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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.NumberUtils;
/** Encapsulates a 3D vector. Allows chaining operations by returning a reference to itself in all modification methods.
* @author [email protected] */
public class Vector3 implements Serializable {
private static final long serialVersionUID = 3840054589595372522L;
/** the x-component of this vector **/
public float x;
/** the x-component of this vector **/
public float y;
/** the x-component of this vector **/
public float z;
/** Static temporary vector. Use with care! Use only when sure other code will not also use this.
* @see #tmp() **/
public final static Vector3 tmp = new Vector3();
/** Static temporary vector. Use with care! Use only when sure other code will not also use this.
* @see #tmp() **/
public final static Vector3 tmp2 = new Vector3();
/** Static temporary vector. Use with care! Use only when sure other code will not also use this.
* @see #tmp() **/
public final static Vector3 tmp3 = new Vector3();
public final static Vector3 X = new Vector3(1, 0, 0);
public final static Vector3 Y = new Vector3(0, 1, 0);
public final static Vector3 Z = new Vector3(0, 0, 1);
public final static Vector3 Zero = new Vector3(0, 0, 0);
/** Constructs a vector at (0,0,0) */
public Vector3 () {
}
/** Creates a vector with the given components
* @param x The x-component
* @param y The y-component
* @param z The z-component */
public Vector3 (float x, float y, float z) {
this.set(x, y, z);
}
/** Creates a vector from the given vector
* @param vector The vector */
public Vector3 (Vector3 vector) {
this.set(vector);
}
/** Creates a vector from the given array. The array must have at least 3 elements.
*
* @param values The array */
public Vector3 (float[] values) {
this.set(values[0], values[1], values[2]);
}
/** Sets the vector to the given components
*
* @param x The x-component
* @param y The y-component
* @param z The z-component
* @return this vector for chaining */
public Vector3 set (float x, float y, float z) {
this.x = x;
this.y = y;
this.z = z;
return this;
}
/** Sets the components of the given vector
*
* @param vector The vector
* @return This vector for chaining */
public Vector3 set (Vector3 vector) {
return this.set(vector.x, vector.y, vector.z);
}
/** Sets the components from the array. The array must have at least 3 elements
*
* @param values The array
* @return this vector for chaining */
public Vector3 set (float[] values) {
return this.set(values[0], values[1], values[2]);
}
/** @return a copy of this vector */
public Vector3 cpy () {
return new Vector3(this);
}
/** NEVER EVER SAVE THIS REFERENCE! Do not use this unless you are aware of the side-effects, e.g. other methods might call this
* as well.
*
* @return a temporary copy of this vector */
public Vector3 tmp () {
return tmp.set(this);
}
/** NEVER EVER SAVE THIS REFERENCE! Do not use this unless you are aware of the side-effects, e.g. other methods might call this
* as well.
*
* @return a temporary copy of this vector */
public Vector3 tmp2 () {
return tmp2.set(this);
}
/** NEVER EVER SAVE THIS REFERENCE! Do not use this unless you are aware of the side-effects, e.g. other methods might call this
* as well.
*
* @return a temporary copy of this vector */
Vector3 tmp3 () {
return tmp3.set(this);
}
/** Adds the given vector to this vector
*
* @param vector The other vector
* @return This vector for chaining */
public Vector3 add (Vector3 vector) {
return this.add(vector.x, vector.y, vector.z);
}
/** Adds the given vector to this component
* @param x The x-component of the other vector
* @param y The y-component of the other vector
* @param z The z-component of the other vector
* @return This vector for chaining. */
public Vector3 add (float x, float y, float z) {
return this.set(this.x + x, this.y + y, this.z + z);
}
/** Adds the given value to all three components of the vector.
*
* @param values The value
* @return This vector for chaining */
public Vector3 add (float values) {
return this.set(this.x + values, this.y + values, this.z + values);
}
/** Subtracts the given vector from this vector
* @param a_vec The other vector
* @return This vector for chaining */
public Vector3 sub (Vector3 a_vec) {
return this.sub(a_vec.x, a_vec.y, a_vec.z);
}
/** Subtracts the other vector from this vector.
