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How to use LookRotation to rotate an object based on hand positions?

I'm creating an interaction system for a VR game and I'm struggling with two hand interactions. I'm using the Quaternion.LookRotation() method to generate the rotation of the grabbed object based on the positions and rotations of the hands. The forward part is pretty simple:
Vector3 fwd = (primaryHand.position - secondaryHand.position).normalized;
The "up" part is what I have difficulty with. Initially I tried using the average up direction of both hands:
Vector3 avgUp = Quaternion.Slerp(primaryHand.rotation, secondaryHand.rotation, 0.5f) * Vector3.up;
There is an issue with this approach: the hand's up vector might get aligned with the fwd vector, which causes the object to flip over when it goes over it. Here is a simple illustration of the problem:
The light green arrows represent the up direction of the hands, while the dark green is the calculated direction used as an argument for the LookRotation() method.
The obvious solution seems to be to pick a different fixed vector instead of "up", one which won't be so easily aligned with the fwd vector. In the example it could be a vector aligned with the fingers. But keep in mind that there are no restrictions on initial hand rotation so no matter which vector you choose the hands can always happen to be rotated so that the vectors align. And even if you pick the an optimal vector dynamically (one that is perpendicular to fwd), it's still at best 90 degrees from aligning with fwd.
To solve this I tried restricting the direction to the values which don't cause problems but this caused another issues (I had difficulties with determining which values are ok and which should be discarded). I feel like I'm doing something wrong here, is there any better solution to this problem?

