Package de.xima.fc.common.geometry

Class Geometry2D

java.lang.Object

de.xima.fc.common.geometry.Geometry2D

public final class Geometry2D
extends Object

Utility class for geometrical operations in a 2D space.

Since:

8.4.0

Method Summary

Modifier and Type	Method	Description
static boolean	areRectanglesOverlapping(Point2DDouble pos1, Rectangular2DDouble size1, Point2DDouble pos2, Rectangular2DDouble size2)	Checks if two 2D rectangles have any overlap.
static boolean	areRectanglesOverlappingOrTouching(Point2DDouble pos1, Rectangular2DDouble size1, Point2DDouble pos2, Rectangular2DDouble size2)	Checks if two 2D rectangles have any overlap.
static OneOfN.OneOf3<ECardinalDirection2D,EPrimaryIntercardinalDirection2D,Unit>	classifyRectangleCardinalPosition(Point2DDouble pos1, Rectangular2DDouble size1, Point2DDouble pos2, Rectangular2DDouble size2)	Classifies the relative position of two non-overlapping rectangles r1 and r2 in a 2D space in regard to their cardinal relationship.
static double	edgeCoordinate(Point2DDouble position, Rectangular2DDouble boundingBox, ECardinalDirection2D direction)	Finds the coordinate of the edge in the specified direction, assuming a rectangular bounding with the given dimensions box positioned at the given position.
static Point2DDouble	interpolateLinearly(Point2DDouble p1, Point2DDouble p2, double ratio)	Linearly interpolates between two points in 2D space and returns a point at the given ratio between the two points.
static double	maxCoordinateInDirection(EAxisPolarity direction, double x, double y)	Returns the maximal coordinate in the specified axis direction for the two given coordinates in 2D space.
static double	maxCoordinateInDirection(EAxisPolarity direction, double a, double b, double c)	Returns the maximal coordinate in the specified axis direction for the 3 given coordinates in 2D space.
static double	maxCoordinateInDirection(EAxisPolarity direction, double a, double b, double c, double d)	Returns the maximal coordinate in the specified axis direction for the 4 given coordinates in 2D space.
static double	maxCoordinateInDirection(ECardinalDirection2D direction, Point2DDouble p1, Point2DDouble p2)	Returns the maximal coordinate in the specified direction for the two given points in 2D space.
static double	offsetPointLine(double px, double py, double lineX1, double lineY1, double lineX2, double lineY2)	Computes the offset of a point from a line segment defined by two points in 2D space.
static double	offsetPointLine(Point2D<?> point, Point2D<?> lineStart, Point2D<?> lineEnd)	Computes the offset of a point from a line segment defined by two points in 2D space.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

areRectanglesOverlapping

public static boolean areRectanglesOverlapping(Point2DDouble pos1,
                                               Rectangular2DDouble size1,
                                               Point2DDouble pos2,
                                               Rectangular2DDouble size2)

Checks if two 2D rectangles have any overlap. Rectangles that are only touching at the edges or corners are not considered overlapping.

Parameters:

pos1 - The position of the first rectangle, i.e. its top-left corner.

size1 - The size of the first rectangle.

pos2 - The position of the second rectangle, i.e. its top-left corner.

size2 - The size of the second rectangle.

Returns:

true if the rectangles overlap, false otherwise.

areRectanglesOverlappingOrTouching

public static boolean areRectanglesOverlappingOrTouching(Point2DDouble pos1,
                                                         Rectangular2DDouble size1,
                                                         Point2DDouble pos2,
                                                         Rectangular2DDouble size2)

Checks if two 2D rectangles have any overlap. Rectangles that are only touching at the edges or corners are also considered overlapping.

Parameters:

pos1 - The position of the first rectangle, i.e. its top-left corner.

size1 - The size of the first rectangle.

pos2 - The position of the second rectangle, i.e. its top-left corner.

size2 - The size of the second rectangle.

Returns:

true if the rectangles overlap or touch each other, false otherwise.

classifyRectangleCardinalPosition

public static OneOfN.OneOf3<ECardinalDirection2D,EPrimaryIntercardinalDirection2D,Unit> classifyRectangleCardinalPosition(Point2DDouble pos1,
                                                                                                                                      Rectangular2DDouble size1,
                                                                                                                                      Point2DDouble pos2,
                                                                                                                                      Rectangular2DDouble size2)

Classifies the relative position of two non-overlapping rectangles r1 and r2 in a 2D space in regard to their cardinal relationship. The possible classifications are:

• NORTH r2 is above r1
• NORTH_EAST r2 is above and to the right of r1
• EAST r2 is to the right of r1
• SOUTH_EAST r2 is below and to the right of r1
• SOUTH r2 is below r1
• SOUTH_WEST r2 is below and to the left of r1
• WEST r2 is to the left of r1
• NORTH_WEST r2 is above and to the left of r1
• UNIT r2 is overlapping with r1

