Cassowary Constraint Equation

Layout isn't a simple thing for a computer to solve and 0:00 many people have attempted to solve the problem in different ways. 0:03 Back in 2001, two computer scientists at the University of Washington, 0:07 Greg Badros and Alan Borning, along with Peter Stuckey 0:12 of the University of Melbourne, wrote a paper detailing their approach and 0:16 called it The Cassowary Linear Arithmetic Constraint Solving Algorithm. 0:20 Cassowary, according to the authors, is an incremental constraint solving toolkit 0:25 that efficiently solves systems of linear equalities and equalities. 0:31 Auto Layout is actually built on top of this algorithm, and 0:36 is pretty good at solving the layout issues in an efficient and rapid manner. 0:40 Auto Layout was introduced in 2012 on iOS, and 0:44 is a constraint-based, descriptive layout system. 0:48 Much of this system is still based on the original premise of 0:52 the Cassowary Algorithm, 0:55 in that relationships between views can be expressed as linear equations. 0:57 Using Auto Layout, rather than specifying coordinate values, we can describe 1:03 the position of a view in relation to its superview or neighboring views. 1:08 We can say that we want a view or label to be centered horizontally in its superview. 1:13 And we want that label to be some distance away from the bottom of its superview. 1:19 In Cassaway, and as an extension, Auto Layout, 1:25 these relationships can be expressed as a series of linear equations. 1:28 For the first description, where we want the label to always be in the horizontal 1:33 center of the superview, we can write an equation that looks something like this. 1:38 label.centerX = superview.centerX. 1:42 And similarly for 1:48 the second description, we can define a linear equation that looks like this. 1:49 We can say label.bottom = superview.bottom- {padding}. 1:54 In Auto Layout, these descriptive linear equations are what we call constraints. 1:59 A constraint provides a fluent layout language that allows 2:05 us to define relationships between views in terms of linear equations. 2:09 While it might seem like there are many different ways to express these 2:14 relationships, they all boil down to a simple equation. 2:18 The As in this equation refer to view attributes. 2:22 What are attributes? 2:27 Don't worry, we'll get to that. 2:28 If we generically call a view an item, our equation looks like this. 2:29 Constraints are relationships described either between attributes on a view, 2:34 or between attributes on two different views. 2:40 So A1 can be an attribute on view 1, and A2 an attribute on view 2. 2:44 A2 can also be an attribute on view 1. 2:51 The M in this equation refers to a multiplier. 2:54 This allows us to modify the relationship by a certain amount. 2:58 The C refers to a constant value, and 3:02 is used to offset the equation by a certain amount. 3:05 Now, people often joke about the fact that the only thing you can change once 3:09 a constraint is created is this value that's called constant. 3:13 So this is essentially the basic premise or 3:18 building block underlying Auto Layout, a constraint equation. 3:21