You can calculate the delta rotations of the hands and apply it to the "base up" of the object (the new up if we only take into account the change in position of hands...which will of course be orthogonal to the axis of the object). Then determine the change in angle that results in that up being rotated with each hand. Average those angles out, then apply those angles with the hand-hand axis using Quaternion.AngleAxis to the "base up" from earlier. Then you have your forward and up for Quaternion.LookRotation).
Below is an example of how you can use this, including VR hand noise simulation. To see the test, create a new scene in unity and attach this to the camera and it will build the scene on play start. There is a grip/release gui that will appear in Play view. You can adjust the hand rotation in Scene view
Vector3 leftHandPosCurrent;
Vector3 rightHandPosCurrent;
Vector3 worldAxisPrev;
Quaternion leftHandRotPrev;
Quaternion leftHandRotCurrent;
Quaternion rightHandRotPrev;
Quaternion rightHandRotCurrent;
bool isGripping;
bool firstFrameGripping;
Rigidbody grippedRB;
Transform leftHand;
Transform rightHand;
Quaternion targetRot;
/*
* On subsequent frames of gripping, calculate deltas in positions and
* rotations, average out the hand's effects, then apply them to the gripped
* object
*/
void HandleGrippedRot()
{
Vector3 worldAxisCurrent = rightHandPosCurrent - leftHandPosCurrent;
if (!firstFrameGripping)
{
Vector3 prevUp = targetRot * Vector3.up;
// we haven't moved the transform based on the hands yet, so
// find the new up would be ignoring hand rotations
Vector3 newUp = Quaternion.FromToRotation(worldAxisPrev,
worldAxisCurrent) * prevUp;
float leftHandAngle = GetDegRot(newUp, leftHandRotPrev,
leftHandRotCurrent, worldAxisCurrent);
float rightHandAngle = GetDegRot(newUp, rightHandRotPrev,
rightHandRotCurrent, worldAxisCurrent);
float avgAngle = (leftHandAngle + rightHandAngle) * 0.5f;
newUp = Quaternion.AngleAxis(avgAngle, worldAxisCurrent) * prevUp;
targetRot = Quaternion.LookRotation(worldAxisCurrent,
newUp);
}
else
{
firstFrameGripping = false;
}
leftHandRotPrev = leftHandRotCurrent;
rightHandRotPrev = rightHandRotCurrent;
worldAxisPrev = worldAxisCurrent;
}
/*
* Given the "up" of the object without taking hand rotations into account
* and the axis, determine how a hand's delta rotation affects that up
* around the axis and return the angle of that rotation
*/
float GetDegRot(Vector3 baseUp, Quaternion prevHandRot, Quaternion curHandRot,
Vector3 axis)
{
Vector3 adjUp = (curHandRot * Quaternion.Inverse(prevHandRot)) * baseUp;
adjUp = Vector3.ProjectOnPlane(adjUp, axis);
return Vector3.SignedAngle(baseUp, adjUp, axis);
}
void Update()
{
AddVRNoise(leftHand);
AddVRNoise(rightHand);
leftHandPosCurrent = leftHand.position;
rightHandPosCurrent = rightHand.position;
leftHandRotCurrent = leftHand.rotation;
rightHandRotCurrent = rightHand.rotation;
if (isGripping)
{
HandleGrippedRot();
}
}
void StartGrip()
{
if (isGripping) return;
isGripping = true;
firstFrameGripping = true;
// grippedTransform is set accordingly at some point
}
void EndGrip()
{
if (!isGripping) return;
isGripping = false;
}
/*
* example of using targetRot to move rb
*/
private void FixedUpdate()
{
if (!isGripping) return;
Quaternion delta = targetRot
* Quaternion.Inverse(grippedRB.transform.rotation);
delta.ToAngleAxis(out float angle, out Vector3 axis);
// convert to shortest angle form
if (angle > 180f)
{
axis = -axis; angle = 360f - angle;
}
grippedRB.angularVelocity = angle * 0.25f * axis;
}
/*
* just for testing purposes
*/
void Start()
{
leftHand = CreateHand(true);
leftHand.position = Vector3.left;
rightHand = CreateHand(false);
rightHand.position = Vector3.right;
CreateArrow();
}
/*
* just for testing purposes
*/
void AddVRNoise(Transform hand)
{
Quaternion noise = Random.rotation;
noise.ToAngleAxis(out float angle, out Vector3 axis);
angle = 100f * Time.deltaTime;
noise = Quaternion.AngleAxis(angle, axis);
Quaternion noisyRot = hand.rotation * noise;
hand.rotation = noisyRot;
}
/*
* just for testing purposes
*/
void OnGUI()
{
if (GUI.Button(new Rect(0, 0, 100, 50), "Grip"))
{
StartGrip();
}
if (GUI.Button(new Rect(100, 0, 100, 50), "Release"))
{
EndGrip();
}
}
/*
* just for testing purposes
*/
Transform CreateHand(bool isLeft)
{
string handName = isLeft ? "Left" : "Right";
GameObject hand = new GameObject($"{handName}hand");
GameObject palm = GameObject.CreatePrimitive(PrimitiveType.Cube);
palm.transform.localScale = new Vector3(0.5f, 0.2f, 1f);
palm.transform.SetParent(hand.transform);
GameObject thumb = GameObject.CreatePrimitive(PrimitiveType.Cube);
thumb.transform.localScale = new Vector3(0.2f, 0.1f, 0.1f);
thumb.transform.SetParent(hand.transform);
thumb.transform.localPosition = new Vector3(isLeft ? 0.32f : -0.32f,
0f, -.31f);
return hand.transform;
}
/*
* just for testing purposes
*/
void CreateArrow()
{
GameObject arrow = new GameObject();
GameObject body = GameObject.CreatePrimitive(PrimitiveType.Cube);
body.transform.localScale = new Vector3(1f, 1f, 5f);
body.transform.SetParent(arrow.transform);
GameObject head = GameObject.CreatePrimitive(PrimitiveType.Cube);
head.transform.SetParent(arrow.transform);
head.transform.localEulerAngles = Vector3.up * 45f;
head.transform.localPosition = new Vector3(0f, 0f, 2.5f);
grippedRB = arrow.AddComponent<Rigidbody>();
grippedRB.useGravity = false;
arrow.transform.position = 2f * Vector3.up;
}

