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Bezier Curves and Splines - MIT OpenCourseWare

Matusik Computer Graphics B zier Curves and Splines Wojciech Matusik MIT CSAIL Anything on your mind concerning Assignment 0? Any questions about the course? Assignment 1 ( Curves & Surfaces) Linear algebra review session 2 Before We Begin Smooth Curves in 2D Useful in their own right Provides basis for surface editing 3 Today This image is in the public domainSource:Wikimedia Commons Polylines Sequence of vertices connected by straight line segments Useful, but not for smooth Curves This is the representation that usually gets drawn in the end (a curve is converted into a polyline) Smooth Curves How do we specify them? A little harder (but not too much) 4 Modeling 1D Curves in 2D A type of smooth curve in 2D/3D Many different uses 2D illustration ( , Adobe Illustrator) Fonts ( , PostScript, TrueType) 3D modeling Animation: trajectories In general: interpolation and approximation 5 Splines ACM 1987 Principles of traditional animation applied to

Bézier Curves in Bernstein Basis • The plane where the curve lies, a 2D vector space • The space of cubic polynomials, a 4D space • Don’t be confused! • The 2D control points can be replaced by 3D points – this yields space curves. ... Bezier Curves and Splines ...

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