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/*******************************************************************************
* Copyright 2011 See AUTHORS file.
*
* 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.badlogic.gdx.math;
import java.io.Serializable;
import com.badlogic.gdx.utils.GdxRuntimeException;
import com.badlogic.gdx.utils.NumberUtils;
/** Encapsulates a 2D vector. Allows chaining methods by returning a reference to itself
* @author [email protected] */
public class Vector2 implements Serializable, Vector {
private static final long serialVersionUID = 913902788239530931L;
public final static Vector2 X = new Vector2(1, 0);
public final static Vector2 Y = new Vector2(0, 1);
public final static Vector2 Zero = new Vector2(0, 0);
/** the x-component of this vector **/
public float x;
/** the y-component of this vector **/
public float y;
/** Constructs a new vector at (0,0) */
public Vector2 () {
}
/** Constructs a vector with the given components
* @param x The x-component
* @param y The y-component */
public Vector2 (float x, float y) {
this.x = x;
this.y = y;
}
/** Constructs a vector from the given vector
* @param v The vector */
public Vector2 (Vector2 v) {
set(v);
}
@Override
public Vector2 cpy () {
return new Vector2(this);
}
public static float len (float x, float y) {
return (float)Math.sqrt(x * x + y * y);
}
@Override
public float len () {
return (float)Math.sqrt(x * x + y * y);
}
public static float len2 (float x, float y) {
return x * x + y * y;
}
@Override
public float len2 () {
return x * x + y * y;
}
@Override
public Vector2 set (Vector2 v) {
x = v.x;
y = v.y;
return this;
}
/** Sets the components of this vector
* @param x The x-component
* @param y The y-component
* @return This vector for chaining */
public Vector2 set (float x, float y) {
this.x = x;
this.y = y;
return this;
}
@Override
public Vector2 sub (Vector2 v) {
x -= v.x;
y -= v.y;
return this;
}
/** Substracts the other vector from this vector.
* @param x The x-component of the other vector
* @param y The y-component of the other vector
* @return This vector for chaining */
public Vector2 sub (float x, float y) {
this.x -= x;
this.y -= y;
return this;
}
@Override
public Vector2 nor () {
float len = len();
if (len != 0) {
x /= len;
y /= len;
}
return this;
}
@Override
public Vector2 add (Vector2 v) {
x += v.x;
y += v.y;
return this;
}
/** Adds the given components to this vector
* @param x The x-component
* @param y The y-component
* @return This vector for chaining */
public Vector2 add (float x, float y) {
this.x += x;
this.y += y;
return this;
}
public static float dot (float x1, float y1, float x2, float y2) {
return x1 * x2 + y1 * y2;
}
@Override
public float dot (Vector2 v) {
return x * v.x + y * v.y;
}
public float dot (float ox, float oy) {
return x * ox + y * oy;
}
@Override
public Vector2 scl (float scalar) {
x *= scalar;
y *= scalar;
return this;
}
/** Multiplies this vector by a scalar
* @return This vector for chaining */
public Vector2 scl (float x, float y) {
this.x *= x;
this.y *= y;
return this;
}
@Override
public Vector2 scl (Vector2 v) {
this.x *= v.x;
this.y *= v.y;
return this;
}
@Override
public Vector2 mulAdd (Vector2 vec, float scalar) {
this.x += vec.x * scalar;
this.y += vec.y * scalar;
return this;
}
@Override
public Vector2 mulAdd (Vector2 vec, Vector2 mulVec) {
this.x += vec.x * mulVec.x;
this.y += vec.y * mulVec.y;
return this;
}
public static float dst (float x1, float y1, float x2, float y2) {
final float x_d = x2 - x1;
final float y_d = y2 - y1;
return (float)Math.sqrt(x_d * x_d + y_d * y_d);
}
@Override
public float dst (Vector2 v) {
final float x_d = v.x - x;
final float y_d = v.y - y;
return (float)Math.sqrt(x_d * x_d + y_d * y_d);
}
/** @param x The x-component of the other vector
* @param y The y-component of the other vector
* @return the distance between this and the other vector */
public float dst (float x, float y) {
final float x_d = x - this.x;
final float y_d = y - this.y;
return (float)Math.sqrt(x_d * x_d + y_d * y_d);
}
public static float dst2 (float x1, float y1, float x2, float y2) {
final float x_d = x2 - x1;
final float y_d = y2 - y1;
return x_d * x_d + y_d * y_d;
}
@Override
public float dst2 (Vector2 v) {
final float x_d = v.x - x;
final float y_d = v.y - y;
