Units and Metrics

This document defines the system of units and metrics used by the Fuchsia graphics system.

Goals

The purpose of this system of units and metrics is to solve the following problems:

  • Define a device-specific unit, the pixel (px), used to describe low-level characteristics of targets or sources of image data.

  • Define a physical unit, the millimeter (mm), used as a physical basis for scale calculations.

  • Define a scalable unit, the pip (pp), used by UI frameworks for layout purposes. Its scale is derived from physical quantities, well-defined configuration parameters, and through the use of empirical models to ensure a consistent visual impact and to optimize usability for a user or group of users across a broad range of devices and viewing environments.

  • Help creators develop intuition about the perceptual significance of individual measurements expressed in scalable units. For example, 14 pp might be generally a good number for small readable text. Please refer to the user interface design guidelines for the actual numbers.

  • Allow software to determine how many pixels to render for optimum fidelity.

  • Allow software to determine known physical relations. For example, it is possible to draw a graduated ruler accurately when the display's physical size and density are accurately known.

System of Units

Fuchsia's graphics systems uses a few units of measure for distinct purposes, as summarized in this table.

Name and Notation Definition Purpose
Pixel (px) Device-specific Rendering and Sampling
Millimeter (mm) Physical Scale Factor Calibration
Pip (pp) Scalable Layout Position and Size

The following sections describe each unit in more detail.

Pixels (px)

The pixel is a device-specific unit of length for expressing dimensions as a range of addressable picture elements for a particular device. For the purposes of this definition, a device is considered to be any target or source of image data such as a display, a camera, or a texture.

It is common to express the size of a planar graphical object in the device's coordinate system in terms of its width and height in whole or fractional pixel units. Similarly it is common to use pixel units to express positions and vectors in that space.

Pixel units are not used to describe depth or elevation.

A pixel can also mean a single addressable picture element which measures exactly 1 px wide by 1 px high.

Details

Fuchsia's graphics system uses pixel units when performing device-specific graphical operations such as when rendering a scene, drawing text, decoding a video, or sampling from a texture.

Pixel units should not be used directly for user interface layout because they are not scalable and therefore cannot adapt across devices; use pip units instead.

Pixel units may have different physical manifestations depending on the device they relate to. It is common for all pixel units of a given device to be of the same physical size and to have a square aspect ratio but this may not be true for some devices.

Examples

  • A 1080p display operating at its native resolution is 1920 px wide by 1080 px high. Assuming each pixel is encoded in 32 bits, a linear frame buffer for this display would require a total of 8294400 bytes (1920 x 1080 x 4).

  • A single frame of YV12 encoded 720p video is 1280 px wide by 720 px high although its effective color resolution is lower due to the use of chroma subsampling.

Millimeters (mm)

The millimeter is a standard unit of length for expressing the physical dimensions and spatial relations of real world objects and their analogues. It is equivalent to 1/1000th of a meter as defined by the International System of Units (SI).

It is common to express the size of physical objects in whole or fractional millimeter units or as ratios involving millimeters such as pixels per millimeter (px/mm).

Details

Fuchsia's graphics system uses known physical measurements in millimeters to calibrate other units, such as pip units (see below). When these physical measurements are not known, the system will use different formulations to compensate for the lack of this information.

Millimeters are commonly used to express physical relationships with other units in the form of ratios, such as the number of pixels per millimeter of a display.

Millimeters should not be used directly for user interface layout because they do not capture the perceptual effects of viewing distance and other usability concerns; use pip units instead.

Examples

  • One particular display might have an active area that is 257.8 mm high by 171.9 mm wide with a pixel density of 8.4 px/mm.

  • The nominal viewing distance of that particular display in a typical viewing environment might be approximately 500 mm.

Pip Units (pp)

The pip is a device-independent scalable unit of length for layout of user interfaces and other graphical content in Fuchsia. Its purpose is to ensure a consistent visual impact and to optimize usability for a user or group of users across a broad range of devices and viewing environments.

It is common to express the size of an idealized planar or volumetric graphical object in terms of its width, height, and depth in whole or fractional pips. Similarly it is common to use pips to express positions and vectors in a user interface.

