--- a/scripts/polynomial/spline.m
+++ b/scripts/polynomial/spline.m
@@ -20,23 +20,22 @@
 ## -*- texinfo -*-
 ## @deftypefn  {Function File} {@var{pp} =} spline (@var{x}, @var{y})
 ## @deftypefnx {Function File} {@var{yi} =} spline (@var{x}, @var{y}, @var{xi})
+## Return the cubic spline interpolant of points @var{x} and @var{y}.
+## 
+## When called with two arguments, return the piecewise polynomial @var{pp}
+## that may be used with @code{ppval} to evaluate the polynomial at specific
+## points.  When called with a third input argument, @code{spline} evaluates
+## the spline at the points @var{xi}.  The third calling form @code{spline
+## (@var{x}, @var{y}, @var{xi})} is equivalent to @code{ppval (spline
+## (@var{x}, @var{y}), @var{xi})}.
 ##
-## Return the cubic spline interpolant of @var{y} at points @var{x}.
-## If called with two arguments, @code{spline} returns the piecewise
-## polynomial @var{pp} that may later be used with @code{ppval} to
-## evaluate the polynomial at specific points.
-## If called with a third input argument, @code{spline} evaluates the
-## spline at the points @var{xi}.  There is an equivalence
-## between @code{ppval (spline (@var{x}, @var{y}), @var{xi})} and
-## @code{spline (@var{x}, @var{y}, @var{xi})}.
-##
-## The variable @var{x} must be a vector of length @var{n}, and @var{y}
-## can be either a vector or array.  In the case where @var{y} is a
-## vector, it can have a length of either @var{n} or @code{@var{n} + 2}.
-## If the length of @var{y} is @var{n}, then the 'not-a-knot' end
-## condition is used.  If the length of @var{y} is @code{@var{n} + 2},
-## then the first and last values of the vector @var{y} are the values
-## of the first derivative of the cubic spline at the end-points.
+## The variable @var{x} must be a vector of length @var{n}.  @var{y} can be
+## either a vector or array.  If @var{y} is a vector it must have a length of
+## either @var{n} or @code{@var{n} + 2}.  If the length of @var{y} is
+## @var{n}, then the "not-a-knot" end condition is used.  If the length of
+## @var{y} is @code{@var{n} + 2}, then the first and last values of the
+## vector @var{y} are the values of the first derivative of the cubic spline
+## at the endpoints.
 ##
 ## If @var{y} is an array, then the size of @var{y} must have the form
 ## @tex
@@ -52,7 +51,7 @@
 ## @ifnottex
 ## @code{[@var{s1}, @var{s2}, @dots{}, @var{sk}, @var{n} + 2]}.
 ## @end ifnottex
-## The array is then reshaped internally to a matrix where the leading
+## The array is reshaped internally to a matrix where the leading
 ## dimension is given by
 ## @tex
 ## $$s_1 s_2 \cdots s_k$$
@@ -61,9 +60,10 @@
 ## @code{@var{s1} * @var{s2} * @dots{} * @var{sk}}
 ## @end ifnottex
 ## and each row of this matrix is then treated separately.  Note that this
-## is exactly the opposite treatment than @code{interp1} and is done
-## for compatibility.
-## @seealso{ppval, mkpp, unmkpp}
+## is exactly opposite to @code{interp1} but is done for @sc{matlab}
+## compatibility.
+##
+## @seealso{pchip, ppval, mkpp, unmkpp}
 ## @end deftypefn
 
 ## This code is based on csape.m from octave-forge, but has been