Module org.arakhne.afc.core.mathgen

Package org.arakhne.afc.math

Class MathUtil

java.lang.Object

org.arakhne.afc.math.MathUtil

public final class MathUtil
extends Object

Mathematic and geometric utilities.

Version:

17.0 2020-01-04 14:41:41

Author:

Stéphane GALLAND, Hamza JAFFALI

Maven Group Id:

org.arakhne.afc.core

Maven Artifact Id:

mathgen

Method Summary

Modifier and Type	Method	Description
static double	clamp(double v, double min, double max)	Clamp the given value to the given range.
static int	clamp(int v, int min, int max)	Clamp the given value to the given range.
static double	clampCyclic(double value, double min, double max)	Clamp the given value to fit between the min and max values according to a cyclic heuristic.
static double	clampToNearestBounds(double value, double minBounds, double maxBounds)	Replies the value clamped to the nearest bounds.
static int	compareEpsilon(double v1, double v2)	Compares its two arguments for order.
static int	compareEpsilon(double v1, double v2, double epsilon)	Compares its two arguments for order.
static double	cot(double angle)	Replies the cotangent of the specified angle.
static double	crd(double angle)	Replies the chord of the specified angle.
static double	csc(double angle)	Replies the cosecant of the specified angle.
static double	exsec(double angle)	Replies the exsecant of the specified angle.
static int	getCohenSutherlandCode(double px, double py, double rxmin, double rymin, double rxmax, double rymax)	Compute the zone where the point is against the given rectangle according to the Cohen-Sutherland algorithm.
static int	getCohenSutherlandCode(int px, int py, int rxmin, int rymin, int rxmax, int rymax)	Compute the zone where the point is against the given rectangle according to the Cohen-Sutherland algorithm.
static int	getCohenSutherlandCode3D(double px, double py, double pz, double rxmin, double rymin, double rzmin, double rxmax, double rymax, double rzmax)	Compute the zone where the point is against the given rectangular prism according to the Cohen-Sutherland algorithm.
static int	getCohenSutherlandCode3D(int px, int py, int pz, int rxmin, int rymin, int rzmin, int rxmax, int rymax, int rzmax)	Compute the zone where the point is against the given rectangular prism according to the Cohen-Sutherland algorithm.
static DoubleRange	getMinMax(double value1, double value2, double value3)	Determine the min and max values from a set of three values.
static double	haversine(double angle)	Replies the half of the versine (aka, haversine) of the specified angle.
static boolean	isEpsilonEqual(double v1, double v2)	Replies if the given values are near.
static boolean	isEpsilonEqual(double v1, double v2, double epsilon)	Replies if the given values are near.
static boolean	isEpsilonZero(double value)	Replies if the given value is near zero.
static boolean	isEpsilonZero(double value, double epsilon)	Replies if the given value is near zero.
static double	max(double... values)	Replies the max value.
static float	max(float... values)	Replies the max value.
static int	max(int... values)	Replies the max value.
static long	max(long... values)	Replies the max value.
static short	max(short... values)	Replies the max value.
static double	min(double... values)	Replies the min value.
static float	min(float... values)	Replies the min value.
static int	min(int... values)	Replies the min value.
static long	min(long... values)	Replies the min value.
static short	min(short... values)	Replies the min value.
static double	sec(double angle)	Replies the secant of the specified angle.
static int	sign(double value)	Returns the sign of the argument; zero if the argument is zero, 1 if the argument is greater than zero, -1 if the argument is less than zero.
static int	signNoZero(double value)	Returns the sign of the argument; 1 if the argument is greater than or equal to zero, -1 if the argument is less than zero.
static double	versin(double angle)	Replies the versine of the specified angle.

Methods inherited from class java.lang.Object

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

Method Detail

sign

@Pure
public static int sign(double value)

Returns the sign of the argument; zero if the argument is zero, 1 if the argument is greater than zero, -1 if the argument is less than zero.

This function differs from Math.signum(double) because it is returning a integer value.

If you would like to treat the zero value as a positive number, see signNoZero(double).

Parameters:

value - the floating-point value whose sign is to be returned

Returns:

the sign of the argument, -1, 0 or 1.

See Also:

signNoZero(double), Math.signum(double)

signNoZero

@Pure
public static int signNoZero(double value)

Returns the sign of the argument; 1 if the argument is greater than or equal to zero, -1 if the argument is less than zero.

This function differs from sign(double) because it assumes the zero value has a positive sign.

Parameters:

value - the floating-point value whose sign is to be returned

Returns:

the sign of the argument, -1 or 1.

Since:

16.0

See Also:

sign(double), Math.signum(double)

clamp

@Pure
public static double clamp(double v,
                           double min,
                           double max)

Clamp the given value to the given range.

If the value is outside the [min;max] range, it is clamp to the nearest bounding value min or max.

Parameters:

v - is the value to clamp.

min - is the min value of the range.

max - is the max value of the range.

Returns:

the value in [min;max] range.

clamp

@Pure
public static int clamp(int v,
                        int min,
                        int max)

Clamp the given value to the given range.