More precisely, the classification is defined as follows:

Case 1 - r2 above r1

r2 is above r1, i.e. the bottom edge of r2 is above the top edge of r1. There are different subcases that classify into 3 categories:

    NORTH             NORTH              NORTH             NORTH_EAST          NORTH_WEST
    ------     |   ----------   |        ----------   |         ------   |   ------
    | r2 |     |   |   r2   |   |        |   r2   |   |         | r2 |   |   | r2 |
    ------     |   ----------   |        ----------   |         ------   |   ------
               |                |                     |                  |
  ----------   |    ------      |   ----------        |   ------         |         ------
  |   r1   |   |    | r1 |      |   |   r1   |        |   | r1 |         |         | r1 |
  ----------   |    ------      |   ----------        |   ------         |         ------
 

• r2 is northeast of r1 if the left edge of r2 is to the right of the right edge of r1.
• r2 is northwest of r1 if the right edge of r2 is to the left of the left edge of r1.
• Otherwise, r2 is north of r1.

Case 2 - r2 below r1

r2 is below r1, i.e. the top edge of r2 is below the bottom edge of r1. There are different subcases that classify into 3 categories:

    SOUTH             SOUTH              SOUTH             SOUTH_WEST         SOUTH_EAST
    ------     |   ----------   |        ----------   |         ------   |   ------
    | r1 |     |   |   r1   |   |        |   r1   |   |         | r1 |   |   | r1 |
    ------     |   ----------   |        ----------   |         ------   |   ------
               |                |                     |                  |
  ----------   |    ------      |   ----------        |   ------         |         ------
  |   r2   |   |    | r2 |      |   |   r2   |        |   | r2 |         |         | r2 |
  ----------   |    ------      |   ----------        |   ------         |         ------
 

• r2 is southeast of r1 if the left edge of r2 is to the right of the right edge of r1.
• r2 is southwest of r1 if the right edge of r2 is to the left of the left edge of r1.
• Otherwise, r2 is south of r1.

Case 3 - r2 right of r1

r2 is to the right of r1, i.e. the left edge of r2 is to the right of the right edge of r1. There are different subcases that classify into 3 categories:

       EAST                    EAST                  EAST               SOUTH_EAST            NORTH_EAST
            ------   |   ------            |   ------            |   ------            |            ------
  ------    |    |   |   |    |   ------   |   |    |            |   |    |            |            |    |
  | r1 |    | r2 |   |   | r1 |   | r2 |   |   | r1 |            |   | r1 |            |            | r2 |
  ------    |    |   |   |    |   ------   |   |    |   ------   |   |    |            |            |    |
            ------   |   ------            |   ------   |    |   |   ------            |            ------
                     |                     |            | r2 |   |            ------   |   ------
                     |                     |            |    |   |            |    |   |   |    |
                     |                     |            ------   |            | r2 |   |   | r1 |
                     |                     |                     |            |    |   |   |    |
                     |                     |                     |            ------   |   ------
 

• r2 is southeast of r1 if the top edge of r2 is below the bottom edge of r1.
• r2 is northeast of r1 if the bottom edge of r2 is above the top edge of r1.
• Otherwise, r2 is east of r1.

Case 4 - r2 left of r1

r2 is to the right of r1, i.e. the right edge of r2 is to the left of the left edge of r1. There are different subcases that classify into 3 categories:

       WEST                    WEST                  WEST               NORTH_WEST            SOUTH_WEST
            ------   |   ------            |   ------            |   ------            |            ------
  ------    |    |   |   |    |   ------   |   |    |            |   |    |            |            |    |
  | r2 |    | r1 |   |   | r2 |   | r1 |   |   | r2 |            |   | r2 |            |            | r1 |
  ------    |    |   |   |    |   ------   |   |    |   ------   |   |    |            |            |    |
            ------   |   ------            |   ------   |    |   |   ------            |            ------
                     |                     |            | r1 |   |            ------   |   ------
                     |                     |            |    |   |            |    |   |   |    |
                     |                     |            ------   |            | r1 |   |   | r2 |
                     |                     |                     |            |    |   |   |    |
                     |                     |                     |            ------   |   ------
 

• r2 is southeast of r1 if the top edge of r2 is below the bottom edge of r1.
• r2 is northeast of r1 if the bottom edge of r2 is above the top edge of r1.
• Otherwise, r2 is east of r1.

If none of these cases apply, the rectangles are overlapping.

Parameters:

pos1 - The position of the first rectangle r1, i.e. its top-left corner.

size1 - The size of the first rectangle r1.

pos2 - The position of the second rectangle r2, i.e. its top-left corner.

size2 - The size of the second rectangle r2.