Dash against slopes using physics in Unity 2D

I'm working on a 2D project in Unity.
The character controller is physics based, so I use rigidbody to move the player. Everything is working fine except when I try to apply a high speed movement to the character, like a dash.
This is how the code looks like.
I just check if the player is dashing, so I increase the Vector2 movement in a certain amount.
private void DashMovement() {
if (isDashing) {
movement.x *= dashFactor;
}
}
I'm also calculating the ground angle, so I set the movement vector to follow the ground inclination.
private void OnSlopeMovement() {
if (isGrounded && !isJumping) {
float moveDistance = Mathf.Abs(movement.x);
float horizontalOnSlope = Mathf.Cos(groundAngle * Mathf.Deg2Rad) * moveDistance * Mathf.Sign(movement.x);
float verticalOnSlope = Mathf.Sin(groundAngle * Mathf.Deg2Rad) * moveDistance;
if (horizontalOnSlope != 0)
movement.x = horizontalOnSlope;
if (isGrounded && verticalOnSlope != 0)
movement.y = verticalOnSlope;
}
SetMaxFallVelocity();
}
So I set the rigidbody velocity for making it move.
private void Move() {
movement.x *= Time.fixedDeltaTime;
if(isGrounded && !isJumping) movement.y *= Time.fixedDeltaTime;
Vector3 targetVelocity = new Vector2(movement.x, movement.y);
PlayerController.rb2d.velocity = Vector3.SmoothDamp(PlayerController.rb2d.velocity, targetVelocity, ref velocity, movementSmoothing);
}
The problem appears when I apply a speed high enough. I understand this issue is because of physics.
I think the ray that checks the ground and is used to calculate the groundAngle doesn't work fast enough to keep track of that movement, so I can not keep the player fixed on the ground.
I would like to find a solution without making the player kinematic, or stopping the dash on slopes.
This is how it looks ingame.
And this is how the rigidbody movement remain right over the ground, following the slopes angle.
EDIT:
This is how I get the ground angle:
private void GroundAngle() {
Vector2 rayOrigin = feetCollider.bounds.center;
rayOrigin.y += 0.1f;
Vector2 rayDirection = (Input.GetAxisRaw("Horizontal") == 0) ? Vector2.right : new Vector2(Input.GetAxisRaw("Horizontal"), 0);
int groundCollisions = Physics2D.RaycastNonAlloc(rayOrigin, Vector2.down, groundResults, Mathf.Infinity, groundMask);
if (groundCollisions > 0) {
groundAngle = Vector2.Angle(groundResults[0].normal, rayDirection) - 90f;
//Debug.DrawRay(rayOrigin, Vector2.down, Color.green);
if (groundAngle > 0 && !isDashing) {
rayOrigin.x += Input.GetAxisRaw("Horizontal") * .125f;
Physics2D.RaycastNonAlloc(rayOrigin, Vector2.down, groundResults, Mathf.Infinity, groundMask);
groundAngle = Vector2.Angle(groundResults[0].normal, rayDirection) - 90f;
//Debug.DrawRay(rayOrigin, Vector2.down, Color.blue);
}
}
}
Thanks to #Ruzhim for the help. I just post a first "solution" for the problem.
According to Ruzhim advises, I've used him code this way.
private void SetPositionAfterTick() {
if (isDashMovement) {
Vector2 currentPosition = new Vector2(transform.position.x, transform.position.y);
currentPosition.y = feetCollider.bounds.min.y;
Vector2 feetPosAfterTick = currentPosition + PlayerController.rb2d.velocity * Time.deltaTime;
float maxFloorCheckDist = .1f;
RaycastHit2D groundCheckAfterTick = Physics2D.Raycast(feetPosAfterTick + Vector2.up * maxFloorCheckDist, Vector2.down, maxFloorCheckDist * 5f);
if (groundCheckAfterTick) {
Vector2 wantedFeetPosAfterTick = groundCheckAfterTick.point;
if (wantedFeetPosAfterTick != feetPosAfterTick) {
//PlayerController.rb2d.transform.position = (wantedFeetPosAfterTick + new Vector2(0f, feetCollider.bounds.min.y - PlayerController.rb2d.position.y));
PlayerController.rb2d.velocity = Vector2.zero;
}
}
}
}
This is how it looks like.
This is good enough to continue polishing that mechanic. I still need to set the position in some way. The rigidbody's position calculation is not working as it
is raised right now, as the condition (wantedFeetPosAfterTick != feetPosAfterTick) is always true, so the character goes throw the floor and fall.
As you can see, I also need to control the down slopes movement, as it uses the slopes movement sometimes, and dash straight forward others.