If the value is outside the [min;max] range, it is clamp to the nearest bounding value min or max.

Parameters:

v - is the value to clamp.

min - is the min value of the range.

max - is the max value of the range.

Returns:

the value in [min;max] range.

isEpsilonZero

@Pure
public static boolean isEpsilonZero(double value)

Replies if the given value is near zero.

Parameters:

value - is the value to test.

Returns:

true if the given value is near zero, otherwise false.

See Also:

Math.ulp(double)

isEpsilonZero

@Pure
public static boolean isEpsilonZero(double value,
                                    double epsilon)

Replies if the given value is near zero.

Parameters:

value - is the value to test.

epsilon - the approximation epsilon. If Double.NaN, the function Math.ulp(double) is used for evaluating the epsilon.

Returns:

true if the given value is near zero, otherwise false.

isEpsilonEqual

@Pure
public static boolean isEpsilonEqual(double v1,
                                     double v2)

Replies if the given values are near.

Parameters:

v1 - first value.

v2 - second value.

Returns:

true if the given v1 is near v2, otherwise false.

See Also:

Math.ulp(double)

isEpsilonEqual

@Pure
public static boolean isEpsilonEqual(double v1,
                                     double v2,
                                     double epsilon)

Replies if the given values are near.

Parameters:

v1 - first value.

v2 - second value.

epsilon - the approximation epsilon. If Double.NaN, the function Math.ulp(double) is used for evaluating the epsilon.

Returns:

true if the given v1 is near v2, otherwise false.

compareEpsilon

@Pure
public static int compareEpsilon(double v1,
                                 double v2)

Compares its two arguments for order. Returns a negative integer, zero, or a positive integer as the first argument is less than, equal to, or greater than the second.

Parameters:

v1 - first value.

v2 - second value.

Returns:

a negative integer, zero, or a positive integer as the first argument is less than, equal to, or greater than the second.

compareEpsilon

@Pure
public static int compareEpsilon(double v1,
                                 double v2,
                                 double epsilon)

Compares its two arguments for order. Returns a negative integer, zero, or a positive integer as the first argument is less than, equal to, or greater than the second.

Parameters:

v1 - first value.

v2 - second value.

epsilon - approximation epsilon. If Double.NaN, the function Math.ulp(double) is used for evaluating the epsilon.

Returns:

a negative integer, zero, or a positive integer as the first argument is less than, equal to, or greater than the second.

max

@Pure
public static double max(double... values)

Replies the max value.

Parameters:

values - are the values to scan.

Returns:

the max value.

max

@Pure
public static float max(float... values)

Replies the max value.

Parameters:

values - are the values to scan.

Returns:

the max value.

max

@Pure
public static int max(int... values)

Replies the max value.

Parameters:

values - are the values to scan.

Returns:

the max value.

max

@Pure
public static long max(long... values)

Replies the max value.

Parameters:

values - are the values to scan.

Returns:

the max value.

max

@Pure
public static short max(short... values)

Replies the max value.

Parameters:

values - are the values to scan.

Returns:

the max value.

min

@Pure
public static double min(double... values)

Replies the min value.

Parameters:

values - are the values to scan.

Returns:

the min value.

min

@Pure
public static float min(float... values)

Replies the min value.

Parameters:

values - are the values to scan.

Returns:

the min value.

min

@Pure
public static int min(int... values)

Replies the min value.

Parameters:

values - are the values to scan.

Returns:

the min value.

min

@Pure
public static long min(long... values)

Replies the min value.

Parameters:

values - are the values to scan.

Returns:

the min value.

min

@Pure
public static short min(short... values)

Replies the min value.

Parameters:

values - are the values to scan.

Returns:

the min value.

clampCyclic

@Pure
public static double clampCyclic(double value,
                                 double min,
                                 double max)

Clamp the given value to fit between the min and max values according to a cyclic heuristic. If the given value is not between the minimum and maximum values, the replied value is modulo the min-max range.

Parameters:

value - the value to clamp.

min - the minimum value inclusive.

max - the maximum value exclusive.

Returns:

the clamped value

clampToNearestBounds

@Pure
public static double clampToNearestBounds(double value,
                                          double minBounds,
                                          double maxBounds)

Replies the value clamped to the nearest bounds. If |value-minBounds| > |value-maxBounds| then the returned value is maxBounds; otherwise it is minBounds.

Parameters:

value - is the value to clamp.

minBounds - is the minimal allowed value.

maxBounds - is the maximal allowed value.

Returns:

minBounds or maxBounds.

getCohenSutherlandCode

@Pure
public static int getCohenSutherlandCode(int px,
                                         int py,
                                         int rxmin,
                                         int rymin,
                                         int rxmax,
                                         int rymax)

Compute the zone where the point is against the given rectangle according to the Cohen-Sutherland algorithm.

Parameters:

px - is the coordinates of the points.

py - is the coordinates of the points.

rxmin - is the min of the coordinates of the rectangle.

rymin - is the min of the coordinates of the rectangle.

rxmax - is the max of the coordinates of the rectangle.

rymax - is the max of the coordinates of the rectangle.

