

2.2.1.9 Spline Identifiers
Splines give you a way to define 'pathways' through your scenes. You specify a series of points, and POVRay
interpolates to make a curve connecting them. Every point along the spline has a numerical value. A good example of a
spline is the path of a moving object: the spline itself would be the path traced out by the object and the
'parameter' would be time; as time changes the object's position moves along the spline. Therefore, given a time
reference you could use this spline to find the position of the object. In fact, splines are very well suited to
animation.
The syntax is:
SPLINE_DECLARATION:
#declare IDENTIFIER =
spline {
[SPLINE_IDENTIFIER] 
[SPLINE_TYPE] 
[Val_1, <Point_1>[,]
Val_2, <Point_2>[,]
...
Val_n, <Point_n>]
}
SPLINE_TYPE:
linear_spline  quadratic_spline  cubic_spline  natural_spline
SPLINE_USAGE:
MySpline(Val)  MySpline(Val, SPLINE_TYPE)
The first item gives the type of interpolation. In a linear_spline , straight lines connect each
point. In a quadratic_spline , a smooth curve defined by a secondorder polynomial connects each
point. In cubic_spline and natural_spline ,
a smooth curve defined by a thirdorder polynomial connects each point. The default is linear_spline .
Following this are a number of float values each followed by a position vector, all separated by commas. Val_1 ,
Val_2 , etc, are the value of the spline parameter at each specific point. The points need not be in order
of their parameter values. If two points have the same parameter value, the second point will replace the first.
Beyond the range of the lowest and highest parameter values, the spline position is fixed at the endpoints.
Note: Because of the way cubic_splines are defined: the first and last points are
tangents rather than points on the spline, cubic_spline interpolation is only valid between the second and
nexttolast points. For all other spline types, interpolation is valid from the first point to the last point. For
tvalues outside the valid range, POVRay returns the value of the nearest valid point.
To use a spline, you place the spline identifier followed by the parameter (in parentheses) wherever you would
normally put a vector, similar to a macro. Splines behave mostly like threedimensional vectors. Here is an
example:
camera { location <0,2,2> look_at 0 }
light_source { <5,30,10> 1 }
#declare MySpline =
spline {
cubic_spline
.25, <0,0,1>
0.00, <1,0,0>
0.25, <0,0,1>
0.50, <1,0,0>
0.75, <0,0,1>
1.00, <1,0,0>
1.25, <0,0,1>
}
#declare ctr = 0;
#while (ctr < 1)
sphere {
MySpline(ctr),.25
pigment { rgb <1ctr,ctr,0> }
}
#declare ctr = ctr + 0.01;
#end
You can also have POVRay evaluate a spline as if it were a different type of spline by specifying the type of
spline after the value to interpolate at, for example:
sphere{ <2,0,2>, .25 pigment{rgb MySpline(clock, linear_spline)}}
Splines are 'intelligent' when it comes to returning vectors. The vector with the most components in the spline
determines the size of the returned vector. This allows vectors from two to five components to be returned by splines.
Also, function splines take the vector size into account. That is, a function containing a spline with five
components will also return a five component vector (aka a color), a function containing a spline with two components
will only return a two component vector and so on.
2.2.1.9.1 Splines and Macros
You can pass functions to macros, how to do this is best explained by an example
#macro Foo( Bar, Val )
#declare Y = Bar(Val).y;
#end
#declare myspline = spline {
1, <4,5>
3, <5,5>
5, <6,5>
}
Foo(myspline, 2)
#debug str(Y,5,5)
#debug "\n"

