Vector3 三维向量

结构体类型

表示 3D的 向量和点。

这个结构用于在 Unity 传递 3D 位置和方向。它包含向量运算的函数。

Vector3.ClampMagnitude

返回原向量的拷贝，并且它的模最大不超过maxLength所指示的长度。 也就是说，限制向量长度到一个特定的长度。

示例：

    using UnityEngine;
    using System.Collections;

    public class ExampleClass : MonoBehaviour {
        public Vector3 centerPt;
        public float radius;
        void Update() {
            Vector3 movement = new Vector3(Input.GetAxis("Horizontal"), 0, Input.GetAxis("Vertical"));
            Vector3 newPos = transform.position + movement;
            Vector3 offset = newPos - centerPt;
            transform.position = centerPt + Vector3.ClampMagnitude(offset, radius);
        }
    }

Vector3.Dot 点乘

两个向量的点乘积。 点积是一个浮点型的值，两个向量的长度相乘，然后乘以它们之间夹角的余弦值。 对于normalized向量，如果他们指向在完全相同的方向，Dot返回1。如果他们指向完全相反的方向，返回-1。对于其他的情况返回一个数（例如：如果是垂直的Dot返回0）。

示例：

    using UnityEngine;
    using System.Collections;

    public class ExampleClass : MonoBehaviour {
        public Transform other;
        void Update() {
            if (other) {
                Vector3 forward = transform.TransformDirection(Vector3.forward);
                Vector3 toOther = other.position - transform.position;
                if (Vector3.Dot(forward, toOther) < 0)
                    print("The other transform is behind me!");

            }
        }
    }

Vector3.Cross 叉乘

两个向量的交叉乘积。 两个向量的叉积乘积结果在垂直于两个输入向量的三分之一个向量。结果的大小等于两个输入相乘，然后乘以输入向量之间的角度的正弦值。你可以确定的方向的结果向量使用“左手法则”。

示例：

    using UnityEngine;
    using System.Collections;

    public class ExampleClass : MonoBehaviour {
        Vector3 GetNormal(Vector3 a, Vector3 b, Vector3 c) {
            Vector3 side1 = b - a;
            Vector3 side2 = c - a;
            return Vector3.Cross(side1, side2).normalized;
        }
    }

Vector3.Lerp 线性差值

两个向量之间的线性插值。 按照分数t在from到to之间插值。这是最常用的寻找一点沿一条线的两个端点之间一些分数的方式（例如，在那些点之间逐渐移动一个对象）。这分数是在范围[ 0…1]。t是夹在 [0…1]之间，当t = 0时，返回from，当t = 1时，返回to。当t = 0.5 返回from和to的中间点。

示例：

    using UnityEngine;
    using System.Collections;

    public class ExampleClass : MonoBehaviour {

        public Transform startMarker;
        public Transform endMarker;
        public float speed = 1.0F;
        private float startTime;
        private float journeyLength;

        void Start() {
            startTime = Time.time;
            journeyLength = Vector3.Distance(startMarker.position, endMarker.position);
        }

        void Update() {
            float distCovered = (Time.time - startTime) * speed;
            float fracJourney = distCovered / journeyLength;
            transform.position = Vector3.Lerp(startMarker.position, endMarker.position, fracJourney);
        }
    }

Vector3.Slerp 球形差值

两个向量之间的弧形插值 通过t数值在from和to之间插值。这与线性内插之间的不同（即， “线性插值” ）是该向量被视为方向而不是空间中的点。返回的向量的方向是由角内插，其大小是from和to的幅度之间进行内插。

示例：

    using UnityEngine;
    using System.Collections;

    public class ExampleClass : MonoBehaviour {
        public Transform sunrise;
        public Transform sunset;
        public float journeyTime = 1.0F;
        private float startTime;

        void Start() {
            startTime = Time.time;
        }

        void Update() {
            Vector3 center = (sunrise.position + sunset.position) * 0.5F;
            center -= new Vector3(0, 1, 0);
            Vector3 riseRelCenter = sunrise.position - center;
            Vector3 setRelCenter = sunset.position - center;
            float fracComplete = (Time.time - startTime) / journeyTime;
            transform.position = Vector3.Slerp(riseRelCenter, setRelCenter, fracComplete);
            transform.position += center;
        }
    }