This is how asker Rubzero implemented the below code to work for them:
private void SetPositionAfterTick() {
if (isDashMovement) {
Vector2 currentPosition = new Vector2(transform.position.x, transform.position.y);
currentPosition.y = feetCollider.bounds.min.y;
Vector2 feetPosAfterTick = currentPosition + PlayerController.rb2d.velocity * Time.deltaTime;
float maxFloorCheckDist = .1f;
RaycastHit2D groundCheckAfterTick = Physics2D.Raycast(feetPosAfterTick + Vector2.up * maxFloorCheckDist,
Vector2.down, maxFloorCheckDist * 5f);
if (groundCheckAfterTick) {
Vector2 wantedFeetPosAfterTick = groundCheckAfterTick.point;
if (wantedFeetPosAfterTick != feetPosAfterTick) {
//PlayerController.rb2d.transform.position = (wantedFeetPosAfterTick + new Vector2(0f, feetCollider.bounds.min.y -
PlayerController.rb2d.position.y));
PlayerController.rb2d.velocity = Vector2.zero;
}
}
}
}
This is how it looks like.
This is good enough to continue polishing that mechanic. I still need
to set the position in some way. The rigidbody's position calculation
is not working as it is raised right now, as the condition
(wantedFeetPosAfterTick != feetPosAfterTick) is always true, so the
character goes throw the floor and fall.
As you can see, I need to control the down slopes movement, as it uses
the slopes movement sometimes, and dash straight forward others.
I agree with AresCaelum; using physics to do slope movement is pretty much the opposite of what you want to be doing if you don't want to preserve momentum when you're done going up/down the slope. Specifically, your problem is here:
float moveDistance = Mathf.Abs(movement.x);
float horizontalOnSlope = Mathf.Cos(groundAngle * Mathf.Deg2Rad) * moveDistance * Mathf.Sign(movement.x);
float verticalOnSlope = Mathf.Sin(groundAngle * Mathf.Deg2Rad) * moveDistance;
This is a problem because the more the player moves horizontally in a frame, the more they will move vertically based on the slope of the ramp they are on. However, this assumption doesn't hold if they should only be traveling up the ramp during only part of the movement during the frame. So, you need a way to handle that situation.
One solution is to use a raycast from where the player would be then if it's above the floor, alter the vertical velocity so that it would place them at that floor's position instead.
First, determine if slope movement has occurred in a physics frame...
private bool slopeMovementOccurred = false;
void FixedUpdate() {
slopeMovementOccurred = false;
// ...
}
private void OnSlopeMovement() {
if (isGrounded && !isJumping) {
slopeMovementOccurred = true;
// ...
}
SetMaxFallVelocity();
}
... and if it has, determine where the player is going to be after the physics update. Then do a physics2d raycast from above that position (by some amount) downward (double the previous amount) to find where the player's position should be, and then change the rb2d.velocity such that it will place the player exactly at the height they should be at.
Assuming you can calculate some kind of Vector2 feetOffset that has the local position of the player's feet:
void FixedUpdate() {
// ...
StickToSlopeLanding();
}
void StickToSlopeLanding() {
if (slopeMovementOccurred) {
Vector2 curVelocity = PlayerController.rb2d.velocity;
Vector2 feetPosAfterTick = PlayerController.transform.position
+ PlayerController.feetOffset
+ curVelocity * Time.deltaTime;
float maxFloorCheckDist = 1.0f;
// determine where the player should "land" after this frame
RaycastHit2D groundCheckAfterTick = Physics2D.Raycast(
feetPosAfterTick + Vector2.up * maxFloorCheckDist,
-Vector2.up, maxFloorCheckDist * 2f);
if (groundCheckAfterTick.collider != null) {
Vector2 wantedFeetPosAfterTick = groundCheckAfterTick.point;
// if basic physics won't take them to landing position
if (wantedFeetPosAfterTick != feetPosAfterTick) {
Vector2 wantedVelocity = curVelocity
+ Vector2.up
* ((wantedFeetPosAfterTick.y - feetPosAfterTick.y)
/ Time.deltaTime);
// adjust velocity so that physics will take them to landing position
PlayerController.rb2d.velocity = wantedVelocity;
// optionally, set a flag so that next frame
// it knows the player should be grounded
}
}
}
}
Hopefully this gets you towards a solution that will work.
Note: you may need to also move the rigidbody so that it doesn't try to clip through the corner at the top of the ramp, and you can determine where to put the rigidbody using another raycast, setting the velocity from that point to be horizontal:
void StickToSlopeLanding() {
if (slopeMovementOccurred) {
Vector2 curVelocity = PlayerController.rb2d.velocity;
Vector2 feetPosAfterTick = PlayerController.transform.position
+ PlayerController.feetOffset
+ curVelocity * Time.deltaTime;
float maxFloorCheckDist = 1.0f;
// determine where the player should "land" after this frame
RaycastHit2D groundCheckAfterTick = Physics2D.Raycast(
feetPosAfterTick + Vector2.up * maxFloorCheckDist,
-Vector2.up, maxFloorCheckDist * 2f);
if (groundCheckAfterTick.collider != null) {
Vector2 wantedFeetPosAfterTick = groundCheckAfterTick.point;
// if basic physics won't take them to landing position
if (wantedFeetPosAfterTick != feetPosAfterTick) {
// look for corner of ramp+landing.
// Offsets ensure we don't raycast from inside/above it
float floorCheckOffsetHeight = 0.01f;
float floorCheckOffsetWidth = 0.5f;
RaycastHit2D rampCornerCheck = Physics2D.Raycast(
wantedFeetPosAfterTick
- floorCheckOffsetHeight * Vector2.up
- floorCheckOffsetWidth * Mathf.Sign(movement.x) * Vector2.right,
Mathf.Sign(movement.x) * Vector2.right);
if (rampCornerCheck.collider != null) {
// put feet at x=corner position
Vector2 cornerPos = Vector2(rampCornerCheck.point.x,
wantedFeetPosAfterTick.y);
PlayerController.rb2d.position = cornerPos
- PlayerController.feetOffset;
// adjust velocity so that physics will take them from corner
// to landing position
Vector2 wantedVelocity = (wantedFeetPosAfterTick - cornerPos)
/ Time.deltaTime;
PlayerController.rb2d.velocity = wantedVelocity;
// optionally, set a flag so that next frame
// it knows the player should be grounded
}
}
}
}
}

