All Implemented Interfaces:

MinkowskiPenetrationSolver
```
public class Epa
extends Object
implements MinkowskiPenetrationSolver
```
Epa, or Expanding Polytope Algorithm, is used to find the penetration depth and vector given the final simplex of Gjk.
Epa expands the given simplex in the direction of the origin until it cannot be expanded any further. Gjk guarantees that the simplex points are on the edge of the Minkowski sum which creates a convex polytope from which to start the Epa algorithm.
Expansion is achieved by breaking edges of the simplex. Find the edge on the simplex closest to the origin, then use that edge's normal to find another support point (using the same support method that Gjk uses). Add the new support point to the simplex between the points that made the closest edge. Repeat this process until the polytope cannot be expanded further.
This implementation has three termination cases:
- If the new support point is not past the edge along the edge normal given some epsilon.
- If the distance between the last support point and the new support point is below a given epsilon.
- Maximum iteration count.
Once Epa terminates, the penetration vector is the current closest edge normal and the penetration depth is the distance from the origin to the edge along the normal.
Epa will terminate in a finite number of iterations if the two shapes are Polygons. If either shape has curved surfaces the algorithm requires an expected accuracy epsilon: distanceEpsilon. In the case that the distanceEpsilon is too small, the maxIterations will prevent the algorithm from running forever.
Since:

1.0.0

Version:

3.2.0

Author:

William Bittle

See Also:

Gjk, EPA (Expanding Polytope Algorithm)

Field Summary

Fields
Modifier and Type	Field	Description
`static double`	`DEFAULT_DISTANCE_EPSILON`	The default `Epa` distance epsilon in meters; near 1E-8
`static int`	`DEFAULT_MAX_ITERATIONS`	The default `Epa` maximum iterations

Constructor Summary

Constructors
Constructor Description

Epa()

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`double`	`getDistanceEpsilon()`	Returns the distance epsilon.
`int`	`getMaxIterations()`	Returns the maximum number of iterations the algorithm will perform before exiting.
`void`	`getPenetration(List<Vector2> simplex, MinkowskiSum minkowskiSum, Penetration penetration)`	Returns the penetration vector and depth in the given `Penetration` object given the final simplex from `Gjk` and `MinkowskiSum`.
`void`	`setDistanceEpsilon(double distanceEpsilon)`	The minimum distance between two iterations of the algorithm.
`void`	`setMaxIterations(int maxIterations)`	Sets the maximum number of iterations the algorithm will perform before exiting.

Methods inherited from class Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - DEFAULT_MAX_ITERATIONS
```
public static final int DEFAULT_MAX_ITERATIONS
```
    The default Epa maximum iterations
    
    See Also:
    
    Constant Field Values
  - DEFAULT_DISTANCE_EPSILON
```
public static final double DEFAULT_DISTANCE_EPSILON
```
    The default Epa distance epsilon in meters; near 1E-8
- Constructor Detail
  - Epa
```
public Epa()
```
- Method Detail
  - getPenetration
```
public void getPenetration(List<Vector2> simplex,
                           MinkowskiSum minkowskiSum,
                           Penetration penetration)
```
    Description copied from interface: MinkowskiPenetrationSolver
    
    Returns the penetration vector and depth in the given Penetration object given the final simplex from Gjk and MinkowskiSum.
    
    Specified by:
    
    getPenetration in interface MinkowskiPenetrationSolver
    
    Parameters:
    
    simplex - the simplex containing the origin
    
    minkowskiSum - the MinkowskiSum
    
    penetration - the Penetration object to fill
  - getMaxIterations
```
public int getMaxIterations()
```
    Returns the maximum number of iterations the algorithm will perform before exiting.
    
    Returns:
    
    int
    
    See Also:
    
    setMaxIterations(int)
  - setMaxIterations
```
public void setMaxIterations(int maxIterations)
```
    Sets the maximum number of iterations the algorithm will perform before exiting.
    
    Parameters:
    
    maxIterations - the maximum number of iterations in the range [5, ∞]
    
    Throws:
    
    IllegalArgumentException - if maxIterations is less than 5
  - getDistanceEpsilon
```
public double getDistanceEpsilon()
```
    Returns the distance epsilon.
    
    Returns:
    
    double
    
    See Also:
    
    setDistanceEpsilon(double)
  - setDistanceEpsilon
```
public void setDistanceEpsilon(double distanceEpsilon)
```
    The minimum distance between two iterations of the algorithm.
    The distance epsilon is used to determine when the algorithm is close enough to the edge of the minkowski sum to conclude that it can no longer expand. This is primarily used when one of the Convex Shapes in question has a curved shape.
    
    Parameters:
    
    distanceEpsilon - the distance epsilon in the range (0, ∞]
    
    Throws:
    
    IllegalArgumentException - if distanceEpsilon is less than or equal to zero

Class Epa

Field Summary

Constructor Summary

Method Summary

Methods inherited from class Object

Field Detail

DEFAULT_MAX_ITERATIONS

DEFAULT_DISTANCE_EPSILON

Constructor Detail

Epa

Method Detail

getPenetration

getMaxIterations

setMaxIterations

getDistanceEpsilon

setDistanceEpsilon