*
* @param x The x-component of the other vector
* @param y The y-component of the other vector
* @param z The z-component of the other vector
* @return This vector for chaining */
public Vector3 sub (float x, float y, float z) {
return this.set(this.x - x, this.y - y, this.z - z);
}
/** Subtracts the given value from all components of this vector
*
* @param value The value
* @return This vector for chaining */
public Vector3 sub (float value) {
return this.set(this.x - value, this.y - value, this.z - value);
}
/** Multiplies all components of this vector by the given value
*
* @param value The value
* @return This vector for chaining */
public Vector3 mul (float value) {
return this.set(this.x * value, this.y * value, this.z * value);
}
/** Divides all components of this vector by the given value
*
* @param value The value
* @return This vector for chaining */
public Vector3 div (float value) {
float d = 1 / value;
return this.set(this.x * d, this.y * d, this.z * d);
}
/** @return The euclidian length */
public float len () {
return (float)Math.sqrt(x * x + y * y + z * z);
}
/** @return The squared euclidian length */
public float len2 () {
return x * x + y * y + z * z;
}
/** @param vector The other vector
* @return Wether this and the other vector are equal */
public boolean idt (Vector3 vector) {
return x == vector.x && y == vector.y && z == vector.z;
}
/** @param vector The other vector
* @return The euclidian distance between this and the other vector */
public float dst (Vector3 vector) {
float a = vector.x - x;
float b = vector.y - y;
float c = vector.z - z;
a *= a;
b *= b;
c *= c;
return (float)Math.sqrt(a + b + c);
}
/** Normalizes this vector to unit length
*
* @return This vector for chaining */
public Vector3 nor () {
float len = this.len();
if (len == 0) {
return this;
} else {
return this.div(len);
}
}
/** @param vector The other vector
* @return The dot product between this and the other vector */
public float dot (Vector3 vector) {
return x * vector.x + y * vector.y + z * vector.z;
}
/** Sets this vector to the cross product between it and the other vector.
* @param vector The other vector
* @return This vector for chaining */
public Vector3 crs (Vector3 vector) {
return this.set(y * vector.z - z * vector.y, z * vector.x - x * vector.z, x * vector.y - y * vector.x);
}
/** Sets this vector to the cross product between it and the other vector.
* @param x The x-component of the other vector
* @param y The y-component of the other vector
* @param z The z-component of the other vector
* @return This vector for chaining */
public Vector3 crs (float x, float y, float z) {
return this.set(this.y * z - this.z * y, this.z * x - this.x * z, this.x * y - this.y * x);
}
/** Multiplies the vector by the given matrix.
* @param matrix The matrix
* @return This vector for chaining */
public Vector3 mul (Matrix4 matrix) {
float l_mat[] = matrix.val;
return this.set(x * l_mat[Matrix4.M00] + y * l_mat[Matrix4.M01] + z * l_mat[Matrix4.M02] + l_mat[Matrix4.M03], x
* l_mat[Matrix4.M10] + y * l_mat[Matrix4.M11] + z * l_mat[Matrix4.M12] + l_mat[Matrix4.M13], x * l_mat[Matrix4.M20] + y
* l_mat[Matrix4.M21] + z * l_mat[Matrix4.M22] + l_mat[Matrix4.M23]);
}
/** Multiplies this vector by the given matrix dividing by w. This is mostly used to project/unproject vectors via a perspective
* projection matrix.
*
* @param matrix The matrix.
* @return This vector for chaining */
public Vector3 prj (Matrix4 matrix) {
float l_mat[] = matrix.val;
float l_w = x * l_mat[Matrix4.M30] + y * l_mat[Matrix4.M31] + z * l_mat[Matrix4.M32] + l_mat[Matrix4.M33];
return this.set((x * l_mat[Matrix4.M00] + y * l_mat[Matrix4.M01] + z * l_mat[Matrix4.M02] + l_mat[Matrix4.M03]) / l_w, (x
* l_mat[Matrix4.M10] + y * l_mat[Matrix4.M11] + z * l_mat[Matrix4.M12] + l_mat[Matrix4.M13])
/ l_w, (x * l_mat[Matrix4.M20] + y * l_mat[Matrix4.M21] + z * l_mat[Matrix4.M22] + l_mat[Matrix4.M23]) / l_w);
}
/** Multiplies this vector by the first three columns of the matrix, essentially only applying rotation and scaling.
*
* @param matrix The matrix
* @return This vector for chaining */
public Vector3 rot (Matrix4 matrix) {
float l_mat[] = matrix.val;
return this.set(x * l_mat[Matrix4.M00] + y * l_mat[Matrix4.M01] + z * l_mat[Matrix4.M02], x * l_mat[Matrix4.M10] + y
* l_mat[Matrix4.M11] + z * l_mat[Matrix4.M12], x * l_mat[Matrix4.M20] + y * l_mat[Matrix4.M21] + z * l_mat[Matrix4.M22]);
}
/** @return Wether this vector is a unit length vector */
public boolean isUnit () {
return this.len() == 1;
}
/** @return Wether this vector is a zero vector */
public boolean isZero () {
return x == 0 && y == 0 && z == 0;
}
/** Linearly interpolates between this vector and the target vector by alpha which is in the range [0,1]. The result is stored
* in this vector.
