Unity3D研究院之主角面朝方向一定区域内对象角度计算（四十五）
2015-10-20 19:58
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http://www.xuanyusong.com/archives/1977
写在前面的话，前两天有个朋友在QQ上问我 如何获取主角面朝方向一定区域中的敌人对象。这个命题看似简单，其实里面蕴含了很多数学方面的东西。今天刚好有时间我就彻底的把这个疑问写在博客中。希望可以帮助到他。在上代码之前请大家跟我先做几个简单的练习题，角度向量的计算一定要学会，不然后面的东西会很难懂。
1.已知3D坐标，和一个旋转角度，以及一段距离，求目标点的3D坐标。
已知当前点为Target，目标点沿着Target的Y轴旋转30度，沿着Target的X轴延伸10米求目标点的3D坐标？
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | using UnityEngine; using System.Collections; public class Test : MonoBehaviour { public Transform Target; void LateUpdate () { Quaternion rotation = Quaternion.Euler(0f,30f,0f) * Target.rotation; Vector3 newPos = rotation * new Vector3(10f,0f,0f); Debug.DrawLine(newPos,Vector3.zero,Color.red); Debug.Log("newpos " + newPos +" nowpos " + Target.position + " distance " + Vector3.Distance(newPos,Target.position)); } } |
2.已知3D模型的角度求它的向量。
已知3D模型Target，Y轴旋转30度后向前平移。
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | using UnityEngine; using System.Collections; public class Test : MonoBehaviour { public Transform Target; void LateUpdate () { if(Input.GetMouseButton(0)) { Quaternion rotation = Quaternion.Euler(0f,30f,0f) * Target.rotation; Vector3 newPos = rotation * Vector3.forward; Target.Translate(newPos.x,newPos.y,newPos.z); } } } |
这是一个比较简单的例子，大家应该都能看明白。
| 1 2 | Target.transform.LookAt(new Vector3 (100f,200f,300f)); Target.Translate(Vector3.forward); |
在看看下面这段代码
| 1 2 3 | Vector3 vecn = (TargetCube.position - Target.position).normalized; Target.Translate(vecn *0.1f); |
向量不仅可以进行X Y Z轴的移动，同样可以进行旋转 ，下面这段代码就是让向量沿着Y轴旋转30度。
| 1 2 3 4 5 | Vector3 vecn = (TargetCube.position - Target.position).normalized; vecn = Quaternion.Euler(0f,30f,0f) * vecn; Target.Translate(vecn *0.1f); |
假设我们需要计算主角面前5米内所有的对象时。以主角为圆心计算面前5米外的一个点，为了让大家看清楚我现将这条线绘制出来。
| 1 2 3 4 5 6 7 | private float distance = 5f; void Update () { Quaternion r= transform.rotation; Vector3 f0 = (transform.position + (r *Vector3.forward) * distance); Debug.DrawLine(transform.position,f0,Color.red); } |
接下来，我们需要计算主角面前的一个发散性的角度。假设主角看到的是向左30度，向右30度在这个区域。
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | private float distance = 5f; void Update () { Quaternion r= transform.rotation; Vector3 f0 = (transform.position + (r *Vector3.forward) * distance); Debug.DrawLine(transform.position,f0,Color.red); Quaternion r0= Quaternion.Euler(transform.rotation.eulerAngles.x,transform.rotation.eulerAngles.y - 30f,transform.rotation.eulerAngles.z); Quaternion r1= Quaternion.Euler(transform.rotation.eulerAngles.x,transform.rotation.eulerAngles.y + 30f,transform.rotation.eulerAngles.z); Vector3 f1 = (transform.position + (r0 *Vector3.forward) * distance); Vector3 f2 = (transform.position + (r1 *Vector3.forward) * distance); Debug.DrawLine(transform.position,f1,Color.red); Debug.DrawLine(transform.position,f2,Color.red); Debug.DrawLine(f0,f1,Color.red); Debug.DrawLine(f0,f2,Color.red); } |
最后就是简单的套用公式，计算一个点是否在三角形内，在本文中就是计算敌人的点是否在面前的这两个三角形内。