The pip unit has a equilateral cube aspect ratio: objects whose width, height, and depth have equal dimension in pip units will have an equal apparent width, height, and depth when rendered to the output device.

A pip unit square is a square which measures 1 pp wide by 1 pp high.

A pip unit cube is a cube which measures 1 pp wide by 1 pp high by 1 pp deep.

Pip units are used at design time and on the device at run time to provide a form of scale invariance.

  • At design time, the developer uses pip units to describe the size and position of idealized graphical objects based on the user interface design guidelines.

  • At run time, the system dynamically calculates an appropriate *pip unit transformation to map pip units to pixel units for each output device. This transformation takes into account the device pixel density, nominal viewing distance, and other factors to maintain a consistent visual impact across a range of configurations. It is adjusted as needed whenever any of its underlying factors changes.

  • Changes in the pip unit transformation affect the level of detail required to maintain graphical fidelity. For example, if the pip to pixel ratio increases by a factor of two, then a view may need to allocate textures twice as many pixels wide and tall to prevent content from becoming blurry at that scale. The view's node metrics provide the necessary information to determine the required level of detail.

  • Because the scene graph is dimensioned in scalable units, its overall layout is invariant under camera movements; only the level of detail changes. This would not be true if the scene graph were dimensions in pixels.

  • By convention, the local coordinate system of the root node of each view is one-to-one with pips. Thus the contents of each view can be directly measured in pips assuming no other local coordinate transformations are applied by the view to its content.

Details

Fuchsia's graphics system uses pip units extensively for layout in the scene graph and applies a transformation at rendering time.

The pip unit transformation is a combination of the following factors.

  • Aspect ratio correction: Preserves equal apparent width, height, and depth for objects of equal width, height, and depth in pip units.

  • Angular size correction: Adapts the scale of objects to a common resolution- independent baseline taking into account the physical pixel density and the nominal viewing distance. Although pip units scale proportionally with angular resolution, other corrections cause them not to have a constant apparent angular size in practice.

  • Ergonomic correction: Adapts the scale of objects to compensate for the information architecture needs of particular classes of devices due to how they are intended to be used, allowing for the presentation of more or less information in the same canvas.

  • Perceptual correction: Adapts the scale of objects to compensate for perceptual effects which occur based on the user's context and viewing environment.

  • User correction: Adapts the scale of objects to compensate for user preferences such as their accessibility needs. This term has no effect when default user settings are in effect.

See Display Metrics for more details about how the pip unit transformation is actually determined and used.

Examples

  • 1 pp on a handheld information device typically used at arm's length with default settings corresponds to a visual angle of approximately 0.0255 degrees. This is similar to the Android density-independent pixel (dp) unit.

  • By comparison, the CSS Reference Pixel is defined to have a visual angle of 0.0213 degrees.

Metrics

Fuchsia's graphics system provides APIs for programs to access scale factors, physical dimensions, and other information essential to adapting graphical output for a particular rendering context.

These properties are collectively known as Metrics and are summarized in the following tables.

Display Metrics

Display metrics describe the physical characteristics of a particular display and its basic scale factors.

Name Unit Definition
Scalable Width pp Width of visible content area in pips
Scalable Height pp Height of visible content area in pips
Pip Scale X px/pp Nominal pixels per pip unit in X
Pip Scale Y px/pp Nominal pixels per pip unit in Y
Pip Density pp/mm Physical pip unit density (optional)
Display Width px Width of visible content area in pixels
Display Height px Height of visible content area in pixels
Physical Width mm Width of visible content area in millimeters (optional)
Physical Height mm Height of visible content area in millimeters (optional)

View Metrics

View metrics describe the local layout constraints of an individual user interface component based on the view is embedded into the view hierarchy.

Views receive this information at runtime in the form of ViewProperties. View properties may change dynamically in response to view hierarchy changes which affect the view's layout.

Name Unit Definition
View Width pp Width constraint in pips
View Height pp Height constraint in pips
View Max Elevation pp Maximum elevation in pips

The view is generally expected to layout its content so as to fill the available width and height at elevation zero.

Since views can be three dimensional, the maximum elevation places an upper bound on the elevation of the airspace which the view is allowed to use.

