2D Objects : BPF / BPC
The BPF and BPC boxes
OM offers two types of objects for the manipulation of 2D curves :
the BPF and BPC objects - Break Point Function[1] and Break-Point Curve .
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Properties
Definition
A BPF represents a function as a set of 2D points with increasing x values.
In the mathematical sense, a BPF can be considered as a function y = f(x).
A break-point function defined by points (0 0), (14 46), (43 9), (89 19) and (97 , -1).
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A break-point curve defined by points (8,6) (90,41) (15,42) and (101,3).
A BPC is a free curve defined in a 2D plane.
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Inputs and Outputs
BPF and BPC objects have four inputs and outputs :
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“self” : as in every object box, represents the object instance itself - BPF or BPC
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” x-points” : abscissa, a list of positive or negative numbers
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” y -points” : ordinates, a list of positive or negative numbers
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“decimals” : a number of decimals representing the approximation or step value of the points.
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Creating BPF or BPC in a Patch
The BPF or BPC points can be set by connecting lists of values to the “x-points” and “y-points” inputs, or with the BPF/BPC editor.
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X-Points Order in BPFs
In a BPF, x-points must be in a strictly increasing order.
If the list is not ordered correctly, the points will be created from the y-points values and sorted automatically before the actual BPF is created.
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Incomplete Coordinates Lists
If the x or y list is shorter than the other, the last interval in the shorter list is repeated until the right number of points is reached.
For instance, this allows to create a BPF with a list of y-points and a periodic x interval.
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Decimals and BPF/BPC Precision
Rounding or increasing precision of the point coordinates with “decimals”.
The “ decimals” input determines the number of decimals per coordinates , that is, the precision of the curve.
Coordinates are therefore rounded according to the number of decimals.
If “decimals”= 0, all coordinates are rounded to the closest integer.
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References :
- Break Point Function
A “break-point” function is a function defined by a finite number of points (x,y).
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