Vector3.MoveTowards

当前的地点移向目标。 这个函数的返回值是一个点maxdistancedelta单位更接近于目标/点沿着当前的和目标之间的线。如果目标是比maxdistancedelta /然后返回值将等于目标接近（即移动不会超过目标）。maxdistancedelta负值可以用来从目标推开该向量。

示例：

    using UnityEngine;
    using System.Collections;

    public class ExampleClass : MonoBehaviour {
        public Transform target;
        public float speed;

        void Update() {
            float step = speed * Time.deltaTime;
            transform.position = Vector3.MoveTowards(transform.position, target.position, step);
        }
    }

Vector3.SmoothDamp

随着时间的推移，逐渐改变一个向量朝向预期的目标。 向量由一些像弹簧阻尼器函数平滑，这将永远不会超过。最常见的用途是相机平滑跟随。

示例：

    using UnityEngine;
    using System.Collections;

    public class ExampleClass : MonoBehaviour {
        public Transform target;
        public float smoothTime = 0.3F;
        private Vector3 velocity = Vector3.zero;

        void Update() {
            Vector3 targetPosition = target.TransformPoint(new Vector3(0, 5, -10));
            transform.position = Vector3.SmoothDamp(transform.position, targetPosition, ref velocity, smoothTime);
        }
    }

Vector3.RotateTowards 转向

当前的向量转向目标。

这个函数类似于MoveTowards除了将向量被视为一个方向，而不是一个位置上。当前向量将被旋转朝向目标方向由maxRadiansDelta的角度，虽然会恰好落在目标，而不是超过。如果当前的大小和目标的是不同的，那么结果的幅度将被线性地旋转过程中进行插值。如果一个负值用于maxRadiansDelta ，向量会转离目标/直到它指向完全相反的方向，然后停止。

示例：

    using UnityEngine;
    using System.Collections;

    public class ExampleClass : MonoBehaviour {
        public Transform target;
        public float speed;

        void Update() {
            Vector3 targetDir = target.position - transform.position;
            float step = speed * Time.deltaTime;
            Vector3 newDir = Vector3.RotateTowards(transform.forward, targetDir, step, 0.0F);
            Debug.DrawRay(transform.position, newDir, Color.red);
            transform.rotation = Quaternion.LookRotation(newDir);
        }
    }

源码

using System;
using System.Runtime.InteropServices;
using scm = System.ComponentModel;
using uei = UnityEngine.Internal;

namespace UnityEngine
{
    // Representation of 3D vectors and points.
    [StructLayout(LayoutKind.Sequential)]
    public partial struct Vector3
    {
        public const float kEpsilon = 0.00001F;

        // X component of the vector.
        public float x;
        // Y component of the vector.
        public float y;
        // Z component of the vector.
        public float z;

        // Linearly interpolates between two vectors.
        public static Vector3 Lerp(Vector3 a, Vector3 b, float t)
        {
            t = Mathf.Clamp01(t);
            return new Vector3(
                a.x + (b.x - a.x) * t,
                a.y + (b.y - a.y) * t,
                a.z + (b.z - a.z) * t
                );
        }

        // Linearly interpolates between two vectors without clamping the interpolant
        public static Vector3 LerpUnclamped(Vector3 a, Vector3 b, float t)
        {
            return new Vector3(
                a.x + (b.x - a.x) * t,
                a.y + (b.y - a.y) * t,
                a.z + (b.z - a.z) * t
                );
        }

        // Moves a point /current/ in a straight line towards a /target/ point.
        public static Vector3 MoveTowards(Vector3 current, Vector3 target, float maxDistanceDelta)
        {
            Vector3 toVector = target - current;
            float dist = toVector.magnitude;
            if (dist <= maxDistanceDelta || dist < float.Epsilon)
                return target;
            return current + toVector / dist * maxDistanceDelta;
        }

        [uei.ExcludeFromDocs]
        public static Vector3 SmoothDamp(Vector3 current, Vector3 target, ref Vector3 currentVelocity, float smoothTime, float maxSpeed)
        {
            float deltaTime = Time.deltaTime;
            return SmoothDamp(current, target, ref currentVelocity, smoothTime, maxSpeed, deltaTime);
        }

