Develop Reference

How to get the signed angle of a quaternion on an arbitrary axis

I'm trying to make an airplane controller, I am kind of aiming for something between arcade and realistic, so I want the plane to turn with a force proportional to the roll.
I haven't coded in any adjustments and I'm still prototyping the whole thing, but I encountered a problem with getting the signed rotation angle while using quaternions, I had a look at Determining if quarternion rotation is clockwise or counter clockwise here on SO but I am having trouble generalizing the solution to the (almost) arbitrary plane the rotation can be at.
What I made by now:
private void FixedUpdate()
{
float desiredYaw = _yaw * _rotationSpeed * Time.fixedDeltaTime;
float desiredPitch = -_pitch * _rotationSpeed * Time.fixedDeltaTime;
float rotationStepSize = _throttle * Time.fixedDeltaTime;
Quaternion toRotate = Quaternion.Euler(desiredPitch, 0, desiredYaw);
Quaternion straighRotation = Quaternion.LookRotation(_transform.forward, Vector3.up );
_rotation = _transform.rotation * toRotate;
float turningForce = Quaternion.Angle( _rotation, straighRotation );
_rigidbody.MoveRotation( _rotation );
_rigidbody.AddTorque( turningForce * _rotationForce * rotationStepSize * Vector3.up );
_rigidbody.AddRelativeForce( _speed * rotationStepSize * Vector3.forward );
}
EDIT: I realized I'm calculating the turning force using the roll rather then the yaw, that was intended just wrong wording, corrected now.

Since all you need is a factor that describes how downward the plane's right is, you can just use the y component of the plane's right for that. No need to bring in quaternions or even trigonometry. Explanation in comments:
private void FixedUpdate()
{
// ...
// Calculate how downward local right is in range [-1,1]
// The more downward, the more tilted right the plane is
// positive = tilted right
// negative = tilted left
float turnFactor = -_transform.right.y;
// Could do things to modify turnFactor to affect easing here.
// For instance, if turning rate should start slower then rapidly increase:
// turnFactor = Mathf.Sign(turnFactor) * turnFactor * turnFactor;
// Use factor and _rotationForce member to calculate torque, apply along
// global up.
// We expect to call this every fixed frame so we can just use the default
// ForceMode of ForceMode.Force which multiplies fixed delta time inside.
_rigidbody.AddTorque(_rotationForce * turnFactor * Vector3.up);
// ...
}

Diagonal speed is too fast

How can I keep the diagonal speed to be the same as the horizontal and vertical speed without clamping any value or using ".normaized". I tryed to normalize the values but I lost the joystick values between 1 and 0. Here is my code :
void ListenInput()
{
Vector3 rightDirection = camera.right;
Vector3 frontDirection = camera.GetForwardFromAngleY();
move = new Vector2(
Input.GetAxis("Horizontal"),
Input.GetAxis("Vertical")
);
MoveCharacter(rightDirection * move.x);
MoveCharacter(frontDirection * move.y);
}
void MoveCharacter(Vector3 velocity)
{
transform.position += velocity * Time.deltaTime * runningSpeed;
}

Here, you should clamp the magnitude of the input Vector2.
For example with Vector2.ClampMagnitude() from the Unity API.
That will keep the input non-binary and prevent the diagonal from getting larger than purely horizontal/vertical inputs.
void ListenInput()
{
Vector3 rightDirection = camera.right;
Vector3 frontDirection = camera.GetForwardFromAngleY();
move = new Vector2(
Input.GetAxis("Horizontal"),
Input.GetAxis("Vertical")
);
move = Vector2.ClampMagnitude(move, 1f);
MoveCharacter(rightDirection * move.x);
MoveCharacter(frontDirection * move.y);
}
void MoveCharacter(Vector3 velocity)
{
transform.position += velocity * Time.deltaTime * runningSpeed;
}