Node Metrics

Node metrics describe the local rendering context of a node in the scene graph based on the characteristics of the rendering target into which the node is projected and the transformations applied by the node's ancestors.

Nodes receive this information at runtime in the form of MetricsEvents. Node metrics may change dynamically in response to scene graph changes which affect the node's projection into the rendering target.

Name Unit Definition
Pip Unit Scale X px/pp Nominal pixels per pip unit in X
Pip Unit Scale Y px/pp Nominal pixels per pip unit in Y
Pip Unit Density pp/mm Physical pip unit density (optional)

The pip unit scale factor is important for deciding the resolution of textures needed to achieve optimum fidelity on the rendering target. For example, given a uniform pip unit scale factor of 2.5, the ideal texture size to fill a a 150 pp by 100 pp rectangle is 375 px by 250 px.

The pip unit density is useful for mapping scalable dimensions to or from physical dimensions, although this may not be possible if the rendering target's physical resolution is unknown.

These metrics are designed to consider the overall context of the node in the scene graph. For example, if an ancestor of the node applies a 200% scale transformation to the subtree containing the node, then the node will receive an updated metrics event containing values which are scaled up by 200%. This informs the node that it may need to allocate higher resolution textures to maintain optimum fidelity.

TODO(SCN-378): Node metrics currently do not take into account the effects of certain transformations such as perspective projections and rotations which could affect the necessary level of detail required to maintain optimum fidelity or the accuracy of physical registration. We should consider introducing additional factors in Scenic to help estimate these effects.

Model Parameters

The Fuchsia graphics system automatically calculates metrics based on an empirical model using information about a display's physical characteristics, its viewing environment, user preferences, and other contextual cues.

For this model to function correctly, it needs accurate parameters.

In particular, when a model parameter is not accurately known a priori, such as the display's exact physical size and pixel density, then it must be reported as having an unknown value.

Do not provide fake or poorly estimated input parameters; report them as unknown instead. The display model is responsible for choosing sensible defaults based on what actually is known.

In some situations, it may be appropriate to prompt the end-user to supply missing information during setup to optimize fidelity.

Refer to the DisplayModel class for more details.

TODO(SCN-379): Document specific calibration procedures and expected accuracy bounds for each model parameter.

Display Information

The display information describes the physical characteristics of a particular display.

Name Unit Definition
Display Width px Width of visible content area
Display Height px Height of visible content area
Physical Width mm Width of visible content area (optional)
Physical Height mm Height of visible content area (optional)
Pixel Density px/mm Pixel density of active area (optional)

Environment Information

The environment information describes the physical characteristics of how a display is typically used and perceived in a given environment.

Name Unit Definition
Usage usage Intended usage of the display (optional)
Viewing Distance mm Nominal apparent viewing distance (optional)

The usage classification expresses how a particular display is intended to be used in a given context. This information helps the system select appropriate defaults and adjust the information architecture to suit the role of that display.

  • Unknown: The role of the display is unknown.
  • Handheld: The display is mounted in a device which is typically supported by the user in one or both hands. The user interface will be optimized for single-user direct manipulation. Like a phone or tablet.
  • Close: The display is mounted in a device which is typically located well within arm's reach of the user. The user interface will be optimized for single-user direct and indirect manipulation. Like a laptop.
  • Near: The display is mounted in a device which is typically located at arm's reach from the user. The user interface will be optimized for single-user indirect manipulation. Like a desktop.
  • Far: The display is mounted in a device which is typically located well beyond arm's reach of the user or a group of users and is intended to be viewed from a variety of distances. The user interface will be optimized for single-user and multi-user interaction and media consumption. Like a TV.

The viewing distance estimates how far away objects presented on the display at a zero elevation will appear to the user.

User Information

The user information describes the user's preferences and accessibility needs which may override some of the behavior of the model.

Name Unit Definition
User Scale Factor pp/pp Magnification Ratio (default is 1.0)

The user scale factor allows users to uniformly scale the entire user interface by multiplying the pip unit scale factor with a user specified ratio. This has the effect of increasing or decreasing the apparent angular size of graphical objects and correspondingly decreasing or increasing the amount of available space for layout measured in pips.