aim4.util

Class GeomMath

java.lang.Object

aim4.util.GeomMath

public final class GeomMath
extends Object

Class of static utility methods for geometric computation.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	GeomMath.IntersectionPoint A class for storing the result of findLineLineIntersection.

Field Summary

Fields

Modifier and Type	Field and Description
static double	HALF_PI Math.PI / 2.0
static double	ONE_AND_HALF_PI Math.PI * 3.0 / 2.0
static double	PI Math.PI
static double	QUARTER_PI Math.PI / 4.0
static double	TWO_PI Math.PI * 2.0

Method Summary

Methods

Modifier and Type	Method and Description
static double	angleDiff(double ang1, double ang2) Determine the angle between two angles.
static double	angleToPoint(Point2D p, Point2D startPoint) Find the angle of the heading to a point from a given starting point.
static double	canonicalAngle(double angle) Get the "canonical" angle.
static Point2D	centroid(List<Point2D> points) Find the centroid of a list of points.
static double	crossProduct(Point2D p1, Point2D p2) Compute the cross product of two 2D vectors.
static double	dotProduct(Point2D p1, Point2D p2) Compute the dot product of two 2D vectors.
static Area	filledArea(Shape s) Find the Area corresponding to the provided Shape with all holes filled in.
static Point2D	findLineLineIntersection(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4) Compute the intersection of two lines defined by two points each.
static Point2D	findLineLineIntersection(Line2D l1, Line2D l2) Compute the intersection of two lines.
static GeomMath.IntersectionPoint	findLineLineIntersection(Point2D p1, double slope1, Point2D p2, double slope2) Compute the intersection of two lines defined by two points each.
static boolean	intervalsOverlap(double t1start, double t1end, double t2start, double t2end) Determine whether two intervals overlap.
static String	ordinalize(int num) Turn a cardinal number into an ordinal number.
static Point2D	polarAdd(Point2D p, double r, double theta) Find a point displaced by the given distance in the given direction.
static List<Double>	polygonalShapeAreas(Shape s) Given a polygonal, non-overlapping Shape, return the areas of the closed portions of the shape.
static Point2D	polygonalShapeCentroid(Shape s) Given a polygonal Shape, return the centroid of the shape.
static List<Line2D>	polygonalShapePerimeterSegments(Shape s) Given a polygonal Shape, return a list of segments describing its perimeter.
static List<List<Point2D>>	polygonalSubShapeVertices(Shape s) Given a polygonal Shape, return a list of lists of points that are the vertices of the closed polygonal sub-shapes.
static double	quadraticFormula(double a, double b, double c) Solve the quadratic formula ax2 + bx + c = 0 given coefficients a, b, and c, returning the minimum nonnegative root, or the largest root if both are negative.
static List<Area>	subareas(Shape s) Find all the subareas of a Shape.
static Point2D	subtract(Point2D p1, Point2D p2) Subtract two 2D vectors.

Methods inherited from class java.lang.Object

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

Field Detail

QUARTER_PI

public static final double QUARTER_PI

Math.PI / 4.0

See Also:

Constant Field Values

HALF_PI

public static final double HALF_PI

Math.PI / 2.0

See Also:

Constant Field Values

PI

public static final double PI

Math.PI

See Also:

Constant Field Values

ONE_AND_HALF_PI

public static final double ONE_AND_HALF_PI

Math.PI * 3.0 / 2.0

See Also:

Constant Field Values

TWO_PI

public static final double TWO_PI

Math.PI * 2.0

See Also:

Constant Field Values

Method Detail

ordinalize

public static String ordinalize(int num)

Turn a cardinal number into an ordinal number.

Parameters:

num - the cardinal number

Returns:

the ordinal version of the given number

canonicalAngle

public static double canonicalAngle(double angle)

Get the "canonical" angle. This is used for recentering angles in [0.0, 2*Pi).

Parameters:

angle - the angle

Returns:

an equivalent angle that is greater than or equal to 0.0 and less than 2*PI

angleToPoint

public static double angleToPoint(Point2D p,
                  Point2D startPoint)

Find the angle of the heading to a point from a given starting point.

Parameters:

p - the point to which to find the angle

startPoint - the point from which to start

Returns:

the angle of the heading to the first point when starting at the second point

polarAdd

public static Point2D polarAdd(Point2D p,
               double r,
               double theta)

Find a point displaced by the given distance in the given direction.

Parameters:

p - the starting point

r - the distance to move from the point

theta - the angle at which to move from the point

Returns:

the point displaced the given distance in the given direction from the original point

subtract

public static Point2D subtract(Point2D p1,
               Point2D p2)

Subtract two 2D vectors.

Parameters:

p1 - the first vector

p2 - the second vector

Returns:

a Point representing the subtraction of the second vector from the first

dotProduct

public static double dotProduct(Point2D p1,
                Point2D p2)

Compute the dot product of two 2D vectors.

Parameters:

p1 - the first vector

p2 - the second vector

Returns:

the dot product of the two vectors

crossProduct

public static double crossProduct(Point2D p1,
                  Point2D p2)

Compute the cross product of two 2D vectors.