return x_d * x_d + y_d * y_d;
}
/** @param x The x-component of the other vector
* @param y The y-component of the other vector
* @return the squared distance between this and the other vector */
public float dst2 (float x, float y) {
final float x_d = x - this.x;
final float y_d = y - this.y;
return x_d * x_d + y_d * y_d;
}
@Override
public Vector2 limit (float limit) {
return limit2(limit * limit);
}
@Override
public Vector2 limit2 (float limit2) {
float len2 = len2();
if (len2 > limit2) {
return scl((float)Math.sqrt(limit2 / len2));
}
return this;
}
@Override
public Vector2 clamp (float min, float max) {
final float len2 = len2();
if (len2 == 0f) return this;
float max2 = max * max;
if (len2 > max2) return scl((float)Math.sqrt(max2 / len2));
float min2 = min * min;
if (len2 < min2) return scl((float)Math.sqrt(min2 / len2));
return this;
}
@Override
public Vector2 setLength (float len) {
return setLength2(len * len);
}
@Override
public Vector2 setLength2 (float len2) {
float oldLen2 = len2();
return (oldLen2 == 0 || oldLen2 == len2) ? this : scl((float)Math.sqrt(len2 / oldLen2));
}
/** Converts this {@code Vector2} to a string in the format {@code (x,y)}.
* @return a string representation of this object. */
@Override
public String toString () {
return "(" + x + "," + y + ")";
}
/** Sets this {@code Vector2} to the value represented by the specified string according to the format of {@link #toString()}.
* @param v the string.
* @return this vector for chaining */
public Vector2 fromString (String v) {
int s = v.indexOf(',', 1);
if (s != -1 && v.charAt(0) == '(' && v.charAt(v.length() - 1) == ')') {
try {
float x = Float.parseFloat(v.substring(1, s));
float y = Float.parseFloat(v.substring(s + 1, v.length() - 1));
return this.set(x, y);
} catch (NumberFormatException ex) {
// Throw a GdxRuntimeException
}
}
throw new GdxRuntimeException("Malformed Vector2: " + v);
}
/** Left-multiplies this vector by the given matrix
* @param mat the matrix
* @return this vector */
public Vector2 mul (Matrix3 mat) {
float x = this.x * mat.val[0] + this.y * mat.val[3] + mat.val[6];
float y = this.x * mat.val[1] + this.y * mat.val[4] + mat.val[7];
this.x = x;
this.y = y;
return this;
}
/** Calculates the 2D cross product between this and the given vector.
* @param v the other vector
* @return the cross product */
public float crs (Vector2 v) {
return this.x * v.y - this.y * v.x;
}
/** Calculates the 2D cross product between this and the given vector.
* @param x the x-coordinate of the other vector
* @param y the y-coordinate of the other vector
* @return the cross product */
public float crs (float x, float y) {
return this.x * y - this.y * x;
}
/** @return the angle in degrees of this vector (point) relative to the x-axis. Angles are towards the positive y-axis
* (typically counter-clockwise) and between 0 and 360.
* @deprecated use {@link #angleDeg()} instead. */
@Deprecated
public float angle () {
float angle = (float)Math.atan2(y, x) * MathUtils.radiansToDegrees;
if (angle < 0) angle += 360;
return angle;
}
/** @return the angle in degrees of this vector (point) relative to the given vector. Angles are towards the negative y-axis
* (typically clockwise) between -180 and +180
* @deprecated use {@link #angleDeg(Vector2)} instead. Be ware of the changes in returned angle to counter-clockwise and the
* range. */
@Deprecated
public float angle (Vector2 reference) {
return (float)Math.atan2(crs(reference), dot(reference)) * MathUtils.radiansToDegrees;
}
/** @return the angle in degrees of this vector (point) relative to the x-axis. Angles are towards the positive y-axis
* (typically counter-clockwise) and in the [0, 360) range. */
public float angleDeg () {
float angle = (float)Math.atan2(y, x) * MathUtils.radiansToDegrees;
if (angle < 0) angle += 360;
return angle;
}
/** @return the angle in degrees of this vector (point) relative to the given vector. Angles are towards the positive y-axis
* (typically counter-clockwise.) in the [0, 360) range */
public float angleDeg (Vector2 reference) {
float angle = (float)Math.atan2(reference.crs(this), reference.dot(this)) * MathUtils.radiansToDegrees;
if (angle < 0) angle += 360;
return angle;
}
/** @return the angle in radians of this vector (point) relative to the x-axis. Angles are towards the positive y-axis.
