Lecture

Bezier Curves: Fundamentals and Applications

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In course

CS-341: Computer graphics

The students study and apply fundamental concepts and algorithms of computer graphics for rendering, geometry synthesis, and animation. They design and implement their own interactive graphics programs. ...

Description

This lecture covers the fundamentals of Bezier curves, starting with the de Casteljau algorithm for curve generation and the geometric interpretation of control points. It also explains the Bernstein basis and recursion for evaluating Bezier polynomials. The lecture concludes with practical applications of Bezier curves in 2D vector drawing, 3D computer-aided design, and true-type fonts.

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Instructor

Mark Pauly

Mark Pauly is a full professor at the School of Computer and Communication Sciences at EPFL. Prior to joining EPFL, he was assistant professor at the CS department of ETH Zurich since April 2005. From August 2003 to March 2005 he was a postdoctoral scholar at Stanford University, where he also held a position as visiting assistant professor during the summer of 2005. He received his Ph.D. degree (with distinction) in 2003 from ETH Zurich and his M.S. degree (with highest honors) in 1999 from TU Kaiserslautern. His research interests include computer graphics and animation, shape modeling and analysis, geometry processing, architectural geometry, and digital fabrication. He received the ETH medal for outstanding dissertation, was awarded the Eurographics Young Researcher Award in 2006 and the Eurographics Outstanding Technical Contributions Award in 2016.

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Related concepts (18)

AutoCAD

AutoCAD is a 2D and 3D computer-aided design (CAD) software application for desktop, web, and mobile developed by Autodesk. It was first released in December 1982 for the CP/M and IBM PC platforms as a desktop app running on microcomputers with internal graphics controllers. Initially a DOS application, subsequent versions were later released for other platforms including Classic Mac OS (1992), Microsoft Windows (1992), web browsers (2010), iOS (2010), macOS (2010), and Android (2011).

Vector graphics

Vector graphics is a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as points, lines, curves and polygons. The associated mechanisms may include vector display and printing hardware, vector data models and file formats, as well as the software based on these data models (especially graphic design software, computer-aided design, and geographic information systems).

BRL-CAD

BRL-CAD is a constructive solid geometry (CSG) solid modeling computer-aided design (CAD) system. It includes an interactive geometry editor, ray tracing support for graphics rendering and geometric analysis, computer network distributed framebuffer support, scripting, image-processing and signal-processing tools. The entire package is distributed in source code and form. Although BRL-CAD can be used for a variety of engineering and graphics applications, the package's primary purpose continues to be the support of ballistic and electromagnetic analyses.

Vector graphics editor

A vector graphic editor is a computer program that allows users to compose and edit vector graphic s interactively on a computer and save them in one of many popular vector graphic formats, such as EPS, PDF, , SVG, or VML. Vector editors are often contrasted with bitmap editors, and their capabilities complement each other. Vector editors are often better for page layout, typography, logos, sharp-edged artistic illustrations (e.g. cartoons, clip art, complex geometric patterns), technical illustrations, diagramming and flowcharting.

Bézier surface

Bézier surfaces are a species of mathematical spline used in computer graphics, computer-aided design, and finite element modeling. As with Bézier curves, a Bézier surface is defined by a set of control points. Similar to interpolation in many respects, a key difference is that the surface does not, in general, pass through the central control points; rather, it is "stretched" toward them as though each were an attractive force. They are visually intuitive and, for many applications, mathematically convenient.

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