Returns:

The relative position of the first rectangle to the second rectangle, never null.

edgeCoordinate

public static double edgeCoordinate(Point2DDouble position,
                                    Rectangular2DDouble boundingBox,
                                    ECardinalDirection2D direction)

Finds the coordinate of the edge in the specified direction, assuming a rectangular bounding with the given dimensions box positioned at the given position.

   position
      |
      |
      v      NORTH
      +-----------------+         ^
      |                 |         |
 WEST |                 | EAST    | height
      |                 |         |
      +-----------------+         v
             SOUTH

      <----------------->
             width
 

Parameters:

position - the position of the rectangle, i.e. its top-left corner.

boundingBox - The dimensions of the rectangle.

direction - The direction of the edge.

Returns:

The coordinate of the edge in the specified direction.

interpolateLinearly

public static Point2DDouble interpolateLinearly(Point2DDouble p1,
                                                Point2DDouble p2,
                                                double ratio)

Linearly interpolates between two points in 2D space and returns a point at the given ratio between the two points.

 interpolateLinearly(p1, p2, ratio) = p1 + ratio * (p2 - p1)
 

Parameters:

p1 - The first point in 2D space. null is treated as the origin (0, 0).

p2 - The second point in 2D space. null is treated as the origin (0, 0).

ratio - The ratio between the two points, where 0.0 is p1 and 1.0 is p2.

Returns:

A new point between p1 and p2 at the given ratio.

maxCoordinateInDirection

public static double maxCoordinateInDirection(ECardinalDirection2D direction,
                                              Point2DDouble p1,
                                              Point2DDouble p2)

Returns the maximal coordinate in the specified direction for the two given points in 2D space.

• NORTH: returns the minimum y-coordinate of the two points
• EAST: returns the maximum x-coordinate of the two points
• SOUTH: returns the maximum y-coordinate of the two points
• WEST: returns the minimum x-coordinate of the two points

Parameters:

direction - The direction in which to find the maximum coordinate

p1 - The first point in 2D space

p2 - The second point in 2D space

Returns:

The maximum coordinate in the specified direction.

maxCoordinateInDirection

public static double maxCoordinateInDirection(EAxisPolarity direction,
                                              double x,
                                              double y)

Returns the maximal coordinate in the specified axis direction for the two given coordinates in 2D space.

• POSITIVE: returns the maximum of the two coordinates
• NEGATIVE: returns the minimum of the two coordinates

Parameters:

direction - The direction in which to find the maximum coordinate

x - The first coordinate

y - The second coordinate

Returns:

The maximum coordinate in the specified direction.

maxCoordinateInDirection

public static double maxCoordinateInDirection(EAxisPolarity direction,
                                              double a,
                                              double b,
                                              double c)

Returns the maximal coordinate in the specified axis direction for the 3 given coordinates in 2D space.

• POSITIVE: returns the maximum of the two coordinates
• NEGATIVE: returns the minimum of the two coordinates

Parameters:

direction - The direction in which to find the maximum coordinate

a - The first coordinate

b - The second coordinate

c - The third coordinate

Returns:

The maximum coordinate in the specified direction.

maxCoordinateInDirection

public static double maxCoordinateInDirection(EAxisPolarity direction,
                                              double a,
                                              double b,
                                              double c,
                                              double d)

Returns the maximal coordinate in the specified axis direction for the 4 given coordinates in 2D space.

• POSITIVE: returns the maximum of the two coordinates
• NEGATIVE: returns the minimum of the two coordinates

Parameters:

direction - The direction in which to find the maximum coordinate

a - The first coordinate

b - The second coordinate

c - The third coordinate

d - The fourth coordinate

Returns:

The maximum coordinate in the specified direction.

offsetPointLine

public static double offsetPointLine(double px,
                                     double py,
                                     double lineX1,
                                     double lineY1,
                                     double lineX2,
                                     double lineY2)

Computes the offset of a point from a line segment defined by two points in 2D space. The offset is the oriented distance, its sign indicates whether the point is to the left or right of the line segment. If the offset is positive, the point is to the left of the line segment (when looking from the start point to the end point). If the offset is negative, the point is to the right of the line segment.

If the line start and end point are the same, returns the positive distance between the point and the center of the line's start and end point.

Parameters:

px - The x-coordinate of the point.

py - The y-coordinate of the point.

lineX1 - The x-coordinate of the first point of the line segment.

lineY1 - The y-coordinate of the first point of the line segment.

lineX2 - The x-coordinate of the second point of the line segment.

lineY2 - The y-coordinate of the second point of the line segment.

Returns:

The offset of the point from the line segment.

offsetPointLine

public static double offsetPointLine(Point2D<?> point,
                                     Point2D<?> lineStart,
                                     Point2D<?> lineEnd)

Computes the offset of a point from a line segment defined by two points in 2D space. The offset is the oriented distance, its sign indicates whether the point is to the left or right of the line segment. If the line start and end point are the same, returns the distance between the point and the center of the line's start and end point.

Parameters:

point - The point to compute the offset for.

lineStart - The start point of the line segment.

lineEnd - The end point of the line segment.

Returns:

The offset of the point from the line segment.