# spline4

This Catmull-Rom spline function is an optimized version of spline for the special case of only four knots.

spline4(t, knot1, knot2, knot3, knot4)
Returns the Catmull-Rom interpolation of the given knot values at the given parameter position.
COPY/// @func   spline4(t, knot1, knot2, knot3, knot4)
///
/// @desc   Returns the Catmull-Rom interpolation of the given
///         knot values at the given parameter position.
///
///         This is an optimized version of spline() for the special
///         case of four knots. See spline() for more details.
///
/// @param  {real}      t           interpolation parameter [0..1]
/// @param  {real}      knot1       1st spline knot value
/// @param  {real}      knot2       2nd spline knot value
/// @param  {real}      knot3       3rd spline knot value
/// @param  {real}      knot4       4th spline knot value
///
/// @return {real}      value on the spline
///

function spline4(t, knot1, knot2, knot3, knot4)
{
var k0, k3, c3, c2, c1, c0;
if (t <= 0) return knot2;
if (t >= 1) return knot3;
k0 = -0.5 * knot1;
k3 = 0.5 * knot4;
c3 = k0 + 1.5 * knot2 - 1.5 * knot3 + k3;
c2 = knot1 - 2.5 * knot2 + 2 * knot3 - k3;
c1 = k0 + 0.5 * knot3;
c0 = knot2;
return ((c3 * t + c2) * t + c1) * t + c0;
}


Contributors: xot

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