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Splitting curves
Using de Casteljau's algorithm, we can also find all the points we need to split up a Bézier curve into two, smaller curves, which taken together form the original curve. When we construct de Casteljau's skeleton for some value t, the procedure gives us all the points we need to split a curve at that t value: one curve is defined by all the inside skeleton points found prior to our on-curve point, with the other curve being defined by all the inside skeleton points after our on-curve point.
implementing curve splitting
We can implement curve splitting by bolting some extra logging onto the de Casteljau function:
left=[]
right=[]
function drawCurve(points[], t):
if(points.length==1):
left.add(points[0])
right.add(points[0])
draw(points[0])
else:
newpoints=array(points.size-1)
for(i=0; i<newpoints.length; i++):
if(i==0):
left.add(points[i])
if(i==newpoints.length-1):
right.add(points[i+1])
newpoints[i] = (1-t) * points[i] + t * points[i+1]
drawCurve(newpoints, t)
After running this function for some value t, the left and right arrays will contain all the coordinates for two new curves - one to the "left" of our t value, the other on the "right". These new curves will have the same order as the original curve, and can be overlaid exactly on the original curve.
This is best illustrated with an animated graphic (click to play/pause):