# CGGeometry Various structures and associated functions for 2D geometric primitives. ## Discussion The data structure represents a point in a two-dimensional coordinate system. The data structure represents the location and dimensions of a rectangle. The data structure represents the dimensions of width and height. A , , or structure does not explicitly define the unit of measure for its member quantities. A point’s x- and y-coordinates or a size’s width and height are unitless quantities—whether such measurements are treated as pixels, scale-factor-independent points, texture elements (texels), or some other unit depends on the API using the measurement, and on the context in which that API is used. For example, a structure specifying the frame of an or object defines the view’s dimensions in points, not pixels. However, the effects of using a structure in a [`CGContext`](/documentation/CoreGraphics/CGContext) drawing operation depend on the scale factor associated with that context. Where not otherwise specified, you can assume that a , , or structure is defined in points, not pixels. (For details, see [Drawing and Printing Guide for iOS](https://developer.apple.com/library/archive/documentation/2DDrawing/Conceptual/DrawingPrintingiOS/Introduction/Introduction.html#//apple_ref/doc/uid/TP40010156) or [High Resolution Guidelines for OS X](https://developer.apple.com/library/archive/documentation/GraphicsAnimation/Conceptual/HighResolutionOSX/Introduction/Introduction.html#//apple_ref/doc/uid/TP40012302).) The height and width stored in a data structure can be negative. For example, a rectangle with an origin of `[0.0, 0.0]` and a size of `[10.0,10.0]` is exactly equivalent to a rectangle with an origin of `[10.0, 10.0]` and a size of `[-10.0,-10.0]`. Your application can standardize a rectangle—that is, ensure that the height and width are stored as positive values—by calling the `CGRectStandardize` function. All functions described in this reference that take data structures as inputs implicitly standardize those rectangles before calculating their results. For this reason, your applications should avoid directly reading and writing the data stored in the data structure. Instead, use the functions described here to manipulate rectangles and to retrieve their characteristics. ## Topics ### Creating a Dictionary Representation from a Geometric Primitive [`CGPointCreateDictionaryRepresentation`](/documentation/CoreGraphics/CGPointCreateDictionaryRepresentation(_:)) Returns a dictionary representation of the specified point. [`CGSizeCreateDictionaryRepresentation`](/documentation/CoreGraphics/CGSizeCreateDictionaryRepresentation(_:)) Returns a dictionary representation of the specified size. [`CGRectCreateDictionaryRepresentation`](/documentation/CoreGraphics/CGRectCreateDictionaryRepresentation(_:)) Returns a dictionary representation of the provided rectangle. ### Creating a Geometric Primitive from a Dictionary Representation [`CGPointMakeWithDictionaryRepresentation`](/documentation/CoreGraphics/CGPointMakeWithDictionaryRepresentation(_:_:)) Fills in a point using the contents of the specified dictionary. [`CGSizeMakeWithDictionaryRepresentation`](/documentation/CoreGraphics/CGSizeMakeWithDictionaryRepresentation(_:_:)) Fills in a size using the contents of the specified dictionary. [`CGRectMakeWithDictionaryRepresentation`](/documentation/CoreGraphics/CGRectMakeWithDictionaryRepresentation(_:_:)) Fills in a rectangle using the contents of the specified dictionary. ### Creating a Geometric Primitive from Values [`CGPointMake`](/documentation/CoreGraphics/CGPointMake(_:_:)) Returns a point with the specified coordinates. [`CGRectMake`](/documentation/CoreGraphics/CGRectMake(_:_:_:_:)) Returns a rectangle with the specified coordinate and size values. [`CGSizeMake`](/documentation/CoreGraphics/CGSizeMake(_:_:)) Returns a size with the specified dimension values. [`CGVectorMake`](/documentation/CoreGraphics/CGVectorMake(_:_:)) Returns a vector with the specified dimension values. ### Modifying Rectangles [`CGRectDivide`](/documentation/CoreGraphics/CGRectDivide) Divides