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/******************************************************************************* * Copyright 2011 See AUTHORS file./*from w ww . j a v a2s . c o m*/ * * 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 badlogicgames@gmail.com */ 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; } }