我有一个dataframe，看起来像这样：

df <- data.frame(dates = c("2020-12-31", "2021-01-31"),
                 x1 = c(0.50, 0.60),
                 x3 = c(1.00, 0.90),
                 x5 = c(1.50, 1.80),
                 x7 = c(2.00, 2.10),
                 x12 = c(2.50, 2.60),
                 x15 = c(3.00, 3.10))

我想插值使用样条曲线之间的每列（并添加一列之间存储插值）。因为每一行都是一个日期，所以每一行只能逐行跨列插值。我希望输出看起来像这样：

df_inter <- data.frame(dates = c("2020-12-31", "2021-01-31"),
                       x1 = c(0.50, 0.60),
                       x2 = c(0.75, 0.65),
                       x3 = c(1.00, 0.90),
                       x4 = c(1.25, 1.35),
                       x5 = c(1.50, 1.80),
                       x6 = c(1.75, 1.95),
                       x7 = c(2.00, 2.10),
                       x8 = c(2.10, 2.20),
                       x9 = c(2.20, 2.30),
                       x10 = c(2.30, 2.40),
                       x11 = c(2.40, 2.50), 
                       x12 = c(2.50, 2.60),
                       x13 = c(2.70, 2.80),
                       x14 = c(2.70, 2.90),
                       x15 = c(3.00, 3.10))

真实的的dataframe有几百行。