# Point Collection

What Organize collections of point-like objects to locate repeating elements.

When Most designed artifacts have repeating elements. These may vary by their both their absolute position and their spatial relationships with nearby repeating elements. Use this pattern when you are able to think about the size and location of repeating elements in terms of a set of defining points.

Why A collection of points organized to capture the intended spatial relationships can greatly simplify the process of further model development. This saves time and effort in both modeling and reuse of a model in new contexts.

How Point-like objects may be located in Euclidean space or parametric space, so a collection can be specified in either space. Euclidean space is the familiar space of everyday life. It can be represented through Cartesian, polar or spherical coordinates. Most curves and surfaces (those defined internally by parametric equations) also define a "coordinate system" that defines locations on the curve or surface. Unlike those of Cartesian space, these parametric formulations may not preserve constant distance, either geometrically or along the defining object.

Use a collection of point-like objects as the input to define other repeating
elements. The logical structure of a collection is important - it provides the
relationships through which points can be used to define objects. For instance,
a collection structured as 2D array provides for each point
P_{ij}
easy access to the surrounding points, that is,
P_{gh}
where
g is in
{i-1, i, i+1} and
h is in
{j-1, j, j+1}.
A collection structured as a tree provides for each point
P,
easy access to
parent(P) and
children(P).