org.locationtech.jts.triangulate.quadedge

Class TrianglePredicate

java.lang.Object

org.locationtech.jts.triangulate.quadedge.TrianglePredicate

public class TrianglePredicate
extends Object

Algorithms for computing values and predicates associated with triangles. For some algorithms extended-precision implementations are provided, which are more robust (i.e. they produce correct answers in more cases). Also, some more robust formulations of some algorithms are provided, which utilize normalization to the origin.

Author:

Martin Davis

Constructor Summary

Constructors

Constructor and Description
TrianglePredicate()

Method Summary

Modifier and Type	Method and Description
static boolean	isInCircleCC(Coordinate a, Coordinate b, Coordinate c, Coordinate p) Computes the inCircle test using distance from the circumcentre.
static boolean	isInCircleDDFast(Coordinate a, Coordinate b, Coordinate c, Coordinate p)
static boolean	isInCircleDDNormalized(Coordinate a, Coordinate b, Coordinate c, Coordinate p)
static boolean	isInCircleDDSlow(Coordinate a, Coordinate b, Coordinate c, Coordinate p) Tests if a point is inside the circle defined by the triangle with vertices a, b, c (oriented counter-clockwise).
static boolean	isInCircleNonRobust(Coordinate a, Coordinate b, Coordinate c, Coordinate p) Tests if a point is inside the circle defined by the triangle with vertices a, b, c (oriented counter-clockwise).
static boolean	isInCircleNormalized(Coordinate a, Coordinate b, Coordinate c, Coordinate p) Tests if a point is inside the circle defined by the triangle with vertices a, b, c (oriented counter-clockwise).
static boolean	isInCircleRobust(Coordinate a, Coordinate b, Coordinate c, Coordinate p) Tests if a point is inside the circle defined by the triangle with vertices a, b, c (oriented counter-clockwise).
static DD	triAreaDDFast(Coordinate a, Coordinate b, Coordinate c)
static DD	triAreaDDSlow(DD ax, DD ay, DD bx, DD by, DD cx, DD cy) Computes twice the area of the oriented triangle (a, b, c), i.e., the area is positive if the triangle is oriented counterclockwise.

Methods inherited from class java.lang.Object

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

Constructor Detail

TrianglePredicate

public TrianglePredicate()

Method Detail

isInCircleNonRobust

public static boolean isInCircleNonRobust(Coordinate a,
                                          Coordinate b,
                                          Coordinate c,
                                          Coordinate p)

Tests if a point is inside the circle defined by the triangle with vertices a, b, c (oriented counter-clockwise). This test uses simple double-precision arithmetic, and thus may not be robust.

Parameters:

a - a vertex of the triangle

b - a vertex of the triangle

c - a vertex of the triangle

p - the point to test

Returns:

true if this point is inside the circle defined by the points a, b, c

isInCircleNormalized

public static boolean isInCircleNormalized(Coordinate a,
                                           Coordinate b,
                                           Coordinate c,
                                           Coordinate p)

Tests if a point is inside the circle defined by the triangle with vertices a, b, c (oriented counter-clockwise). This test uses simple double-precision arithmetic, and thus is not 100% robust. However, by using normalization to the origin it provides improved robustness and increased performance.

Based on code by J.R.Shewchuk.

Parameters:

a - a vertex of the triangle

b - a vertex of the triangle

c - a vertex of the triangle

p - the point to test

Returns:

true if this point is inside the circle defined by the points a, b, c

isInCircleRobust

public static boolean isInCircleRobust(Coordinate a,
                                       Coordinate b,
                                       Coordinate c,
                                       Coordinate p)

Tests if a point is inside the circle defined by the triangle with vertices a, b, c (oriented counter-clockwise). This method uses more robust computation.

Parameters:

a - a vertex of the triangle

b - a vertex of the triangle

c - a vertex of the triangle

p - the point to test

Returns:

true if this point is inside the circle defined by the points a, b, c

isInCircleDDSlow

public static boolean isInCircleDDSlow(Coordinate a,
                                       Coordinate b,
                                       Coordinate c,
                                       Coordinate p)

Tests if a point is inside the circle defined by the triangle with vertices a, b, c (oriented counter-clockwise). The computation uses DD arithmetic for robustness.

Parameters:

a - a vertex of the triangle

b - a vertex of the triangle

c - a vertex of the triangle

p - the point to test

Returns:

true if this point is inside the circle defined by the points a, b, c

triAreaDDSlow

public static DD triAreaDDSlow(DD ax,
                               DD ay,
                               DD bx,
                               DD by,
                               DD cx,
                               DD cy)

Computes twice the area of the oriented triangle (a, b, c), i.e., the area is positive if the triangle is oriented counterclockwise. The computation uses DD arithmetic for robustness.

Parameters:

ax - the x ordinate of a vertex of the triangle

ay - the y ordinate of a vertex of the triangle

bx - the x ordinate of a vertex of the triangle

by - the y ordinate of a vertex of the triangle

cx - the x ordinate of a vertex of the triangle

cy - the y ordinate of a vertex of the triangle

isInCircleDDFast

public static boolean isInCircleDDFast(Coordinate a,
                                       Coordinate b,
                                       Coordinate c,
                                       Coordinate p)

triAreaDDFast

public static DD triAreaDDFast(Coordinate a,
                               Coordinate b,
                               Coordinate c)

isInCircleDDNormalized

public static boolean isInCircleDDNormalized(Coordinate a,
                                             Coordinate b,
                                             Coordinate c,
                                             Coordinate p)

isInCircleCC

public static boolean isInCircleCC(Coordinate a,
                                   Coordinate b,
                                   Coordinate c,
                                   Coordinate p)

Computes the inCircle test using distance from the circumcentre. Uses standard double-precision arithmetic.

In general this doesn't appear to be any more robust than the standard calculation. However, there is at least one case where the test point is far enough from the circumcircle that this test gives the correct answer.

 LINESTRING
 (1507029.9878 518325.7547, 1507022.1120341457 518332.8225183258,
 1507029.9833 518325.7458, 1507029.9896965567 518325.744909031)
 

Parameters:

a - a vertex of the triangle

b - a vertex of the triangle

c - a vertex of the triangle

p - the point to test

Returns:

true if this point is inside the circle defined by the points a, b, c