At the places where the polynomial pieces connect

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at the places where the polynomial pieces connect Analogy: Can be considered as a flexible strip used to produce a smooth curve through a designated set of points. Several small weights are distributed along the length of the strip to hold it in position on the drafting table as the curve is drawn. The term is used to describe a piecewise polynomial function used to represent or draw a curve. Spline surfaces: Splines are connected to form spline surfaces.
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Specifying Curves – Some Terminologies Control Points A set of points that influence the curve’s shape Knots Control points that lie on the curve Interpolating Splines Curves that pass through all of the control points (knots) Approximating Splines Polynomials are fitted to general control-point path without necessarily passing through any of the control points
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Specifying Curves Convex Hull The convex polygon boundary that encloses a set of control points. Imagine a rubber band stretched around the control points such that each of them is either on the perimeter of the hull or inside it. Useful for finding e.g. if a certain point lies on the curve or not, (in some cases)? Control Graph Set of connected line segments joining the control points in an ordered set.
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Convex Hull
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Control Graph
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Control Type local control
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  • Fall '19
  • Convex hull, Cubic Hermite spline, Interpolating Splines

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