# Generally can be fitted to any number of control

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Generally can be fitted to any number of control points The no. of control points to be approximated and their relative position defines the degree of Bezier polynomial A Bezier curve is a polynomial of degree one less than the number of control points used. The curve always passes through first and last control points Bézier curve lies within the convex hull of the control points – good control over the curve It provides global control – change to one control point affects the overall shape of the curve
Quadratic Bezier Curve
Cubic Bezier Curves
B-Spline Curves Most widely used class of approximating splines Two advantages over Bezier splines The degree of a B-Spline polynomial can be set independent of the number of control points B-splines allow local control over the shape of a spline curve First and last control points need not to be knots. None of the control points have to essentially lie on the curve B-spline curves satisfy the strong convex hull property, so they have a finer shape control. B-spline curves require more information and a more complex theory than Bézier curves.
References Interactive Computer Graphics, A top-Down Approach Using WebGL, Edward Angel Computer Graphics with OpenGL, Hearn and Baker

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• Fall '19
• Convex hull, Cubic Hermite spline, Interpolating Splines

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