# Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# Point

Point[p]
is a graphics and geometry primitive that represents a point at p.

Point[{p1,p2,}]
represents a collection of points.

## Details and OptionsDetails and Options

• Point can be used as a geometric region or a graphics primitive.
• Point can be used in Graphics and Graphics3D.
• In graphics, the points can be Scaled, Offset, ImageScaled, and Dynamic expressions.
• Graphics renderings is affected by directives such as PointSize and color.
• The following options and settings can be used in graphics:
•  VertexColors None vertex colors VertexNormals None effective vertex normals for shading

## Background & ContextBackground & Context

• Point is a graphics and geometry primitive that represents a geometric point. The position of a Point in -dimensional space is specified as a list argument consisting of Cartesian coordinate values, where RegionEmbeddingDimension can be used to determine the dimension for a given Point expression. A collection of points may be represented as a list of -tuples inside a single Point primitive (a "multi-point"). The coordinates of Point objects may have exact or approximate values.
• Point objects can be visually formatted in two and three dimensions using Graphics and Graphics3D, respectively. Point objects can also be used in geographical maps using GeoGraphics and GeoPosition (e.g. GeoGraphics[Point[GeoPosition[{38.9,-77.0}]]]). Finally, Point may serve as a region specification over which a computation should be performed.
• While points themselves have dimension 0 (as reported by the RegionDimension function), Point objects in formatted graphics expressions are by default styled to appear "larger" than a 0-dimensional mathematical point. Furthermore, in graphical visualizations, points are displayed at the same size regardless of possibly differing distances from the view point. The appearance of Point objects in graphics can be modified by specifying sizing directives such as PointSize and AbsolutePointSize, color directives such as Red, the transparency directive Opacity, and the style option Antialiasing. In addition, the colors of multi-points may be specified using VertexColors, while the shading and simulated lighting of multi-points within Graphics3D may be specified using VertexNormals.
• GeometricTransformation and more specific transformation functions such as Translate and Rotate can be used to change the coordinates at which a Point object is displayed while leaving the underlying Point expression untouched.
• Other graphics primitives such as Circle, Disk, Sphere, and Ball may resemble those of stylized Point objects. Locator is another point-like interactive object that represents a draggable locator object in a graphic.
• While the Point primitive explicitly appears in graphics and geometric region specification expressions, it should be noted that coordinates are commonly represented as bare lists in other contexts in the Wolfram Language. Examples of this type include coordinate specifications appearing inside other graphics primitives (e.g. Line[{{0, 0},{1,1}}]), arguments to Locator (e.g. Graphics[Locator[{0,2}]]), and when using Nearest to compute a nearest point. A number of functions (e.g. RegionNearest, RegionCentroid, ArgMin, and ArgMax) also naturally return bare lists of coordinates as opposed to explicit Point objects, while others (e.g. Solve and NSolve) return solution "points" as lists of variable replacement rules (e.g. ).

## ExamplesExamplesopen allclose all

### Basic Examples  (5)Basic Examples  (5)

A single point:

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Multiple points:

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Points in 3D:

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Differently styled points:

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Count and centroid:

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