Lecture

Parametric Curves: Basics and Applications

Related lectures (29)

Explores involutes and Bezier curves, essential in computer-aided design.

Covers Bezier curves, de Casteljau Algorithm, properties, derivatives, splines, and end-points.

Explores the fundamentals and applications of Bezier curves, focusing on their construction, properties, and practical uses in design and modeling.

Covers the basics of Bezier curves and introduces Bernstein polynomials.

Explains tangent vectors of curves and the construction and applications of Bézier curves in computer graphics.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Explores geometric modeling using splines and freeform deformation for creating smooth surfaces and deformable objects in 3D space.

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

Covers the representation of plane curves and the nature of obtained curves.

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

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

Explores parametric curves, focusing on finding envelopes and caustics.

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

Covers the calculation of areas using integrals for geometric regions defined by curves and parametric equations.

Introduces Bezier curves, covering generation algorithms, control points interpretation, and practical applications in design and fonts.

Covers Descartes' Folium, a parametric curve with specific equations and properties, including domain boundaries and tangent vector analysis.

Introduces working with surfaces, polysurfaces, and solids in Rhino, covering rendering, material editing, and mesh creation.

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

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

Covers revisions on calculus, derivation rules, interpolation, and tangent vectors.