*
* @param target The target vector
* @param alpha The interpolation coefficient
* @return This vector for chaining. */
public Vector3 lerp (Vector3 target, float alpha) {
Vector3 r = this.mul(1.0f - alpha);
r.add(target.tmp().mul(alpha));
return r;
}
/** Spherically interpolates between this vector and the target vector by alpha which is in the range [0,1]. The result is
* stored in this vector.
*
* @param target The target vector
* @param alpha The interpolation coefficient
* @return This vector for chaining. */
public Vector3 slerp (Vector3 target, float alpha) {
float dot = dot(target);
if (dot > 0.99995 || dot < 0.9995) {
this.add(target.tmp().sub(this).mul(alpha));
this.nor();
return this;
}
if (dot > 1) dot = 1;
if (dot < -1) dot = -1;
float theta0 = (float)Math.acos(dot);
float theta = theta0 * alpha;
Vector3 v2 = target.tmp().sub(x * dot, y * dot, z * dot);
v2.nor();
return this.mul((float)Math.cos(theta)).add(v2.mul((float)Math.sin(theta))).nor();
}
/** {@inheritDoc} */
public String toString () {
return x + "," + y + "," + z;
}
/** Returns the dot product between this and the given vector.
*
* @param x The x-component of the other vector
* @param y The y-component of the other vector
* @param z The z-component of the other vector
* @return The dot product */
public float dot (float x, float y, float z) {
return this.x * x + this.y * y + this.z * z;
}
/** Returns the squared distance between this point and the given point
*
* @param point The other point
* @return The squared distance */
public float dst2 (Vector3 point) {
float a = point.x - x;
float b = point.y - y;
float c = point.z - z;
a *= a;
b *= b;
c *= c;
return a + b + c;
}
/** Returns the squared distance between this point and the given point
*
* @param x The x-component of the other point
* @param y The y-component of the other point
* @param z The z-component of the other point
* @return The squared distance */
public float dst2 (float x, float y, float z) {
float a = x - this.x;
float b = y - this.y;
float c = z - this.z;
a *= a;
b *= b;
c *= c;
return a + b + c;
}
public float dst (float x, float y, float z) {
return (float)Math.sqrt(dst2(x, y, z));
}
/** {@inheritDoc} */
@Override
public int hashCode () {
final int prime = 31;
int result = 1;
result = prime * result + NumberUtils.floatToIntBits(x);
result = prime * result + NumberUtils.floatToIntBits(y);
result = prime * result + NumberUtils.floatToIntBits(z);
return result;
}
/** {@inheritDoc} */
@Override
public boolean equals (Object obj) {
if (this == obj) return true;
if (obj == null) return false;
if (getClass() != obj.getClass()) return false;
Vector3 other = (Vector3)obj;
if (NumberUtils.floatToIntBits(x) != NumberUtils.floatToIntBits(other.x)) return false;
if (NumberUtils.floatToIntBits(y) != NumberUtils.floatToIntBits(other.y)) return false;
if (NumberUtils.floatToIntBits(z) != NumberUtils.floatToIntBits(other.z)) return false;
return true;
}
/**
* Compares this vector with the other vector, using the supplied
* epsilon for fuzzy equality testing.
* @param obj
* @param epsilon
* @return whether the vectors are the same.
*/
public boolean epsilonEquals(Vector3 obj, float epsilon) {
if(obj == null) return false;
if(Math.abs(obj.x - x) > epsilon) return false;
if(Math.abs(obj.y - y) > epsilon) return false;
if(Math.abs(obj.z - z) > 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 z, float epsilon) {
if(Math.abs(x - this.x) > epsilon) return false;
if(Math.abs(y - this.y) > epsilon) return false;
if(Math.abs(z - this.z) > epsilon) return false;
return true;
}
/** Scales the vector components by the given scalars.
*
* @param scalarX
* @param scalarY
* @param scalarZ */
public Vector3 scale (float scalarX, float scalarY, float scalarZ) {
x *= scalarX;
y *= scalarY;
z *= scalarZ;
return this;
}
}
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