a source rectangle into two component rectangles. [`CGRectInset`](/documentation/CoreGraphics/CGRectInset(_:_:_:)) Returns a rectangle that is smaller or larger than the source rectangle, with the same center point. [`CGRectIntegral`](/documentation/CoreGraphics/CGRectIntegral(_:)) Returns the smallest rectangle that results from converting the source rectangle values to integers. [`CGRectIntersection`](/documentation/CoreGraphics/CGRectIntersection(_:_:)) Returns the intersection of two rectangles. [`CGRectOffset`](/documentation/CoreGraphics/CGRectOffset(_:_:_:)) Returns a rectangle with an origin that is offset from that of the source rectangle. [`CGRectStandardize`](/documentation/CoreGraphics/CGRectStandardize(_:)) Returns a rectangle with a positive width and height. [`CGRectUnion`](/documentation/CoreGraphics/CGRectUnion(_:_:)) Returns the smallest rectangle that contains the two source rectangles. ### Comparing Values [`CGPointEqualToPoint`](/documentation/CoreGraphics/CGPointEqualToPoint-c.macro) Returns whether two points are equal. [`CGSizeEqualToSize`](/documentation/CoreGraphics/CGSizeEqualToSize-c.macro) Returns whether two sizes are equal. [`CGRectEqualToRect`](/documentation/CoreGraphics/CGRectEqualToRect(_:_:)) Returns whether two rectangles are equal in size and position. [`CGRectIntersectsRect`](/documentation/CoreGraphics/CGRectIntersectsRect(_:_:)) Returns whether two rectangles intersect. ### Checking for Membership [`CGRectContainsPoint`](/documentation/CoreGraphics/CGRectContainsPoint(_:_:)) Returns whether a rectangle contains a specified point. [`CGRectContainsRect`](/documentation/CoreGraphics/CGRectContainsRect(_:_:)) Returns whether the first rectangle contains the second rectangle. ### Getting Min, Mid, and Max Values [`CGRectGetMinX`](/documentation/CoreGraphics/CGRectGetMinX(_:)) Returns the smallest value for the x-coordinate of the rectangle. [`CGRectGetMinY`](/documentation/CoreGraphics/CGRectGetMinY(_:)) Returns the smallest value for the y-coordinate of the rectangle. [`CGRectGetMidX`](/documentation/CoreGraphics/CGRectGetMidX(_:)) Returns the x- coordinate that establishes the center of a rectangle. [`CGRectGetMidY`](/documentation/CoreGraphics/CGRectGetMidY(_:)) Returns the y-coordinate that establishes the center of the rectangle. [`CGRectGetMaxX`](/documentation/CoreGraphics/CGRectGetMaxX(_:)) Returns the largest value of the x-coordinate for the rectangle. [`CGRectGetMaxY`](/documentation/CoreGraphics/CGRectGetMaxY(_:)) Returns the largest value for the y-coordinate of the rectangle. ### Getting Height and Width [`CGRectGetHeight`](/documentation/CoreGraphics/CGRectGetHeight(_:)) Returns the height of a rectangle. [`CGRectGetWidth`](/documentation/CoreGraphics/CGRectGetWidth(_:)) Returns the width of a rectangle. ### Checking Rectangle Characteristics [`CGRectIsEmpty`](/documentation/CoreGraphics/CGRectIsEmpty(_:)) Returns whether a rectangle has zero width or height, or is a null rectangle. [`CGRectIsNull`](/documentation/CoreGraphics/CGRectIsNull(_:)) Returns whether the rectangle is equal to the null rectangle. [`CGRectIsInfinite`](/documentation/CoreGraphics/CGRectIsInfinite(_:)) Returns whether a rectangle is infinite. ### Data Types ### Constants [`CGRectInfinite`](/documentation/CoreGraphics/CGRectInfinite) A rectangle that has infinite extent. [Geometric Zeros](/documentation/CoreGraphics/geometric-zeros) A zero point, zero rectangle, or zero size. [`CGRectNull`](/documentation/CoreGraphics/CGRectNull) The null rectangle, representing an invalid value. [CGFloat Informational Macros](/documentation/CoreGraphics/cgfloat-informational-macros) Informational macros for the `CGFloat` type. ## See Also [Quartz 2D Programming Guide](https://developer.apple.com/library/archive/documentation/GraphicsImaging/Conceptual/drawingwithquartz2d/Introduction/Introduction.html#//apple_ref/doc/uid/TP30001066) --- Copyright © 2026 Apple Inc. All rights reserved. | [Terms of Use](https://www.apple.com/legal/internet-services/terms/site.html) | [Privacy Policy](https://www.apple.com/privacy/privacy-policy)