Returns:

the zone

See Also:

MathConstants.COHEN_SUTHERLAND_BOTTOM, MathConstants.COHEN_SUTHERLAND_TOP, MathConstants.COHEN_SUTHERLAND_LEFT, MathConstants.COHEN_SUTHERLAND_RIGHT, MathConstants.COHEN_SUTHERLAND_INSIDE

getCohenSutherlandCode

@Pure
public static int getCohenSutherlandCode(double px,
                                         double py,
                                         double rxmin,
                                         double rymin,
                                         double rxmax,
                                         double rymax)

Compute the zone where the point is against the given rectangle according to the Cohen-Sutherland algorithm.

This function considers that if a point coordinate is equal to the a border coordinate of the rectangle, it is inside the rectangle.

Parameters:

px - is the coordinates of the points.

py - is the coordinates of the points.

rxmin - is the min of the coordinates of the rectangle.

rymin - is the min of the coordinates of the rectangle.

rxmax - is the max of the coordinates of the rectangle.

rymax - is the max of the coordinates of the rectangle.

Returns:

the zone

See Also:

MathConstants.COHEN_SUTHERLAND_BOTTOM, MathConstants.COHEN_SUTHERLAND_TOP, MathConstants.COHEN_SUTHERLAND_LEFT, MathConstants.COHEN_SUTHERLAND_RIGHT, MathConstants.COHEN_SUTHERLAND_INSIDE

getCohenSutherlandCode3D

@Pure
public static int getCohenSutherlandCode3D(int px,
                                           int py,
                                           int pz,
                                           int rxmin,
                                           int rymin,
                                           int rzmin,
                                           int rxmax,
                                           int rymax,
                                           int rzmax)

Compute the zone where the point is against the given rectangular prism according to the Cohen-Sutherland algorithm.

Parameters:

px - is the coordinates of the point.

py - is the coordinates of the point.

pz - is the coordinates of the point.

rxmin - is the min of the coordinates of the rectangular prism.

rymin - is the min of the coordinates of the rectangular prism.

rzmin - is the min of the coordinates of the rectangular prism.

rxmax - is the max of the coordinates of the rectangular prism.

rymax - is the max of the coordinates of the rectangular prism.

rzmax - is the max of the coordinates of the rectangular prism.

Returns:

the zone

getCohenSutherlandCode3D

@Pure
public static int getCohenSutherlandCode3D(double px,
                                           double py,
                                           double pz,
                                           double rxmin,
                                           double rymin,
                                           double rzmin,
                                           double rxmax,
                                           double rymax,
                                           double rzmax)

Compute the zone where the point is against the given rectangular prism according to the Cohen-Sutherland algorithm.

This function considers that if a point coordinate is equal to the a border coordinate of the rectangle, it is inside the rectangle.

Parameters:

px - is the coordinates of the point.

py - is the coordinates of the point.

pz - is the coordinates of the point.

rxmin - is the min of the coordinates of the rectangular prism.

rymin - is the min of the coordinates of the rectangular prism.

rzmin - is the min of the coordinates of the rectangular prism.

rxmax - is the max of the coordinates of the rectangular prism.

rymax - is the max of the coordinates of the rectangular prism.

rzmax - is the max of the coordinates of the rectangular prism.

Returns:

the zone

getMinMax

public static DoubleRange getMinMax(double value1,
                                    double value2,
                                    double value3)

Determine the min and max values from a set of three values.

This function has an algorithm that is efficient for 3 values.

If one of the value is Double.NaN, it is ignored. If all the values are Double.NaN, the function replies null.

Parameters:

value1 - the first value.

value2 - the second value.

value3 - the third value.

Returns:

the min max range; or null.

Since:

13.0

csc

@Pure
public static double csc(double angle)

Replies the cosecant of the specified angle.

csc(a) = 1/sin(a)

Parameters:

angle - the angle.

Returns:

the cosecant of the angle.

sec

@Pure
public static double sec(double angle)

Replies the secant of the specified angle.

csc(a) = 1/cos(a)

Parameters:

angle - the angle.

Returns:

the secant of the angle.

cot

@Pure
public static double cot(double angle)

Replies the cotangent of the specified angle.

csc(a) = 1/tan(a)

Parameters:

angle - the angle.

Returns:

the cotangent of the angle.

versin

@Pure
public static double versin(double angle)

Replies the versine of the specified angle.

versin(a) = 1 - cos(a)

Parameters:

angle - the angle.

Returns:

the versine of the angle.

exsec

@Pure
public static double exsec(double angle)

Replies the exsecant of the specified angle.

exsec(a) = sec(a) - 1

Parameters:

angle - the angle.

Returns:

the exsecant of the angle..

crd

@Pure
public static double crd(double angle)

Replies the chord of the specified angle.

crd(a) = 2 sin(a/2)

Parameters:

angle - the angle.

Returns:

the chord of the angle.

haversine

@Pure
public static double haversine(double angle)

Replies the half of the versine (aka, haversine) of the specified angle.

haversine(a) = sin2(a/2) = (1-cos(a)) / 2

Parameters:

angle - the angle.

Returns:

the half of the versine of the angle.