HomogeneousPoint2D.java
/*
* Copyright (C) 2017 Alberto Irurueta Carro (alberto@irurueta.com)
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.irurueta.geometry;
import java.io.Serializable;
import java.util.Objects;
/**
* Subclass of Point2D defining an homogeneous 2D point.
* An homogeneous 2d point is defined by three coordinates: (x,y,w), where
* x and y are the horizontal and vertical coordinates, respectively, and w
* is a normalization (homogenization) factor. Homogeneous 2d points at
* infinity are expressed using w=0 (x,y,0) where (x,y) describe the direction
* of the 2d point towards infinity.
* Inhomogeneous 2d points can be transformed into homogeneous 2d points by
* setting the w coordinate to one (w=1, not at infinity) as follows:
* Inhomogeneous 2d point (x,y) -< Homogeneous 2d point (x,y,1).
*/
public class HomogeneousPoint2D extends Point2D implements Serializable {
/**
* Default threshold to consider a point is located at infinity.
*/
private static final double DEFAULT_INFINITY_THRESHOLD = 1e-10;
/**
* Machine precision.
*/
private static final double PRECISION = 1e-12;
/**
* Defines the X coordinate of an homogeneous 2D point.
*/
private double x;
/**
* Defines the Y coordinate of an homogeneous 2D point.
*/
private double y;
/**
* Defines the W coordinate of an homogeneous 2D point.
*/
private double w;
/**
* Determines whether this point is already normalized.
*/
private boolean normalized;
/**
* Empty constructor.
*/
public HomogeneousPoint2D() {
super();
x = y = 0.0;
w = 1.0;
normalized = false;
}
/**
* Constructor of this class. This constructor sets a new homogeneous
* v array containing the coordinates X, Y and W of the given point.
*
* @param v Array of length 3 containing the 2D coordinates of an
* homogeneous point.
* @throws IllegalArgumentException Raised when the size of the array is
* different of 3.
*/
public HomogeneousPoint2D(final double[] v) {
super();
setCoordinates(v);
}
/**
* Constructor of this class. This constructor sets a new homogeneous 2D
* point using the coordinates X, Y and W of the given point.
*
* @param x X coordinate of the given 2D point.
* @param y Y coordinate of the given 2D point.
* @param w W coordinate of the given 2D point.
*/
public HomogeneousPoint2D(final double x, final double y, final double w) {
this.x = x;
this.y = y;
this.w = w;
normalized = false;
}
/**
* This constructor sets a new homogeneous 2D point using as initialization
* provided Point2D instance.
*
* @param point Point to initialize new instance to.
*/
public HomogeneousPoint2D(final Point2D point) {
setCoordinates(point);
}
/**
* Returns the X coordinate of the given homogeneous 2D point instance.
*
* @return X coordinate.
*/
public double getX() {
return x;
}
/**
* Sets the X coordinate of this homogeneous point.
*
* @param x X coordinate.
*/
public void setX(final double x) {
this.x = x;
normalized = false;
}
/**
* Returns the Y coordinate of the given homogeneous 2D point instance.
*
* @return Y coordinate.
*/
public double getY() {
return y;
}
/**
* Sets the Y coordinate of this homogeneous point.
*
* @param y Y coordinate.
*/
public void setY(final double y) {
this.y = y;
normalized = false;
}
/**
* Returns the W coordinate of the given homogeneous 2D point instance.
*
* @return W coordinate.
*/
public double getW() {
return w;
}
/**
* Sets the W coordinate of this homogeneous point.
*
* @param w W coordinate.
*/
public void setW(final double w) {
this.w = w;
normalized = false;
}
/**
* Sets the coordinates of this homogeneous 2D point by using provided X,
* Y and W coordinates.
*
* @param x X coordinate.
* @param y Y coordinate.
* @param w W coordinate.
*/
public void setCoordinates(final double x, final double y, final double w) {
this.x = x;
this.y = y;
this.w = w;
normalized = false;
}
/**
* Sets the coordinates of a 2d point using an array containing its
* coordinates.
*
* @param v Array containing the coordinates of the point.
* @throws IllegalArgumentException Raised if provided array does not have
* a valid size.
*/
@Override
public final void setCoordinates(final double[] v) {
if (v.length != POINT2D_HOMOGENEOUS_COORDINATES_LENGTH) {
throw new IllegalArgumentException();
} else {
x = v[0];
y = v[1];
w = v[2];
normalized = false;
}
}
/**
* Sets coordinates of this instance using the coordinates of provided 2D
* point.
*
* @param point Input point.