        [uei.ExcludeFromDocs]
        public static Vector3 SmoothDamp(Vector3 current, Vector3 target, ref Vector3 currentVelocity, float smoothTime)
        {
            float deltaTime = Time.deltaTime;
            float maxSpeed = Mathf.Infinity;
            return SmoothDamp(current, target, ref currentVelocity, smoothTime, maxSpeed, deltaTime);
        }

        // Gradually changes a vector towards a desired goal over time.
        public static Vector3 SmoothDamp(Vector3 current, Vector3 target, ref Vector3 currentVelocity, float smoothTime, [uei.DefaultValue("Mathf.Infinity")]  float maxSpeed, [uei.DefaultValue("Time.deltaTime")]  float deltaTime)
        {
            smoothTime = Mathf.Max(0.0001F, smoothTime);
            float omega = 2F / smoothTime;

            float x = omega * deltaTime;
            float exp = 1F / (1F + x + 0.48F * x * x + 0.235F * x * x * x);
            Vector3 change = current - target;
            Vector3 originalTo = target;

            float maxChange = maxSpeed * smoothTime;
            change = Vector3.ClampMagnitude(change, maxChange);
            target = current - change;

            Vector3 temp = (currentVelocity + omega * change) * deltaTime;
            currentVelocity = (currentVelocity - omega * temp) * exp;
            Vector3 output = target + (change + temp) * exp;

            if (Vector3.Dot(originalTo - current, output - originalTo) > 0)
            {
                output = originalTo;
                currentVelocity = (output - originalTo) / deltaTime;
            }

            return output;
        }

        // Access the x, y, z components using [0], [1], [2] respectively.
        public float this[int index]
        {
            get
            {
                switch (index)
                {
                    case 0: return x;
                    case 1: return y;
                    case 2: return z;
                    default:
                        throw new IndexOutOfRangeException("Invalid Vector3 index!");
                }
            }

            set
            {
                switch (index)
                {
                    case 0: x = value; break;
                    case 1: y = value; break;
                    case 2: z = value; break;
                    default:
                        throw new IndexOutOfRangeException("Invalid Vector3 index!");
                }
            }
        }

        // Creates a new vector with given x, y, z components.
        public Vector3(float x, float y, float z) { this.x = x; this.y = y; this.z = z; }
        // Creates a new vector with given x, y components and sets /z/ to zero.
        public Vector3(float x, float y) { this.x = x; this.y = y; z = 0F; }

        // Set x, y and z components of an existing Vector3.
        public void Set(float newX, float newY, float newZ) { x = newX; y = newY; z = newZ; }

        // Multiplies two vectors component-wise.
        public static Vector3 Scale(Vector3 a, Vector3 b) { return new Vector3(a.x * b.x, a.y * b.y, a.z * b.z); }

        // Multiplies every component of this vector by the same component of /scale/.
        public void Scale(Vector3 scale) { x *= scale.x; y *= scale.y; z *= scale.z; }

        // Cross Product of two vectors.
        public static Vector3 Cross(Vector3 lhs, Vector3 rhs)
        {
            return new Vector3(
                lhs.y * rhs.z - lhs.z * rhs.y,
                lhs.z * rhs.x - lhs.x * rhs.z,
                lhs.x * rhs.y - lhs.y * rhs.x);
        }

        // used to allow Vector3s to be used as keys in hash tables
        public override int GetHashCode()
        {
            return x.GetHashCode() ^ (y.GetHashCode() << 2) ^ (z.GetHashCode() >> 2);
        }

        // also required for being able to use Vector3s as keys in hash tables
        public override bool Equals(object other)
        {
            if (!(other is Vector3)) return false;

            Vector3 rhs = (Vector3)other;
            return x.Equals(rhs.x) && y.Equals(rhs.y) && z.Equals(rhs.z);
        }

        // Reflects a vector off the plane defined by a normal.
        public static Vector3 Reflect(Vector3 inDirection, Vector3 inNormal)
        {
            return -2F * Dot(inNormal, inDirection) * inNormal + inDirection;
        }

        // *undoc* --- we have normalized property now
        public static Vector3 Normalize(Vector3 value)
        {
            float mag = Magnitude(value);
            if (mag > kEpsilon)
                return value / mag;
            else
                return zero;
        }

