized Curves in 2D

Covers the concept of parametrized curves in 2D and their properties.

Surface Orientation: Canonical Edge and Parametrization

Explains canonical surface edge orientation and parametrization using cylindrical coordinates.

Rotating Vectors in Physics 1

Explores rotating vectors in physics, emphasizing the norm-angular speed relationship and various coordinate systems.

Implicit Surface Parametrizations

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

Geometric Curve Reparameterization

Covers the reparameterization of geometric curves and the concept of 'same geometric curve'.

Shells I: Mechanics of Slender Structures

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

Parametrized Curves in 2D: Examples and Properties

Explores parametrized curves in 2D, including segments, straight lines, and circles with trigonometric functions.

Understanding Jacobian and Normal Vectors in Surfaces

Clarifies the use of Jacobian, normal vectors in surfaces, and arccos(z) constraints.

Surface Integrals: Regular Parametrization

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

Understanding Normal Vectors in Calculus

Delves into normal vectors in calculus, clarifying their role in integrals and parameterization of edges.

Parameterization of Curves

Explores parameterization of curves, emphasizing continuous settings and accurate curve representation through various examples.

Curve Parameterization

Explores curve parametrization, including setting curves, trace, and direction preservation.

Stereographic Projection: Sphere Parameterization

Explores stereographic projection and sphere parameterization, emphasizing regularity and line independence.

Vectorial Geometry: Affine Subspaces

Covers affine subspaces, lines, planes, intersections, cross product, and distance calculations in vectorial geometry.

Parametric Curves and Derivatives

Explores parametric curves, derivatives, equivalence of paths, and local behavior of functions.

Surface Integrals: Orientation and Computation

Explores orientable surfaces, scalar field integrals, and practical applications through examples with a sphere and a cone.

Surface Integrals: Scalar Fields

Covers the concept of surface integrals for scalar fields, focusing on regular, orientable surfaces in 3D space.

Surface Integrals and Parametrization

Explores the analogy between curves and surfaces, emphasizing the importance of choosing parameters for normal vectors.

Regular Curves and Constant Speed

Covers regular curves and constant speed, with examples of circles and helices.