* (typically counter-clockwise) */
public float angleRad () {
return (float)Math.atan2(y, x);
}
/** @return the angle in radians of this vector (point) relative to the given vector. Angles are towards the positive y-axis.
* (typically counter-clockwise.) */
public float angleRad (Vector2 reference) {
return (float)Math.atan2(reference.crs(this), reference.dot(this));
}
/** Sets the angle of the vector in degrees relative to the x-axis, towards the positive y-axis (typically counter-clockwise).
* @param degrees The angle in degrees to set.
* @deprecated use {@link #setAngleDeg(float)} instead. */
@Deprecated
public Vector2 setAngle (float degrees) {
return setAngleRad(degrees * MathUtils.degreesToRadians);
}
/** Sets the angle of the vector in degrees relative to the x-axis, towards the positive y-axis (typically counter-clockwise).
* @param degrees The angle in degrees to set. */
public Vector2 setAngleDeg (float degrees) {
return setAngleRad(degrees * MathUtils.degreesToRadians);
}
/** Sets the angle of the vector in radians relative to the x-axis, towards the positive y-axis (typically counter-clockwise).
* @param radians The angle in radians to set. */
public Vector2 setAngleRad (float radians) {
this.set(len(), 0f);
this.rotateRad(radians);
return this;
}
/** Rotates the Vector2 by the given angle, counter-clockwise assuming the y-axis points up.
* @param degrees the angle in degrees
* @deprecated use {@link #rotateDeg(float)} instead. */
@Deprecated
public Vector2 rotate (float degrees) {
return rotateRad(degrees * MathUtils.degreesToRadians);
}
/** Rotates the Vector2 by the given angle around reference vector, counter-clockwise assuming the y-axis points up.
* @param degrees the angle in degrees
* @param reference center Vector2
* @deprecated use {@link #rotateAroundDeg(Vector2, float)} instead. */
@Deprecated
public Vector2 rotateAround (Vector2 reference, float degrees) {
return this.sub(reference).rotateDeg(degrees).add(reference);
}
/** Rotates the Vector2 by the given angle, counter-clockwise assuming the y-axis points up.
* @param degrees the angle in degrees */
public Vector2 rotateDeg (float degrees) {
return rotateRad(degrees * MathUtils.degreesToRadians);
}
/** Rotates the Vector2 by the given angle, counter-clockwise assuming the y-axis points up.
* @param radians the angle in radians */
public Vector2 rotateRad (float radians) {
float cos = (float)Math.cos(radians);
float sin = (float)Math.sin(radians);
float newX = this.x * cos - this.y * sin;
float newY = this.x * sin + this.y * cos;
this.x = newX;
this.y = newY;
return this;
}
/** Rotates the Vector2 by the given angle around reference vector, counter-clockwise assuming the y-axis points up.
* @param degrees the angle in degrees
* @param reference center Vector2 */
public Vector2 rotateAroundDeg (Vector2 reference, float degrees) {
return this.sub(reference).rotateDeg(degrees).add(reference);
}
/** Rotates the Vector2 by the given angle around reference vector, counter-clockwise assuming the y-axis points up.
