go.mobile/geom: coordinate system and unit of length

LGTM=nigeltao
R=nigeltao, ruiu
CC=adg, davidday, golang-codereviews
https://golang.org/cl/140940044

geom/doc.go

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+// Copyright 2014 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+/*
+Pacakge geom defines a two-dimensional coordinate system.
+
+The coordinate system is based on an left-handed Cartesian plane.
+That is, X increases to the right and Y increases down. For (x,y),
+
+	(0,0) → (1,0)
+	  ↓   ↘
+	(0,1)   (1,1)
+
+The display window places the origin (0, 0) in the upper-left corner of
+the screen. Positions on the plane are measured in typographic points,
+1/72 of an inch, which is represented by the Pt type.
+
+Any interface that draws to the screen using types from the geom
+package scales the number of pixels to maintain a Pt as 1/72 of an inch.
+*/
+package geom
+
+/*
+Notes on the various underlying coordinate systems.
+
+Both Android and iOS (UIKit) use upper-left-origin coordinate systems
+with for events, however they have different units.
+
+UIKit measures distance in points. A point is a single-pixel on a
+pre-Retina display. UIKit maintains a scale factor that to turn points
+into pixels. On current retina devices, the scale factor is 2.0.
+
+A UIKit point does not correspond to a fixed physical distance, as the
+iPhone has a 163 DPI/PPI (326 PPI retina) display, and the iPad has a
+132 PPI (264 retina) display. Points are 32-bit floats.
+
+Even though point is the official UIKit term, they are commonly called
+pixels. Indeed, the units were equivalent until the retina display was
+introduced.
+
+N.b. as a UIKit point is unrelated to a typographic point, it is not
+related to this packages's Pt and Point types.
+
+More details about iOS drawing:
+
+https://developer.apple.com/library/ios/documentation/2ddrawing/conceptual/drawingprintingios/GraphicsDrawingOverview/GraphicsDrawingOverview.html
+
+Android uses pixels. Sub-pixel precision is possible, so pixels are
+represented as 32-bit floats. The ACONFIGURATION_DENSITY enum provides
+the screen DPI/PPI, which varies frequently between devices.
+
+It would be tempting to adopt the pixel, given the clear pixel/DPI split
+in the core android events API. However, the plot thickens:
+
+http://developer.android.com/training/multiscreen/screendensities.html
+
+Android promotes the notion of a density-independent pixel in many of
+their interfaces, often prefixed by "dp". 1dp is a real physical length,
+as "independent" means it is assumed to be 1/160th of an inch and is
+adjusted for the current screen.
+
+In addition, android has a scale-indepdendent pixel used for expressing
+a user's preferred text size. The user text size preference is a useful
+notion not yet expressed in the geom package.
+
+For the sake of clarity when working across platforms, the geom package
+tries to put distance between it and the word pixel.
+*/

geom/geom.go

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+// Copyright 2014 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package geom
+
+import "fmt"
+
+// Pt is a length.
+//
+// The unit Pt is a typographical point, 1/72 of an inch (0.3527 mm).
+//
+// It can be be converted to a length in current device pixels by
+// multiplying with Scale after app initialization is complete.
+type Pt float32
+
+// Px converts the length to current device pixels.
+func (p Pt) Px() float32 { return float32(p) * Scale }
+
+func (p Pt) String() string { return fmt.Sprintf("%.2fpt", p) }
+
+// Point is a point in a two-dimensional plane.
+type Point struct {
+	X, Y Pt
+}
+
+func (p Point) String() string { return fmt.Sprintf("Point(%.2f, %.2f)", p.X, p.Y) }
+
+// Scale is the number of pixels in a single Pt on the current device.
+//
+// There are a wide variety of pixel densities in existing phones and
+// tablets, so apps should be written to expect various non-integer
+// Scale values. In general, work in Pt.
+//
+// Not valid until app initialization has completed.
+var Scale float32
+
+// Width is the width of the device screen.
+// Not valid until app initialization has completed.
+var Width Pt
+
+// Height is the height of the device screen.
+// Not valid until app initialization has completed.
+var Height Pt