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 | using UnityEngine; using System.Collections; public class MyTest : MonoBehaviour { public Transform cube; private float distance = 5f; void Update () { Quaternion r= transform.rotation; Vector3 f0 = (transform.position + (r *Vector3.forward) * distance); Debug.DrawLine(transform.position,f0,Color.red); Quaternion r0= Quaternion.Euler(transform.rotation.eulerAngles.x,transform.rotation.eulerAngles.y - 30f,transform.rotation.eulerAngles.z); Quaternion r1= Quaternion.Euler(transform.rotation.eulerAngles.x,transform.rotation.eulerAngles.y + 30f,transform.rotation.eulerAngles.z); Vector3 f1 = (transform.position + (r0 *Vector3.forward) * distance); Vector3 f2 = (transform.position + (r1 *Vector3.forward) * distance); Debug.DrawLine(transform.position,f1,Color.red); Debug.DrawLine(transform.position,f2,Color.red); Debug.DrawLine(f0,f1,Color.red); Debug.DrawLine(f0,f2,Color.red); Vector3 point = cube.position; if(isINTriangle(point,transform.position,f1,f0) || isINTriangle(point,transform.position,f2,f0) ) { Debug.Log("cube in this !!!"); }else { Debug.Log("cube not in this !!!"); } } private float triangleArea(float v0x,float v0y,float v1x,float v1y,float v2x,float v2y) { return Mathf.Abs((v0x * v1y + v1x * v2y + v2x * v0y - v1x * v0y - v2x * v1y - v0x * v2y) / 2f); } bool isINTriangle(Vector3 point,Vector3 v0,Vector3 v1,Vector3 v2) { float x = point.x; float y = point.z; float v0x = v0.x; float v0y = v0.z; float v1x = v1.x; float v1y = v1.z; float v2x = v2.x; float v2y = v2.z; float t = triangleArea(v0x,v0y,v1x,v1y,v2x,v2y); float a = triangleArea(v0x,v0y,v1x,v1y,x,y) + triangleArea(v0x,v0y,x,y,v2x,v2y) + triangleArea(x,y,v1x,v1y,v2x,v2y); if (Mathf.Abs(t - a) <= 0.01f) { return true; }else { return false; } } } |
注意，上图中我的视野选择了两个三角形，如果你需要视野目标点是椭圆形的话，那么可以多设置一些三角形。但是这样就会非常消耗效率，我觉得这里完全可以使用1个三角形，，只是正对的目标点会出现一些偏差，影响其实并不会很大。如下图所示
代码简单的修改一下即可。
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 | using UnityEngine; using System.Collections; public class MyTest : MonoBehaviour { public Transform cube; private float distance = 5f; void Update () { Quaternion r= transform.rotation; Vector3 f0 = (transform.position + (r *Vector3.forward) * distance); Debug.DrawLine(transform.position,f0,Color.red); Quaternion r0= Quaternion.Euler(transform.rotation.eulerAngles.x,transform.rotation.eulerAngles.y - 30f,transform.rotation.eulerAngles.z); Quaternion r1= Quaternion.Euler(transform.rotation.eulerAngles.x,transform.rotation.eulerAngles.y + 30f,transform.rotation.eulerAngles.z); Vector3 f1 = (transform.position + (r0 *Vector3.forward) * distance); Vector3 f2 = (transform.position + (r1 *Vector3.forward) * distance); Debug.DrawLine(transform.position,f1,Color.red); Debug.DrawLine(transform.position,f2,Color.red); Debug.DrawLine(f1,f2,Color.red); Vector3 point = cube.position; if(isINTriangle(point,transform.position,f1,f2)) { Debug.Log("cube in this !!!"); }else { Debug.Log("cube not in this !!!"); } } private float triangleArea(float