# Changing a control point only affects the curve

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Changing a control point only affects the curve locally Makes it easy to control the shape of the curve In opposition to: global control Example (local control): Moving one control points affect locally
Parametric Continuity Conditions To ensure smooth transition from one section of a piecewise parametric curve to the next, we can impose various continuity conditions at the connection points. Controls continuity and smoothness between parametric curves
a) Geometric Continuity: G0: curves are joined G1: first derivatives are proportional at joint point, same direction but not necessarily same length G2: first and second derivatives are proportional b) Parametric Continuity: C0: curves are joined C1: first derivatives are equal (magnitude and direction) C2: first and second derivatives are equal. If t is the time, this implies the acceleration is continuous. Cn: all derivatives up to and including the nth are equal.
Interpolating Splines Hermite Interpolation Defined by two points (P 0 and P 1 ) and two tangents Controlled locally Cardinal Splines Needs four points. Calculates the tangents by using two extra control points Kochanek-Bartels Splines Same as cardinal, with extra parameters, tension, bias Hermite Spline
Bezier Curves An approximating spline Specify at least two extra control points for joining the splines

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

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