Parameters:

p1 - the first vector

p2 - the second vector

Returns:

the cross product of the two vectors

findLineLineIntersection

public static Point2D findLineLineIntersection(Line2D l1,
                               Line2D l2)

Compute the intersection of two lines.

Parameters:

l1 - the first line

l2 - the second line

Returns:

the intersection point of the two lines

findLineLineIntersection

public static Point2D findLineLineIntersection(double x1,
                               double y1,
                               double x2,
                               double y2,
                               double x3,
                               double y3,
                               double x4,
                               double y4)

Compute the intersection of two lines defined by two points each. Undefined behavior if the lines are parallel.

Parameters:

x1 - the x coordinate of the first point of the first line

y1 - the y coordinate of the first point of the first line

x2 - the x coordinate of the second point of the first line

y2 - the y coordinate of the second point of the first line

x3 - the x coordinate of the first point of the second line

y3 - the y coordinate of the first point of the second line

x4 - the x coordinate of the second point of the second line

y4 - the y coordinate of the second point of the second line

Returns:

the intersection point of the two lines.

findLineLineIntersection

public static GeomMath.IntersectionPoint findLineLineIntersection(Point2D p1,
                                                  double slope1,
                                                  Point2D p2,
                                                  double slope2)

Compute the intersection of two lines defined by two points each. Undefined behavior if the lines are parallel.

Parameters:

p1 - an intercepting point of the first line

slope1 - the slope of the first line

p2 - an intercepting point of the second line

slope2 - the slope of the second line

Returns:

the intersection point of the two lines, with the distances between the intersection points and the intercepting points.

polygonalSubShapeVertices

public static List<List<Point2D>> polygonalSubShapeVertices(Shape s)

Given a polygonal Shape, return a list of lists of points that are the vertices of the closed polygonal sub-shapes.

Parameters:

s - the polygonal Shape

Returns:

the lists of sub-shape vertices

Throws:

IllegalArgumentException - if the Shape is not polygonal

polygonalShapePerimeterSegments

public static List<Line2D> polygonalShapePerimeterSegments(Shape s)

Given a polygonal Shape, return a list of segments describing its perimeter.

Parameters:

s - the polygonal Shape

Returns:

a list of segments describing the perimeter of the Shape

Throws:

IllegalArgumentException - if the Shape is not polygonal

polygonalShapeAreas

public static List<Double> polygonalShapeAreas(Shape s)

Given a polygonal, non-overlapping Shape, return the areas of the closed portions of the shape. If the Shape is not polygonal or it overlaps itself, behavior is undefined.

Parameters:

s - the polygonal Shape

Returns:

the areas of the closed portions of the Shape

polygonalShapeCentroid

public static Point2D polygonalShapeCentroid(Shape s)

Given a polygonal Shape, return the centroid of the shape. If the Shape is not polygonal, behavior is undefined.

Parameters:

s - the polygonal Shape

Returns:

the centroid of the Shape

centroid

public static Point2D centroid(List<Point2D> points)

Find the centroid of a list of points.

Parameters:

points - the List of Points

Returns:

the centroid of the Points

filledArea

public static Area filledArea(Shape s)

Find the Area corresponding to the provided Shape with all holes filled in. Takes the union of all the subareas according to subareas(Shape s).

Parameters:

s - the Shape to fill in

Returns:

an Area representing the Shape with all holes filled in

subareas

public static List<Area> subareas(Shape s)

Find all the subareas of a Shape. This means that if a Shape is defined as a Shape with a piece missing from it, this will return both an Area for the full Shape as well as one for the hole in the middle. If multiple pieces exist, they will each be returned individually.

Parameters:

s - the Shape to deconstruct.

Returns:

a List of subareas that make up the Shape

quadraticFormula

public static double quadraticFormula(double a,
                      double b,
                      double c)

Solve the quadratic formula ax² + bx + c = 0 given coefficients a, b, and c, returning the minimum nonnegative root, or the largest root if both are negative.

Parameters:

a - the coefficient of the x² term

b - the coefficient of the x term

c - the constant term

Returns:

the minimum nonnegative root, or the largest root if both are negative

intervalsOverlap

public static boolean intervalsOverlap(double t1start,
                       double t1end,
                       double t2start,
                       double t2end)

Determine whether two intervals overlap. This is determined by checking if either of two things is true: the start of the first interval falls inside the duration of the second interval, or the start of the second interval falls within the duration of the first interval. If neither is true, they cannot overlap.

Parameters:

t1start - the start of the first interval

t1end - the end of the first interval

t2start - the start of the second interval

t2end - the end of the second interval

Returns:

whether the provided two intervals overlap

angleDiff

public static double angleDiff(double ang1,
               double ang2)

Determine the angle between two angles. This includes the cases where the shortest angle between the two crosses the positive X axis.

Parameters:

ang1 - the first angle

ang2 - the second angle

Returns:

the angle between the two given angles