v0x,float v0y,float v1x,float v1y,float v2x,float v2y) { return Mathf.Abs((v0x * v1y + v1x * v2y + v2x * v0y - v1x * v0y - v2x * v1y - v0x * v2y) / 2f); } bool isINTriangle(Vector3 point,Vector3 v0,Vector3 v1,Vector3 v2) { float x = point.x; float y = point.z; float v0x = v0.x; float v0y = v0.z; float v1x = v1.x; float v1y = v1.z; float v2x = v2.x; float v2y = v2.z; float t = triangleArea(v0x,v0y,v1x,v1y,v2x,v2y); float a = triangleArea(v0x,v0y,v1x,v1y,x,y) + triangleArea(v0x,v0y,x,y,v2x,v2y) + triangleArea(x,y,v1x,v1y,v2x,v2y); if (Mathf.Abs(t - a) <= 0.01f) { return true; }else { return false; } } } |
代码：
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 | using UnityEngine; using System.Collections; public class MyTest : MonoBehaviour { public Transform cube; private float distance = 5f; void Update () { Quaternion r= transform.rotation; Vector3 left = (transform.position + (r *Vector3.left) * distance); Debug.DrawLine(transform.position,left,Color.red); Vector3 right = (transform.position + (r *Vector3.right) * distance); Debug.DrawLine(transform.position,right,Color.red); Vector3 leftEnd = (left + (r *Vector3.forward) * distance); Debug.DrawLine(left,leftEnd,Color.red); Vector3 rightEnd = (right + (r *Vector3.forward) * distance); Debug.DrawLine(right,rightEnd,Color.red); Debug.DrawLine(leftEnd,rightEnd,Color.red); Vector3 point = cube.position; if(isINRect(point,leftEnd,rightEnd,right,left)) { Debug.Log("cube in this !!!"); }else { Debug.Log("cube not in this !!!"); } } private float Multiply(float p1x , float p1y, float p2x,float p2y, float p0x,float p0y) { return ((p1x - p0x) * (p2y - p0y) - (p2x - p0x) * (p1y - p0y)); } bool isINRect(Vector3 point,Vector3 v0,Vector3 v1,Vector3 v2,Vector3 v3) { float x = point.x; float y = point.z; float v0x = v0.x; float v0y = v0.z; float v1x = v1.x; float v1y = v1.z; float v2x = v2.x; float v2y = v2.z; float v3x = v3.x; float v3y = v3.z; if (Multiply(x,y, v0x,v0y, v1x,v1y) * Multiply(x,y, v3x,v3y, v2x,v2y) <= 0 && Multiply(x,y, v3x,v3y, v0x,v0y) * Multiply(x,y, v2x,v2y, v1x,v1y) <= 0) return true; else return false; } } |
马上过年了，雨松MOMO在这里祝福大家2013年幸幸福福的过日子，嘿嘿。
2013年4月补充
感谢楼下朋友给我的留言。， 我在补充一下这篇博客。
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | using UnityEngine; using System.Collections; public class NewBehaviourScript : MonoBehaviour { public Transform target; void Update() { float distance = Vector3.Distance(target.position,transform.position); Quaternion right = transform.rotation * Quaternion.AngleAxis(30,Vector3.up); Quaternion left = transform.rotation * Quaternion.AngleAxis(30,Vector3.down); Vector3 n = transform.position + (Vector3.forward * distance); Vector3 leftPoint = left * n ; Vector3 rightPoint = right *n ; Debug.DrawLine(transform.position,leftPoint,Color.red); Debug.DrawLine(transform.position,rightPoint,Color.red); Debug.DrawLine(rightPoint,leftPoint,Color.red); } } |
这里我以角色左右个30度。 这样就可以根据两个模型的距离以及角度来判断了。。
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