Question

我正在使用Unity制作游戏，但我遇到了数学问题。我有一个半径为10且中心为（0,0,0）的球体。我希望相机在那个球体周围移动，但我找不到任何方法来做我想做的事情。我在X轴和Y轴上移动相机（因此在球体外面得到一个点）我想设置它的Z轴，这样相机就会回到球体上，我正在使用这个等式：r ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 =＆gt; z ^ 2 = r ^ 2 - x ^ 2 - y ^ 2 但它没有用......请帮助我

修改

这是我的代码（在c＃中）：

    private void OnMouseDrag()
{
    var newX = mainCameraTransform.position.x + Input.GetAxis("Mouse X");
    var newY = mainCameraTransform.position.y + Input.GetAxis("Mouse Y");
    var maxDistance = 10.0f;
    newX = Mathf.Clamp(newX, -maxDistance * 0.85f, maxDistance * 0.85f);
    newY = Mathf.Clamp(newY, 1.0f * 0.85f, maxDistance * 0.85f);
    var newZ = Mathf.Sqrt(Mathf.Abs(maxDistance * maxDistance - newX * newX - newY * newY));

    mainCameraTransform.position = new Vector3(newX, newY, newZ);
    mainCameraTransform.LookAt(Vector3.zero);
}

正如你所看到的，我使用Clamp来保持X和Y小于半径，但它没有帮助......

Answer 1

您必须按圆圈限制2D坐标

len = Mathf.Sqrt(newX * newX + newY * newY);
//perhaps you have Len or Hypot function in your Math library

if len > maxDistance then
     newX = maxDistance * newX / len
     newY = maxDistance * newY / len;

Answer 2

这还没有经过测试，但它应该非常接近

value Payment-method ::= credit-card : cb

Answer 3

将此脚本拖放到相机上，使用鼠标右键将其围绕目标进行环绕

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class OrbitAroundObject : MonoBehaviour {

    public Transform target;
    public float distance = 10.0f;
    public float xSpeed = 120.0f;
    public float ySpeed = 120.0f;

    public float yMinLimit = -20f;
    public float yMaxLimit = 80f;

    public float distanceMin = .5f;
    public float distanceMax = 15f;

    public float smoothTime = 2f;

    public float zoomSpeed = 1;

    float rotationYAxis = 0.0f;
    float rotationXAxis = 0.0f;

    float velocityX = 0.0f;
    float velocityY = 0.0f;

    // Use this for initialization
    void Start() {
        Vector3 angles = transform.eulerAngles;
        rotationYAxis = angles.y;
        rotationXAxis = angles.x;

        // Make the rigid body not change rotation
        if (GetComponent<Rigidbody>()) {
            GetComponent<Rigidbody>().freezeRotation = true;
        }
    }

    void LateUpdate() {
        if (target) {
            if (Input.GetMouseButton(1)) {
                velocityX += xSpeed * Input.GetAxis("Mouse X") * 0.02f;
                velocityY += ySpeed * Input.GetAxis("Mouse Y") * 0.02f;
            }

            //distance -= (Input.mouseScrollDelta.y*Time.deltaTime);
            distance = Mathf.Lerp(distance, distance-(Input.mouseScrollDelta.y*zoomSpeed) , Time.deltaTime * smoothTime);
            distance = Mathf.Clamp(distance, distanceMin, distanceMax);

            rotationYAxis += velocityX;
            rotationXAxis -= velocityY;

            rotationXAxis = ClampAngle(rotationXAxis, yMinLimit, yMaxLimit);

            //Quaternion fromRotation = Quaternion.Euler(transform.rotation.eulerAngles.x, transform.rotation.eulerAngles.y, 0);
            Quaternion toRotation = Quaternion.Euler(rotationXAxis, rotationYAxis, 0);
            Quaternion rotation = toRotation;


            Vector3 negDistance = new Vector3(0.0f, 0.0f, -distance);
            Vector3 position = rotation * negDistance + target.position;

            transform.rotation = rotation;
            transform.position = position;

            velocityX = Mathf.Lerp(velocityX, 0, Time.deltaTime * smoothTime);
            velocityY = Mathf.Lerp(velocityY, 0, Time.deltaTime * smoothTime);
        }

    }

    public static float ClampAngle(float angle, float min, float max) {
        if (angle < -360F)
            angle += 360F;
        if (angle > 360F)
            angle -= 360F;
        return Mathf.Clamp(angle, min, max);
    }
}

从随机点获取球体表面上的点

3 个答案: