# cassowary

This is a Swift implementation of the cassowary^{1}
simplex solver inspired by the C++ implementation, Kiwi^{2}.

## Constraints

Cassowary supports linear equations and non-strict inequalities. Additionally, a strength may be associated with each constraint in the system, constrolling its importance to the overall solution to the system.

### Defining Variables and Constraints

Variables are the values which the solver is trying to resolve. These
correspond to the `Variable`

type in the implementation. The variables can be
used to create the expressions which form constraints of the system. These must
be added to an instance of the solver.

```
import cassowary
let simplex: Solver = Solver()
let x_l: Variable = Variable("x_l")
let x_r: Variable = Variable("x_r")
let x_m: Variable = Variable("x_m")
simplex.add(constraint: 2.0 * x_m == x_l + x_r)
simplex.add(constraint: x_l + 10.0 <= x_r)
simplex.add(constraint: x_l >= -10.0)
simplex.add(constraint: x_r <= 100.0)
```

This creates a system with three variables (x_{l}, x_{r},
x_{m}) representings points on a line segment. x_{m} is
constrained to the midpoint between x_{l} and x_{r},
x_{l} is constrained to be at least 10 to the left of x_{r}, and
all variables must lie in the range [-10, 100]. All constraints must be
satisfied and are considered as `required`

by the cassowary algorithm.

**NOTE** The same constraint in the same form cannot be added to the solver
multiply. Redundant constraints, as per cassowary, are supported. That is, the
following set of constraints can be added to the solver:

```
x == 10
x + y == 30
y == 20
```

### Managing Constraint Strength

Cassowary supports constraints which are not required but are handled as
best-effort. Such a constraint is modelled as having a *strength* other than
`required`

. The constraints are considered in order of the value of their
strengths. Three standard strengths are defined by default:

`strong`

`medium`

`weak`

We can add a constraint to our previous example to place x_{m} at 50 by
adding a new `weak`

constraint:

`simplex.add(constraint: (x_m == 50.0) | Strength.weak)`

### Edit Variables

The system described thus far has been static. In order to find solutions for
particular value of x_{m}, Cassowary provides the concept of *edit
variables* which allows you to suggest values for the variable before evaluating
the system. These variables can have any strength other than `required`

.

Continuing our example, we could make x_{m} editable and suggest a value
of `60`

for it.

```
simplex.add(variable: x_m, .strong)
simplex.suggest(value: 60.0, for: x_m)
```

### Solving and Updating Variables

This implementation solves the system each time a constraint is added or removed, or when a new value is suggested for an edit variable. However, the variable values are not updated automatically and you must request the solver to update the values.

```
simplex.suggest(value: 90, for: x_m)
simplex.update()
```

**1** https://constraints.cs.washington.edu/solvers/cassowary-tochi.pdf

**2** https://github.com/nucleic/kiwi