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Search Results for “spline”

By Phil Todd
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

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

Tags: spline, circle

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

Tags: parabola, spline, clock

By Phil Todd
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

By admin
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

By admin
Parabolic Spline
This clock is made from four pieces of parabolas.  The 3,9,6 and 12 o'clock positions are midway between the red control points.  The parabolas pieces go from 12 to 3, 3 to 6, 6 to 9 and 9 to 12, and are tangential to the lines joining the control points.

Tags: clock

By Phil Todd
Bezier curvature
The control polygon for this Bezier curve is the trapezoid ABCD.  The circle of curvature at point L on the curve is shown. Can you come up with a formula for the radius of curvature at the ends of the curve?

Tags: Bezier, spline, curvature


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