If you normalize a vector you will make sure it's length is 1. This is a great way to avoid quirks like "diagonal movement is faster than normal movement".
However, the fact that the length is always 1 also means that there is no "move slowly" or "move at full speed" distinction from the joystick. When you say "I lost the joystick values between 1 and 0" is due to this fact.
One way developers get around this is by using a mathematical formula to scale the speed.
You could:
Use the largest value (horizontal or vertical) to control the speed
Use the smallest value
Use a combination of the two
Another way to do this is to store how long ago the movement started, then scale the speed based on that. This method has its own challenges, but is very familiar to players.
Examples
For instance, if I have:
horizontalInput = 1
verticalInput = 0.5
This means my normalized vector looks like this:
I could:
Use the largest value
Move at full speed (1) on the direction of my vector.
Use the smallest value
Move at half speed (0.5) on the direction of my vector.
Use a Use a combination of the two values
For this instance, lets use the following formula: (x+y)/2.
Move at 3/4 speed (0.75) on the direction of my vector.
NOTE: This formula will not "feel" as nice if you have x=0 and y=1, this is just an example. You most likely want to use Min, Max, Avg and if-clauses to control how the speed works.
You can use different formulas and different techniques to make the movement in your game feel like what you want, but take the time to analyze WHY it feels like that.

Control begin and end point object between 2 points

im trying to move a object in unity between 2 points, and at the moment it kinda works strange, i read the documentation and it says that the object begin point is (0,0,0) so my object goes under my other mesh that i have there, and the end point i can actually control, in my case it is 10, i want the object to move between 1.5 and 10(not 0 to 10)
i have this
void Update () {
transform.position = new Vector3(transform.position.x,Mathf.PingPong(Time.time,10.0f), transform.position.z);
}
when i try to put speed on the ball doing this:
void Update () {
transform.position = new Vector3(transform.position.x,Mathf.PingPong(Time.time,10.0f) * 10, transform.position.z);
}
the object does not colide and goes back at the end point it just stop looping and never came back how can i correct this 2 problems?

If your object has a collider, I suggest you move it via its Rigidbody rather than its Transform, to avoid potential collision issues. Try this:
public float MinY = 1.5f; // y position of start point
public float MaxY = 10f; // y position of end point
public float PingPongTime = 1f; // how much time to wait before reverse
public Rigidbody rb; // reference to the rigidbody
void Update()
{
//get a value between 0 and 1
float normalizedTime = Mathf.PingPong(Time.time, PingPongTime) / PingPongTime;
//then multiply it by the delta between start and end point, and add start point to the result
float yPosition = normalizedTime * (MaxY - MinY) + MinY;
//finally update position using rigidbody
rb.MovePosition(new Vector3(rb.position.x, yPosition, rb.position.z));
}
Here you have a better control on the distance to travel, and the speed.
Actually I didn't get exactly what are the problem you faced. But don't forget here and in your try, that you are directly modifying the position of the object, not adding forces or else.
Hope that helps you.

I think you simply misunderstood how the Mathf.PingPong method works :
first argument t is the value you want to "clamp" between 0 and the given length : this is were you want to put the Time.time as you did since this value will increase over time and therefore perpetually oscillate. If you want to increase/decrease the oscillation speed you have to multiply it.
second argument length is the max value of the "clamp" : if you want to increase/decrease the distance (in your case) you have either set it to 0 and multiply the whole Mathf.PingPong(...) by a value or directly give it the wanted value (both implementations will have a different effect.
Mathf.PingPong(Time.time * speed, 1.0f) * value : speed will affect the oscillation speed / value will affect the max value reached AND the speed / time to complete the oscillation (back and forth) will remain the same as value changes and decrease as speed increases
Mathf.PingPong(Time.time * speed, value) : speed will affect the oscillation speed / value will affect the max value reached BUT NOT the speed / time to complete the oscillation (back and forth) will increase as value increases and decrease as speed increases
About your other problems :
If you want to move your object between 1.5 and 10 you have to write something like this :
transform.position = new Vector3(transform.position.x, 1.5f + Mathf.PingPong(Time.time, 10.0f - 1.5f), transform.position.z);.
Also if you want to detect collision, avoid setting position manually as it will mess up with Physics and cause weird behaviors. Best way to move your object while keeping physic working is to do as #Heldap said using Rigidbody.MovePosition.

unity3d - Accelerometer sensitivity

I am testing the accelerometer code in Unity3D 4.3. What I want to do is simple change the object angle while tilting the ipad, to fake view angle like real live. Everything works fine except for the fact that the accelerometer is a bit too sensitive and I can see the GameObject is like of flickering even I put it on table. How can I make it less sensitive so that even when you hold with your hand the angle will change according to the tilt and the object remain steady?
Here are my code:
void Update () {
Vector3 dir = Vector3.zero;
dir.x = Mathf.Round(Input.acceleration.x * 1000.0f) / 1000.0f;
dir.y = Mathf.Round(Input.acceleration.y * 1000.0f) / 1000.0f;
dir.z = Mathf.Round(Input.acceleration.z * 1000.0f) / 1000.0f;
// clamp acceleration vector to the unit sphere
if (dir.sqrMagnitude > 1)
dir.Normalize();
// Make it move 10 meters per second instead of 10 meters per frame...
dir *= Time.deltaTime;
dir *= speed;
acx = dir.x;
acy = dir.y;
acz = dir.z;
transform.rotation = Quaternion.Euler(dir.y-20, -dir.x, 0);
}