        // Makes this vector have a ::ref::magnitude of 1.
        public void Normalize()
        {
            float mag = Magnitude(this);
            if (mag > kEpsilon)
                this = this / mag;
            else
                this = zero;
        }

        // Returns this vector with a ::ref::magnitude of 1 (RO).
        public Vector3 normalized { get { return Vector3.Normalize(this); } }

        // Dot Product of two vectors.
        public static float Dot(Vector3 lhs, Vector3 rhs) { return lhs.x * rhs.x + lhs.y * rhs.y + lhs.z * rhs.z; }

        // Projects a vector onto another vector.
        public static Vector3 Project(Vector3 vector, Vector3 onNormal)
        {
            float sqrMag = Dot(onNormal, onNormal);
            if (sqrMag < Mathf.Epsilon)
                return zero;
            else
                return onNormal * Dot(vector, onNormal) / sqrMag;
        }

        // Projects a vector onto a plane defined by a normal orthogonal to the plane.
        public static Vector3 ProjectOnPlane(Vector3 vector, Vector3 planeNormal)
        {
            return vector - Project(vector, planeNormal);
        }

        // Returns the angle in degrees between /from/ and /to/. This is always the smallest
        public static float Angle(Vector3 from, Vector3 to)
        {
            return Mathf.Acos(Mathf.Clamp(Vector3.Dot(from.normalized, to.normalized), -1F, 1F)) * Mathf.Rad2Deg;
        }

        // The smaller of the two possible angles between the two vectors is returned, therefore the result will never be greater than 180 degrees or smaller than -180 degrees.
        // If you imagine the from and to vectors as lines on a piece of paper, both originating from the same point, then the /axis/ vector would point up out of the paper.
        // The measured angle between the two vectors would be positive in a clockwise direction and negative in an anti-clockwise direction.
        public static float SignedAngle(Vector3 from, Vector3 to, Vector3 axis)
        {
            Vector3 fromNorm = from.normalized, toNorm = to.normalized;
            float unsignedAngle = Mathf.Acos(Mathf.Clamp(Vector3.Dot(fromNorm, toNorm), -1F, 1F)) * Mathf.Rad2Deg;
            float sign = Mathf.Sign(Vector3.Dot(axis, Vector3.Cross(fromNorm, toNorm)));
            return unsignedAngle * sign;
        }

        // Returns the distance between /a/ and /b/.
        public static float Distance(Vector3 a, Vector3 b)
        {
            Vector3 vec = new Vector3(a.x - b.x, a.y - b.y, a.z - b.z);
            return Mathf.Sqrt(vec.x * vec.x + vec.y * vec.y + vec.z * vec.z);
        }

        // Returns a copy of /vector/ with its magnitude clamped to /maxLength/.
        public static Vector3 ClampMagnitude(Vector3 vector, float maxLength)
        {
            if (vector.sqrMagnitude > maxLength * maxLength)
                return vector.normalized * maxLength;
            return vector;
        }

        // *undoc* --- there's a property now
        public static float Magnitude(Vector3 vector) { return Mathf.Sqrt(vector.x * vector.x + vector.y * vector.y + vector.z * vector.z); }

        // Returns the length of this vector (RO).
        public float magnitude { get { return Mathf.Sqrt(x * x + y * y + z * z); } }

        // *undoc* --- there's a property now
        public static float SqrMagnitude(Vector3 vector) { return vector.x * vector.x + vector.y * vector.y + vector.z * vector.z; }

        // Returns the squared length of this vector (RO).
        public float sqrMagnitude { get { return x * x + y * y + z * z; } }

        // Returns a vector that is made from the smallest components of two vectors.
        public static Vector3 Min(Vector3 lhs, Vector3 rhs)
        {
            return new Vector3(Mathf.Min(lhs.x, rhs.x), Mathf.Min(lhs.y, rhs.y), Mathf.Min(lhs.z, rhs.z));
        }

