TYPE: CHOP
TITLE: Area CHOP

This CHOP calculates the area under a channel's graph, which is the same as
calculating the "integral" of a channel, or "integrating" the channel.

It uses the graph of each input channel and calculates the area between the
graph and the 0-value line.  It finds the area between a Start and End index,
which is by default the entire CHOP range.

The area is calculated by adding the channel values for every sample, starting
with the sample at the Start index. Negative values reduce the area. The area
is converted to the Units by dividing by samples per Unit. The cumulative
values are put in the output channels.

This CHOP is particularly useful for calculating a point's position from its
velocity (speed) or acceleration. Given a velocity, a First Order integral
will return the position. Given an acceleration, a Second Order integral will 
return the position, and a First Order integral will return the velocity.

The first input contains the channels to be integrated.

The second input is used to reset the area to zero. At samples where the
second input is zero or less, the area is reset to zero.

The third input is an optional start/end reference. If connected, it will
override the parameters in the Range page and integrate the first input's
channels between the start and end of the reference input.

This CHOP can be time sliced by enabling the Time Slice flag in the Common page.

The Area CHOP can be used to calculate single, double and triple integrals.
It integrates:
~c(
a * i^3  +  b * i^2  +  c * i  +  d.
~c)

The Units parameter affects the output. The output is expressed in value
per sample, value per frame or value per second according to Units.

Parameters
Area
    Order           - Determines the order of the integral to use.
    First Constant  - Constant to add to the entire           /constant1
		      result after integrating once.
    Second Constant - Constant to add to the entire           /constant2
		      result after integrating twice.
    Third Constant  - Constant to add to the entire           /constant3
		      result after integrating three times.

Interval specifying the range to integrate over
    Unit Values     - Determines whether the start and end
		      parameters listed below are absolute or
		      relative to the channel's start and end.
    Start           - The start of the range over which to    /start
		      compute the area.
    End             - The end of the range over which to      /end
		      compute the area.

Local Variables:
    C          - current channel index
    NC         - total number of channels

See also: Math, Slope, Warp
