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2D Objects : BPF / BPC

The BPF and BPC boxes

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 .

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). A break-point function defined by points (0 0), (14 46), (43 9), (89 19) and (97 , -1).

A break-point curve defined by points (8,6) (90,41) (15,42) and (101,3). 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.

Inputs and Outputs

BPF and BPC objects have four inputs and outputs :

  1. “self” : as in every object box, represents the object instance itself - BPF or BPC

  2. ” x-points” : abscissa, a list of positive or negative numbers

  3. ” y -points” : ordinates, a list of positive or negative numbers

  4. “decimals” : a number of decimals representing the approximation or step value of the points.

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.

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.

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.

Decimals and BPF/BPC Precision

Rounding or increasing precision of the point coordinates with "decimals". 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.

References :

A “break-point” function is a function defined by a finite number of points (x,y).

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