        // Returns a vector that is made from the largest components of two vectors.
        public static Vector3 Max(Vector3 lhs, Vector3 rhs)
        {
            return new Vector3(Mathf.Max(lhs.x, rhs.x), Mathf.Max(lhs.y, rhs.y), Mathf.Max(lhs.z, rhs.z));
        }

        static readonly Vector3 zeroVector = new Vector3(0F, 0F, 0F);
        static readonly Vector3 oneVector = new Vector3(1F, 1F, 1F);
        static readonly Vector3 upVector = new Vector3(0F, 1F, 0F);
        static readonly Vector3 downVector = new Vector3(0F, -1F, 0F);
        static readonly Vector3 leftVector = new Vector3(-1F, 0F, 0F);
        static readonly Vector3 rightVector = new Vector3(1F, 0F, 0F);
        static readonly Vector3 forwardVector = new Vector3(0F, 0F, 1F);
        static readonly Vector3 backVector = new Vector3(0F, 0F, -1F);
        static readonly Vector3 positiveInfinityVector = new Vector3(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity);
        static readonly Vector3 negativeInfinityVector = new Vector3(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity);

        // Shorthand for writing @@Vector3(0, 0, 0)@@
        public static Vector3 zero { get { return zeroVector; } }
        // Shorthand for writing @@Vector3(1, 1, 1)@@
        public static Vector3 one { get { return oneVector; } }
        // Shorthand for writing @@Vector3(0, 0, 1)@@
        public static Vector3 forward { get { return forwardVector; } }
        public static Vector3 back { get { return backVector; } }
        // Shorthand for writing @@Vector3(0, 1, 0)@@
        public static Vector3 up { get { return upVector; } }
        public static Vector3 down { get { return downVector; } }
        public static Vector3 left { get { return leftVector; } }
        // Shorthand for writing @@Vector3(1, 0, 0)@@
        public static Vector3 right { get { return rightVector; } }
        // Shorthand for writing @@Vector3(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity)@@
        public static Vector3 positiveInfinity { get { return positiveInfinityVector; } }
        // Shorthand for writing @@Vector3(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity)@@
        public static Vector3 negativeInfinity { get { return negativeInfinityVector; } }

        // Adds two vectors.
        public static Vector3 operator+(Vector3 a, Vector3 b) { return new Vector3(a.x + b.x, a.y + b.y, a.z + b.z); }
        // Subtracts one vector from another.
        public static Vector3 operator-(Vector3 a, Vector3 b) { return new Vector3(a.x - b.x, a.y - b.y, a.z - b.z); }
        // Negates a vector.
        public static Vector3 operator-(Vector3 a) { return new Vector3(-a.x, -a.y, -a.z); }
        // Multiplies a vector by a number.
        public static Vector3 operator*(Vector3 a, float d) { return new Vector3(a.x * d, a.y * d, a.z * d); }
        // Multiplies a vector by a number.
        public static Vector3 operator*(float d, Vector3 a) { return new Vector3(a.x * d, a.y * d, a.z * d); }
        // Divides a vector by a number.
        public static Vector3 operator/(Vector3 a, float d) { return new Vector3(a.x / d, a.y / d, a.z / d); }

        // Returns true if the vectors are equal.
        public static bool operator==(Vector3 lhs, Vector3 rhs)
        {
            // Returns false in the presence of NaN values.
            return SqrMagnitude(lhs - rhs) < kEpsilon * kEpsilon;
        }

        // Returns true if vectors are different.
        public static bool operator!=(Vector3 lhs, Vector3 rhs)
        {
            // Returns true in the presence of NaN values.
            return !(lhs == rhs);
        }

        public override string ToString()
        {
            return UnityString.Format("({0:F1}, {1:F1}, {2:F1})", x, y, z);
        }

        public string ToString(string format)
        {
            return UnityString.Format("({0}, {1}, {2})", x.ToString(format), y.ToString(format), z.ToString(format));
        }

        [System.Obsolete("Use Vector3.forward instead.")]
        public static Vector3 fwd { get { return new Vector3(0F, 0F, 1F); } }
        [System.Obsolete("Use Vector3.Angle instead. AngleBetween uses radians instead of degrees and was deprecated for this reason")]
        public static float AngleBetween(Vector3 from, Vector3 to) { return Mathf.Acos(Mathf.Clamp(Vector3.Dot(from.normalized, to.normalized), -1F, 1F)); }
        [System.Obsolete("Use Vector3.ProjectOnPlane instead.")]
        public static Vector3 Exclude(Vector3 excludeThis, Vector3 fromThat) { return ProjectOnPlane(fromThat, excludeThis); }
    }
}

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