* @param radians the angle in radians
* @param reference center Vector2 */
public Vector2 rotateAroundRad (Vector2 reference, float radians) {
return this.sub(reference).rotateRad(radians).add(reference);
}
/** Rotates the Vector2 by 90 degrees in the specified direction, where >= 0 is counter-clockwise and < 0 is clockwise. */
public Vector2 rotate90 (int dir) {
float x = this.x;
if (dir >= 0) {
this.x = -y;
y = x;
} else {
this.x = y;
y = -x;
}
return this;
}
@Override
public Vector2 lerp (Vector2 target, float alpha) {
final float invAlpha = 1.0f - alpha;
this.x = (x * invAlpha) + (target.x * alpha);
this.y = (y * invAlpha) + (target.y * alpha);
return this;
}
@Override
public Vector2 interpolate (Vector2 target, float alpha, Interpolation interpolation) {
return lerp(target, interpolation.apply(alpha));
}
@Override
public Vector2 setToRandomDirection () {
float theta = MathUtils.random(0f, MathUtils.PI2);
return this.set(MathUtils.cos(theta), MathUtils.sin(theta));
}
@Override
public int hashCode () {
final int prime = 31;
int result = 1;
result = prime * result + NumberUtils.floatToIntBits(x);
result = prime * result + NumberUtils.floatToIntBits(y);
return result;
}
@Override
public boolean equals (Object obj) {
if (this == obj) return true;
if (obj == null) return false;
if (getClass() != obj.getClass()) return false;
Vector2 other = (Vector2)obj;
if (NumberUtils.floatToIntBits(x) != NumberUtils.floatToIntBits(other.x)) return false;
if (NumberUtils.floatToIntBits(y) != NumberUtils.floatToIntBits(other.y)) return false;
return true;
}
@Override
public boolean epsilonEquals (Vector2 other, float epsilon) {
if (other == null) return false;
if (Math.abs(other.x - x) > epsilon) return false;
if (Math.abs(other.y - y) > epsilon) return false;
return true;
}
/** Compares this vector with the other vector, using the supplied epsilon for fuzzy equality testing.
* @return whether the vectors are the same. */
public boolean epsilonEquals (float x, float y, float epsilon) {
if (Math.abs(x - this.x) > epsilon) return false;
if (Math.abs(y - this.y) > epsilon) return false;
return true;
}
/** Compares this vector with the other vector using MathUtils.FLOAT_ROUNDING_ERROR for fuzzy equality testing
* @param other other vector to compare
* @return true if vector are equal, otherwise false */
public boolean epsilonEquals (final Vector2 other) {
return epsilonEquals(other, MathUtils.FLOAT_ROUNDING_ERROR);
}
/** Compares this vector with the other vector using MathUtils.FLOAT_ROUNDING_ERROR for fuzzy equality testing
* @param x x component of the other vector to compare
* @param y y component of the other vector to compare
* @return true if vector are equal, otherwise false */
public boolean epsilonEquals (float x, float y) {
return epsilonEquals(x, y, MathUtils.FLOAT_ROUNDING_ERROR);
}
@Override
public boolean isUnit () {
return isUnit(0.000000001f);
}
@Override
public boolean isUnit (final float margin) {
return Math.abs(len2() - 1f) < margin;
}
@Override
public boolean isZero () {
return x == 0 && y == 0;
}
@Override
public boolean isZero (final float margin) {
return len2() < margin;
}
@Override
public boolean isOnLine (Vector2 other) {
return MathUtils.isZero(x * other.y - y * other.x);
}
@Override
public boolean isOnLine (Vector2 other, float epsilon) {
return MathUtils.isZero(x * other.y - y * other.x, epsilon);
}
@Override
public boolean isCollinear (Vector2 other, float epsilon) {
return isOnLine(other, epsilon) && dot(other) > 0f;
}
@Override
public boolean isCollinear (Vector2 other) {
return isOnLine(other) && dot(other) > 0f;
}
@Override
public boolean isCollinearOpposite (Vector2 other, float epsilon) {
return isOnLine(other, epsilon) && dot(other) < 0f;
}
@Override
public boolean isCollinearOpposite (Vector2 other) {
return isOnLine(other) && dot(other) < 0f;
}
@Override
public boolean isPerpendicular (Vector2 vector) {
return MathUtils.isZero(dot(vector));
}
@Override
public boolean isPerpendicular (Vector2 vector, float epsilon) {
return MathUtils.isZero(dot(vector), epsilon);
}
@Override
public boolean hasSameDirection (Vector2 vector) {
return dot(vector) > 0;
}
@Override
public boolean hasOppositeDirection (Vector2 vector) {
return dot(vector) < 0;
}
@Override
public Vector2 setZero () {
this.x = 0;
this.y = 0;
return this;
}
}