When you load the cubic spline toy into a browser, you should see four coloured dots and a black curve that passes through them all. (This doesn't work with some browsers. See here for a list of known exceptions.) You can use your mouse to drag the dots around. When you do, the curve changes so as to still pass through them all.
The dots are the control points of the cubic spline curve which passes through them all. There are also "control points", but you won't get to see those.
This isn't of much interest. But if you can arrange your browser window so that it's twice as wide as it is long, you'll have access to some controls that leat you change the features of the curve. This page aims to explain what those controls do.
The first control is a set of seven fawn buttons that you can use to change a parameter of the program that calculates the curve (a cubic spline). By clicking a suitable button, you can increase or decrease its value, fast or slowly; and you can change it from positive to negative and back. Its proper value is 6. Other values can generate more interesting results.
Negative values cause the arcs to curve "the wrong way" and render the whole structure "inside-out". This often gives more pleasing results.
Values close to zero prevent sharp curves, leading to structures which extend far from the fixed points. This is why there's a "zoom" option.
The second control is a set of fawn buttons that you can use to change whether the dots (the "fixed points" of the cubic spline are visible. You may want them hidden, so as to better appreciate the curve itself. While the dots are not visible, you won't be able to drag them.
This line also allows you to change the number of dots. You can't have more than twelve, nor fewer than two.
The dots have a cyclic order, which is loosely based on the colours of the rainbow. You can't change that order. It goes red - orange - yellow - lime green - green - cyan - light blue - dark blue - magenta - light grey - mid grey - dark grey. New dots all appear in the same place, but you can always move the top one.
There is always a background grid to the region where the dots start, though it is initially not displayed. You can make make it visible by clicking the checkbox.
The purpose of a grid is to enable more precise placing for the dots. You can have a regular background to place them on, and once you have them nearly right you can use "Snap to grid" to place then precisely on an intersection of the grid. If the dots are outside the area of the visible grid, they still get placed precisely on where there would be an intersction if the visible grid extended that far.
You can also use a "radio button" to select a different grid. For example, if you want a placement of dots that has 7-fold symmetry, you should use the "polar 7" grid.
You can zoom in and out.
If you have exactly four points, and arrange for two of them adjacent in the cycle to be in the same place, and set the parameter close to -0.6, you will get a curve that is tangential to itself in two places. If you then increase the parameter to -0.5, or reduce it to -0.7, the points of tangency become double crossings.
The cubic spline toy itself
The index to these pages
