How do I make an xspline curve symmetric in R? - r

Question

I'm trying to draw a shape using the xspline function in R.
Using a set of control points, I can get the shape but it is asymmetric even though the points and shape values are all symmetric.
How do I draw this shape symmetrically?
This draws the approximate shape but the lines show how it is asymmetric.
curve <- data.frame(x=c(-0.1,-0.1,-0.1,-0.1,0.1,0.1,0.1,0.1,0.1,0.1,-0.1,-0.1,-0.1),y=c(0.1,0.1,0.1,0.3,0.3,0.1,0.1,-0.1,-0.1,-0.3,-0.3,-0.1,-0.1))
plot(curve)
xspline(curve,shape=1,open=F)
lines(x=c(-0.15,0.15),y=c(0.15,0.15),col="red")
lines(x=c(-0.15,0.15),y=c(-0.15,-0.15),col="red")
I have tried changing the shape values for each node but with no success.

Answer 1

Your question are actually two questions in one:
Is the curve (as a mathematical object) symmetric with respect to the x-axis?
Does it seem so in the picture?
Answer 2
Even if Answer 1 were "Yes" (which I doubt, see below), I think the answer is "No." Judging from the documentation, what xspline does is that it evaluates the curve at many points and then plots a polyline connecting these. You can persuade yourself: setting draw to F, the following should give you two arrays, one of x- and one of y-values.
curve <- data.frame(x=c(-0.1,-0.1,-0.1,-0.1,0.1,0.1,0.1,0.1,0.1,0.1,-0.1,-0.1,-0.1),y=c(0.1,0.1,0.1,0.3,0.3,0.1,0.1,-0.1,-0.1,-0.3,-0.3,-0.1,-0.1))
plot(curve)
pts=xspline(curve,shape=1,open=F,draw=F)
pts
I don't think there is any way of controlling the number or density of the evaluation points. So even if your curve (as a mathematical object, blue) is symmetric, its polyline rendering (black) is not necessarily:
This alone might explain the small differences from #Mike's comment.
Answer 1
We don't know exactly how R enforces the curve being closed. Based on the documentation,
For open X-splines, the start and end control points must have a shape of 0 (and non-zero values are silently converted to zero).
I suppose that it adds another control point at the very end, makes it equal to the first one and sets the shape of both of them equal to zero. But this is different from what your control points on the right hand-side of the picture look like! Your control point (0.1, 0.1) is repeated twice (not three times as (-0.1, 0.1) is) and its shape is 1, not 0 (caveat: the control point being repeated three times, maybe this does not have any influence; we would have to check the paper linked from the documentation).
I have adapted this and plotted the curve and its mirrored version so that we see the difference.
curve <- data.frame(
x=c(-0.1,-0.1,-0.1,-0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1,-0.1,-0.1,-0.1),
y=c( 0.1, 0.1, 0.1, 0.3, 0.3, 0.1, 0.1, 0.1,-0.1,-0.1,-0.3,-0.3,-0.1,-0.1))
xswap <- data.frame(
x=c( 0.1, 0.1, 0.1, 0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1, 0.1, 0.1, 0.1),
y=c( 0.1, 0.1, 0.1, 0.3, 0.3, 0.1, 0.1, 0.1,-0.1,-0.1,-0.3,-0.3,-0.1,-0.1))
plot(curve)
xspline(curve,shape=c(0,1,1,1,1,1,1,0,1,1,1,1,1,1),open=F)
xspline(xswap,shape=c(0,1,1,1,1,1,1,0,1,1,1,1,1,1),open=F)
lines(x=c(-0.15,0.15),y=c(0.15,0.15),col="red")
lines(x=c(-0.15,0.15),y=c(-0.15,-0.15),col="red")
To me they seem pretty much overlapping, especially taking the effects from Answer 2 into account.
General recommendations
Unless absolutely necessary, do not repeat control points. This tends to have funny effects on the underlying parametrization. More often than not (in my opinion), repeated control points come from people confusing control points with knots.
When you want symmetry with respect to the x-axis, put the first (and last) control point on it. Then you don't have to worry about finding the corresponding control point whose shape you have to set to 0.
For example,
curve <- data.frame(
x=c(0, 1, 1, 0, -1, -1),
y=c(1, 1, -1, -1, -1, 1))
curve_x_swapped <- data.frame(
x=c(0, -1, -1, 0, 1, 1),
y=c(1, 1, -1, -1, -1, 1))
plot(curve)
xspline(curve, shape=1,open=F)
xspline(curve_x_swapped,shape=1,open=F,border="red")