Get point on sphere's surface from a random point - unity3d

Question

I am creating a game with Unity and I have a math problem.
I have a sphere with a radius of 10 and center of (0, 0, 0).
I want the camera to move around that sphere, but I can't find anywhere a way to do what I want to.
I move the camera in the X axis and the Y axis (and therefore get a point outside of the sphere) and I want to set it's Z axis so the camera would be back on the sphere, I am using this equation: r^2 = x^2 + y^2 + z^2 => z^2 = r^2 - x^2 - y^2
But it doesn't work… Please help me
EDIT
This is my code (in c#):
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);
}
As you can see I used Clamp to keep the X and Y less then the radius but it didn't help…

Answer 1

This isn't tested, but it should be pretty close
private void OnMouseDrag(){
Vector3 newPos = mainCameraTransform.position;
newPos += mainCameraTransform.up * Input.GetAxis("Mouse Y");
newPos += mainCameraTransform.right * Input.GetAxis("Mouse X");
newPos = newPos.normalized * 10f;
mainCameraTransform.position = newPos;
mainCameraTransform.LookAt(Vector3.zero, mainCameraTransform.up);
}

Answer 2

You have to limit 2D coordinates by circle border
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 3

Drag and drop this script on the camera to orbit it around a target using the right mouse button
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);
}
}