*/
@Override
public final void setCoordinates(final Point2D point) {
switch (point.getType()) {
case INHOMOGENEOUS_COORDINATES:
final var inhomPoint = (InhomogeneousPoint2D) point;
x = inhomPoint.getX();
y = inhomPoint.getY();
w = 1.0;
normalized = false;
break;
case HOMOGENEOUS_COORDINATES:
default:
final var homPoint = (HomogeneousPoint2D) point;
x = homPoint.getX();
y = homPoint.getY();
w = homPoint.getW();
normalized = false;
break;
}
}
/**
* Returns X homogeneous coordinate of this 2d point.
*
* @return X homogeneous coordinate.
*/
@Override
public double getHomX() {
return getX();
}
/**
* Returns Y homogeneous coordinate of this 2d point.
*
* @return Y homogeneous coordinate.
*/
@Override
public double getHomY() {
return getY();
}
/**
* Returns W homogeneous coordinate of this 2d point.
*
* @return W homogeneous coordinate.
*/
@Override
public double getHomW() {
return getW();
}
/**
* Sets coordinates of this 2d point instance using provided homogeneous
* coordinates.
*
* @param homX x homogeneous coordinate.
* @param homY y homogeneous coordinate.
* @param homW w homogeneous coordinate.
*/
@Override
public void setHomogeneousCoordinates(final double homX, final double homY, final double homW) {
setCoordinates(homX, homY, homW);
}
/**
* Returns X inhomogeneous coordinate of this 2d point.
*
* @return X inhomogeneous coordinate.
*/
@Override
public double getInhomX() {
return (x / w);
}
/**
* Sets X inhomogeneous coordinate of this 2d point.
*
* @param inhomX inhomogeneous coordinate.
*/
@Override
public void setInhomX(final double inhomX) {
x = inhomX * w;
normalized = false;
}
/**
* Returns Y inhomogeneous coordinate of this 2d point.
*
* @return Y inhomogeneous coordinate.
*/
@Override
public double getInhomY() {
return (y / w);
}
/**
* Sets Y inhomogeneous coordinate of this 2d point.
*
* @param inhomY Y inhomogeneous coordinate.
*/
@Override
public void setInhomY(final double inhomY) {
y = inhomY * w;
normalized = false;
}
/**
* Sets coordinates of this 2d point instance using provided inhomogeneous
* coordinates.
*
* @param inhomX x inhomogeneous coordinate.
* @param inhomY y inhomogeneous coordinate.
*/
@Override
public void setInhomogeneousCoordinates(final double inhomX, final double inhomY) {
x = inhomX;
y = inhomY;
w = 1.0;
normalized = false;
}
/**
* Checks if provided object equals current 2D point.
*
* @param obj Object to compare.
* @return True if both objects are considered to be equal, false otherwise.
*/
@Override
public boolean equals(final Object obj) {
if (!(obj instanceof Point2D point)) {
return false;
}
if (obj == this) {
return true;
}
return equals(point);
}
/**
* Returns hash code value.
*
* @return Hash code value.
*/
@Override
public int hashCode() {
return Objects.hash(x, y, w);
}
/**
* Checks if the homogeneous 2d point described by this instance equals the
* input {@link Point2D} (using a comparison threshold).
*
* @param point Point that will be compared to.
* @param threshold threshold grade of tolerance to determine whether the
* points are equal or not. It is used because due to machine precision, the
* values might not be exactly equal (if not provided
* DEFAULT_COMPARISON_THRESHOLD is used).
* @return True if current point and input point are the same, false
* otherwise.
* @throws IllegalArgumentException Raised if threshold is negative.
*/
@Override
public boolean equals(final Point2D point, final double threshold) {
if (point.getType() == CoordinatesType.INHOMOGENEOUS_COORDINATES) {
return equals((InhomogeneousPoint2D) point, threshold);
} else {
return equals((HomogeneousPoint2D) point, threshold);
}
}
/**
* Checks if the homogeneous 2d point described by this instance equals the
* input HomogeneousPoint2d (using a comparison threshold).
*
* @param point Point that will be compared to.
* @param threshold threshold grade of tolerance to determine whether the
* points are equal or not. It is used because due to machine precision, the
* values might not be exactly equal (if not provided
* DEFAULT_COMPARISON_THRESHOLD is used).
* @return True if current point and input point are the same, false
* otherwise.
* @throws IllegalArgumentException Raised if threshold is negative.
*/
public boolean equals(final HomogeneousPoint2D point, final double threshold) {
if (threshold < MIN_THRESHOLD) {
throw new IllegalArgumentException();
}
normalize();
point.normalize();
// compute sign for the case when points have different sign
final var signThis = (w > 0.0) ? 1.0 : -1.0;
final var signPoint = (point.w > 0.0) ? 1.0 : -1.0;
final var normThis = Math.sqrt(x * x + y * y + w * w) * signThis;
final var normPoint = Math.sqrt(point.x * point.x + point.y * point.y + point.w * point.w) * signPoint;
final var validX = Math.abs(x / normThis - point.x / normPoint) <= threshold;
final var validY = Math.abs(y / normThis - point.y / normPoint) <= threshold;
final var validW = Math.abs(w / normThis - point.w / normPoint) <= threshold;
return (validX && validY && validW);
}
/**
* Checks if the homogeneous 2d point described by this instance equals the
* input HomogeneousPoint2d (using a comparison threshold).
*
* @param point Point that will be compared to.
* @return True if current point and input point are the same, false
* otherwise.
*/
public boolean equals(final HomogeneousPoint2D point) {
return equals(point, DEFAULT_COMPARISON_THRESHOLD);
}
/**
* Checks if the homogeneous 2d point described by this instance equals the
* input InhomogeneousPoint2d (using a comparison threshold).
*
* @param point Point that will be compared to.
* @param threshold threshold grade of tolerance to determine whether the
* points are equal or not. It is used because due to machine precision, the
* values might not be exactly equal (if not provided
* DEFAULT_COMPARISON_THRESHOLD is used).
* @return True if current point and input point are the same, false
* otherwise.
* @throws IllegalArgumentException Raised if threshold is negative.
*/
public boolean equals(final InhomogeneousPoint2D point, final double threshold) {
if (threshold < MIN_THRESHOLD) {
throw new IllegalArgumentException();
}
final var dX = Math.abs(point.getX() - (x / w)) <= threshold;
final var dY = Math.abs(point.getY() - (y / w)) <= threshold;
return (dX && dY);
}
/**
* Checks if the homogeneous 2d point described by this instance equals the
* input InhomogeneousPoint2d (using a comparison threshold).
*
* @param point Point that will be compared to.
* @return True if current point and input point are the same, false
* otherwise.
*/
public boolean equals(final InhomogeneousPoint2D point) {
return equals(point, DEFAULT_COMPARISON_THRESHOLD);
}
/**
* Checks whether this Point2D is at infinity or not.
*
* @return True if the point is at infinity. False otherwise.
*/
@Override
public boolean isAtInfinity() {
return isAtInfinity(DEFAULT_INFINITY_THRESHOLD);
}
/**
* Checks whether this homogeneous 2D point is at infinity or not. An
* homogeneous 2D point is at infinity when W coordinates are equal or close
* to zero.
*
* @param threshold Grade of tolerance to determine whether the point is at
* infinity or not. It is used because due to machine precision, the values
* might not be exactly equal.
* @return True if point is at infinity, false otherwise.
* @throws IllegalArgumentException Raised if threshold is negative.
*/
public boolean isAtInfinity(final double threshold) {
if (threshold < MIN_THRESHOLD) {
throw new IllegalArgumentException();
}
return (Math.abs(w) <= threshold);
}
/**
* Returns the type of coordinates used to represent a Point2D.
*
* @return Type of coordinates of this 2d point.
*/
@Override
public CoordinatesType getType() {
return CoordinatesType.HOMOGENEOUS_COORDINATES;
}
/**
* Method to normalize a 2d point by dividing all homogeneous components by
* its norm. This only applies to homogeneous 2d points, because they are
* defined up to scale.
*/
@SuppressWarnings("DuplicatedCode")
@Override
public void normalize() {
if (!normalized) {
final var norm = Math.sqrt(x * x + y * y + w * w);
if (norm > PRECISION) {
x /= norm;
y /= norm;
w /= norm;
normalized = true;
}
}
}
/**
* Returns boolean indicating whether this point has already been mNormalized
*
* @return True if mNormalized, false otherwise.
*/
@Override
public boolean isNormalized() {
return normalized;
}
/**
* Converts this instance into an inhomogeneous 2D point and returns the
* result as a new inhomogeneous 2D point instance.
*
* @return Converts and returns this point as an inhomogeneous 2D point.
*/
public InhomogeneousPoint2D toInhomogeneous() {
return new InhomogeneousPoint2D(x / w, y / w);
}
/**
* Returns an array containing the coordinates of this Point2D.
*
* @return Array containing coordinates of this Point2D.
*/
@Override
public double[] asArray() {
final var out = new double[POINT2D_HOMOGENEOUS_COORDINATES_LENGTH];
asArray(out);
return out;
}
/**
* Uses provided array to store the coordinates of this HomogeneousPoint2D
*
* @param array Array where coordinates will be stored.
* @throws IllegalArgumentException Raised if length of array is not 3.
*/
@Override
public void asArray(double[] array) {
if (array.length != POINT2D_HOMOGENEOUS_COORDINATES_LENGTH) {
throw new IllegalArgumentException();
}
array[0] = x;
array[1] = y;
array[2] = w;
}
}