Class TrianglePredicate

Hierarchy: Object , TrianglePredicate

public class TrianglePredicate

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.

Authors:: Martin Davis

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 a vertex of the triangle; b - b a vertex of the triangle; c - c a vertex of the triangle; p - p the point to test

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

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 a vertex of the triangle; b - b a vertex of the triangle; c - c a vertex of the triangle; p - p the point to test

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

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 a vertex of the triangle; b - b a vertex of the triangle; c - c a vertex of the triangle; p - p the point to test

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

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 a vertex of the triangle; b - b a vertex of the triangle; c - c a vertex of the triangle; p - p the point to test

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

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 - ax the x ordinate of a vertex of the triangle; ay - ay the y ordinate of a vertex of the triangle; bx - bx the x ordinate of a vertex of the triangle; by - by the y ordinate of a vertex of the triangle; cx - cx the x ordinate of a vertex of the triangle; cy - cy the y ordinate of a vertex of the triangle

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

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

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

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.

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Parameters:: a - a a vertex of the triangle; b - b a vertex of the triangle; c - c a vertex of the triangle; p - p the point to test

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