# Euclid's Muse

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# Search Results for “spline”

##### Not a spline
Where do you put the control points of a cubic spline in order for the spline to be a piece of a parabola? Explore here.  Prove using Geometry Expressions (or by hand).

Tags: spline, parabola

By Duncan
##### Cubic Spline
Many computer drawing programs use cubic splines to represent arcs. Our diagram shows how a spline can be constructed from 4 control points. We highlight that it is a moving average of two parabolas. These parabolas are exactly the string art parabolas.

Tags: spline, curve, parabola

##### Spline Approximation
Spline approximation to a quarter unit circle.  Can you find the best value for parameter a?

Tags: spline, circle

##### Spline Clock
This clock is made from 4 pieces of parabola.  Drag the red 'control points' to change its shape.

Tags: parabola, spline, clock

##### Curve Area
E is the midpoint of AD and F is the midpoint of BC.  A closed curve is made by joining the cubic spline whose control polygon is EABF to the spline whose control polygon is FCDE. Can you identify a relationship between the area of the curve and the area of the polygon ABCD?

Tags: spline, area, quadrilateral

##### Cubic Spline
Cubic Bezier splines are used in many computer drawing packages.  The red dots are control points, which control the shape of the curve.  There are two parametric cubic curves, tangential to the control polygon at 12 o'clock and 6 o'clock.  Drag the control points to see how the curve changes.  Compare with the curve formed by 4 pieces of parabola.

Tags: clock