TAILIEUCHUNG - Lecture Computer graphics - Chapter 8: Curve and Surface

This chapter presents the following content: Parametric curves & splines, cubic splines, hermite, bézier, b-splines, NURBS, subdivision curves & surfaces, appendix: subdivision masks. | Curve and Surface 1 Outline Parametric Curves & Splines Cubic Splines Hermite Bézier B-Splines NURBS Subdivision Curves & Surfaces Appendix: Subdivision Masks 2 How to describe this curve? 3 Control Points We can specify control points to draw the curve 4 Control Points Control points are not a unique specification 5 Polynomials A polynomial is a function of the form: f(t) = antn + an-1tn-1 + + a1t + a0 n is the degree of the polynomial The order of the polynomial is the number of coefficients it has Always: order = degree + 1 Examples: f(t) = a1t + a0 Linear f(t) = a2t2 + a1t + a0 Quadratic f(t) = a3t3 + a2t2 + a1t + a0 Cubic 6 Polynomial Curves Could make a curve that passes through n control points out of a degree (n-1) polynomial Regression, Lagrange interpolation, etc. 7 Polynomial Curves Polynomial curves wiggle too much when forced to fit more and more points. In technical terms this is called overfitting 8 Why Parametric Curves? Parametric curves are very flexible They are .

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