Making Field of view using Raycasts With for loops (Using Unity C#)

Code:
void IdleState ()
{
RaycastHit hit;
for (float i = -ViewWidth; i < ViewWidth; i++)
{
float Iterater = i/20;
if (Physics.Raycast(transform.position, transform.forward + new Vector3(Iterater,0,0), out hit, ViewRange))
{
Debug.DrawRay(transform.position,(transform.forward + new Vector3(Iterater,0,0)).normalized * ViewRange, Color.red);
if (hit.transform.gameObject.layer == LayerMask.NameToLayer("Player"))
{
FoundPlayer(hit.transform);
}
}
}
}
Problem: In Unity I am trying to create a Field of view for an enemy AI by drawing multiple raycasts with for loops. For some reason the raycasts do this:
GIF
I've been trying to fix this for days Please help!
Also the FoundPlayer() function in case you need it:
void FoundPlayer (Transform DetectedObject)
{
float step = TurnSpeed * Time.deltaTime;
Vector3 Direc = DetectedObject.position - transform.position;
Vector3 RotMath = Vector3.RotateTowards(transform.forward, Direc,step,0.0f);
transform.rotation = Quaternion.LookRotation(RotMath);
Vector3 CurrentRot = transform.eulerAngles;
transform.rotation = Quaternion.Euler(0,CurrentRot.y,0);
}
The FoundPlayer() function just rotates the enemy towards the player when one of the raycasts hit it.

Regarding Raycast:
transform.Forward is in world-space coordinates, to which you add some fraction of world-space X-axis offset. What you wanted is to add some fraction of 'local-space' X-axis. transform.Right is the world-space conversion of local-space X-axis. Try:
var rayDirection = (transform.Forward + (Vector3.Scale(transform.Right, new Vector3(Iterater, 0, 0))).normalized;
Regarding Fields of View:
If all you want to do is check what objects are within a FOV, start finding everything within a sphere, then filter those objects to what's within appropriate angles from transform.forward:
float ViewRange = 10;
float hHalfFov = 45; // Horizontal Half-Field of View (Degrees)
float vHalfFov = 45; // Vertical Half-Field of View (Degrees)
void IdleState() {
// Find all colliders within ViewRange
var hits = Physics.OverlapSphere(transform.position, ViewRange);
foreach (var hit in hits) {
if ( hit.gameObject == this.gameObject ) continue; // don't hit self
// Check FOV
var direction = (transform.position - hit.transform.position);
var hDirn = Vector3.ProjectOnPlane(direction, transform.up).normalized; // Project onto transform-relative XY plane to check hFov
var vDirn = Vector3.ProjectOnPlane(direction, transform.right).normalized; // Project onto transform-relative YZ plane to check vFov
var hOffset = Vector3.Dot(hDirn, transform.forward) * Mathf.Rad2Deg; // Calculate horizontal angular offset in Degrees
var vOffset = Vector3.Dot(vDirn, transform.forward) * Mathf.Rad2Deg; // Calculate vertical angular offset in Degrees
if (hOffset > hHalfFov || vOffset > vHalfFov) continue; // Outside of FOV
Debug.DrawLine(transform.position, hit.transform.position, Color.red);
if (hit.transform.gameObject.layer == LayerMask.NameToLayer("Player")) {
FoundPlayer(hit.transform);
}
}
}