You may need to use a low pass filter (s. Exponential Moving Average for a better description regarding software) before using the signal output. I always use native code to get accelerometer and gyroscope values on iPhone so I am not 100% sure how Unity handles this. But from what you are describing the values appear unfiltered.
A low pass filter calculate a weighted average from all your previous values. Having for example a filter factor on 0.1 your weighted average is:
Vector3 aNew = Input.acceleration;
float a = 0.1f * aNew + 0.9f * a;
This way your values are smoothed at the expense of a small delay. Running the accelerometer with 50 Hz you won't notice it.

I couldn't make Kay's example work as it was not multiplying the last part, so here's my small correction:
Vector3 aNew = Input.acceleration;
a = (0.1 * aNew) + (0.9 * a);

Galaxian-like Enemy movement

I'm making a galaxian-like shooter, and my enemy objects have a destination Vector which they travel towards, using this bit of code:
position.X -= (Motion.X / Magnitude) * Speed;
position.Y -= (Motion.Y / Magnitude) * Speed;
Motion is worked out by:
this.Motion = InitialPosition - Destination;
This makes them travel in a straight line towards the destination.
However, I want to make them a bit more interesting, and travel on a sin or cos wave, a bit like Galaxian did.
How can I do this?

You might be better off defining a bezier curve for the movement function than simple functions like a sine wave. Galaxian certainly had more complex movements than that.
Here is a link to a primer on the maths of Bezier curves. It's quite a long document, but does a good job of covering the maths involved, with plenty of examples.
Hope that helps inspire you.

One way to do this would be to create an acceleration factor for the horizontal motion and add that factor to the horizontal speed every tick. So if your horizontal speed for a given enemy was 2 to begin, and your acceleration was -.01, then after 200 ticks the enemy would be going straight down, and after another 200 ticks it would be moving at a horizontal speed of -2. This will give a nice curve.
By determining the speed and acceleration randomly for each enemy (within certain limits determined by experimentation) you can create a nice looking variety of attack profiles without too much effort. This would give a very Galaxian-like motion.
You can do the same thing with the vertical as well, though, of course, the acceleration limits would be very different...for the horizontal acceleration you would probably want to determine a range that was equal in magnitude on either side of 0 (say -.02 to +.02), while for the vertical acceleration, you probably always want the ship to end up going down off the bottom of the screen, so you probably want that acceleration to always end up positive (or negative depending on how you're doing screen coordinates.)

You would do this by utilizing waypoint navigation, in line with your current motion code. You would calculate the waypoints by graphing the sine wave. You would do this by using something to the effect of Destination.Y = Math.Sin(Destination.X) - it's a little difficult to say for sure without seeing your code at large.

Creating an oscillator and moving the enemy (even without momentum) perpendicularly to its direction by an offset equals to the sine or cosine of the oscillator would be enough.
The following example, while working, is clearly just a guideline. I hope it can help you.
var dest = new PointF(200, 100);
var pos = new PointF(30, 140);
var oscAngle = 0d;
var dirAngle = Math.Atan2(dest.Y - pos.Y, dest.X - pos.X);
//Constants for your simulation
const int movSpeed = 2;
const int amp = 2;
const double frequency = Math.PI / 5;
//Inappropriate loop condition, change it to proper
while (true)
{
oscAngle += frequency;
//Scalar offset, you can use Cos as well
var oscDelta = Math.Sin(oscAngle);
//Linear movement
var stepVector = new SizeF((float)(Math.Cos(dirAngle) * movSpeed), (float)(Math.Sin(dirAngle) * movSpeed));
//Oscillating movement, making it transversal by adding 90° to the direction angle
var oscNormalAngle = dirAngle + Math.PI / 2;
//Vector for the oscillation
var oscVector = new SizeF((float)(Math.Cos(oscNormalAngle) * oscDelta) * amp, (float)(Math.Sin(oscNormalAngle) * oscDelta) * amp);
pos += stepVector + oscVector;
//Operate below
}