How do I make a 2D object face the direction it is moving like drifting

As shown in the picture above, I have two GameObjects: the car and the circle. The car follows the circle, and the circle is moving with the cursor. Currently, my car is following the circle from a distance. When the circle moves along the x-axis, I want to rotate the car like it's drifting.
Here is my car follow script:
public class Follow : MonoBehaviour
{
public Transform leader;
public float followSharpness = 0.1f;
Vector3 _followOffset;
void Start()
{
// Cache the initial offset at time of load/spawn:
_followOffset = transform.position - leader.position;
}
void LateUpdate()
{
// Apply that offset to get a target position.
Vector3 targetPosition = leader.position + _followOffset;
//GetComponent<Rigidbody2D>().rotation = 1.5f;
// Keep our y position unchanged.
//targetPosition.y = transform.position.y;
// Smooth follow.
transform.position += (targetPosition - transform.position) * followSharpness;
}
}

You could try to use Transform.LookAt:
void LateUpdate()
{
Vector3 targetPosition = leader.position + _followOffset;
transform.position += (targetPosition - transform.position) * followSharpness;
transform.LookAt(leader);
}
Disclaimer: I'm not able to test that this code works right now, you'll have to try it out and see if it produces the desired result.

So from what you described, is you want to make the car always facing the cursor, so it is always "looking at" the cursor, here is how you can do it:
Vector3 diff = Camera.main.ScreenToWorldPoint(Input.mousePosition) - transform.position;
diff.Normalize();
float rot_z = Mathf.Atan2(diff.y, diff.x) * Mathf.Rad2Deg;
transform.rotation = Quaternion.Euler(0f, 0f, rot_z - 90);
From Answer: LookAt 2D Equivalent ?

Unity2D Smooth Rotation using Slerp

I'm making a patrol script for a game object. I want the object to rotate smoothly and slowly to face it's patrol target.
Unfortunately, the object snaps to it's new location.
I've asked on unity forums and can't get an answer.
How can I get the rotation to be smooth and slow?
Here's my code.
public Transform[] patrol;
public int Currentpoint;
public float moveSpeed;
public Vector3 john = new Vector3(0,1,0);
public Vector3 targetLocation;
void Start()
{
}
void Update()
{
if (transform.position == patrol [Currentpoint].position) {
Currentpoint++;
if (Currentpoint >= patrol.Length) {
Currentpoint = 0;
}
targetLocation = patrol [Currentpoint].position;
Vector3 targetDir = targetLocation - transform.position;
float angle = Mathf.Atan2 (targetDir.y, targetDir.x) * Mathf.Rad2Deg;
transform.localRotation = Quaternion.SlerpUnclamped (transform.localRotation, Quaternion.AngleAxis (angle, Vector3.forward), Time.deltaTime * 3);
Debug.Log (Currentpoint);
}
transform.position = Vector3.MoveTowards (transform.position, patrol [Currentpoint].position, moveSpeed * Time.deltaTime);
}

public static Quaternion Slerp(Quaternion a, Quaternion b, float t); The parameter t is clamped to the range [0, 1]
your times 3 is throwing it out so it is not between 0-1 ... I believe

If you like some mathematics then I have a solution for you.
You want to rotate object around another, like Earth and Sun. May be some other solutions may available but I would do it through LookAt and parametric equation of circle.
x = r * cos(theta) + displacementX
y = r * sin(theta) + displacementY
where r is radius, distance in your case
displacementX and displacementY are the distance from origin. If both (displacementX and displacementY) is 0 then it will rotate around origin (0,0). In other words displacementX and displacementY is the origin of rotation.
In Object(Earth) script, do it as follow
public Transform _sun;
float _theta = 0;
void Start ()
{
StartCoroutine ("ChangeAngle");
}
void Update ()
{
transform.LookAt (_sun);
float newX = (5 * Mathf.Cos (_theta)) + _sun.position.x;
float newY = (5 * Mathf.Sin (_theta)) + _sun.position.y;
transform.position = new Vector3 (newX, newY, _sun.position.z);
}
IEnumerator ChangeAngle ()
{
while (true) {
yield return new WaitForSeconds (0.01f);
_theta += 0.1f;
if (_theta >= 360)
_theta = 0;
}
}
You can further play with it

I found an answer,
It turns out that placing the rotational instructions within the if statement was the problem. I converted the rotation to a function, then placed the function above the general patrol movement in the same loop segment.
I don't know why it worked.
Thanks to everyone for their help.