So, when my i let go off my keys the controller stops like it hits a wall, i tried changing that but all that changed is that now it gets flung into outer space every time i press a key:
float x = Input.GetAxis("Horizontal");
float z = Input.GetAxis("Vertical");
Vector3 newMovement = transform.right * x + transform.forward * z;
momentum = new Vector3(characterController.velocity.x, 0, characterController.velocity.z);
newMovement.y = 0;
if (!newMovement.normalized.Equals(momentum.normalized))
{
Debug.Log("new" + newMovement.normalized);
Debug.Log(momentum.normalized);
momentum = (momentum.magnitude - 2f) > 0 ? momentum.normalized * (momentum.magnitude - 2f) : Vector3.zero;
if (newMovement.x == momentum.x)
momentum.x = 0;
if (newMovement.z == momentum.z)
momentum.z = 0;
}
else
momentum = Vector3.zero;
characterController.Move((newMovement * speed + velocity + momentum) * Time.deltaTime);
Also for some reason even though sometimes both vectors are equal they pass through the if statement(i tried using !=)(both vectors are logged on the first 2 lines of the if statement)
Use https://docs.unity3d.com/ScriptReference/Vector3.SmoothDamp.html, it will gradually slow the movement to zero, depending on the value of smoothTime:
public float smoothTime = 0.3F;
private Vector3 velocity = Vector3.zero;
private Vector3 newMovement;
void Update()
{
newMovement = transform.right * x + transform.forward * z;
transform.position = Vector3.SmoothDamp(transform.position, targetPosition, ref velocity, smoothTime);
}
I want to spin an object around x and rotate y axis to a direction.
Quaternion qr = Quaternion.Euler(transform.eulerAngles.x, 0,0);
transform.rotation = Quaternion.Lerp(transform.rotation,qr,Time.deltaTime*5);
transform.rotation = Quaternion.Euler(xRotation(xRotationSpeed),
transform.eulerAngles.y, 0);
x and y Rotations combined make weird rotations and sometimes even rotate z even though I have it set to 0.
Here is an example that yawing an object while rolling.
Notice that the rotation is applied from right to left.
const float ROLL_SPEED = 120f;
const float YAW_SCALE = 60;
float _lastYawBase;
void Update()
{
var yawBase = Input.GetAxis("Horizontal");
var tsf = transform;
tsf.localRotation =
// 4. apply new yaw
Quaternion.Euler(0, yawBase * YAW_SCALE, 0) *
// 3. roll
Quaternion.Euler(ROLL_SPEED * Time.deltaTime, 0f, 0f) *
// 2. revert last yaw
Quaternion.Euler(0, -_lastYawBase * YAW_SCALE, 0) *
// 1. current rotation
tsf.localRotation;
_lastYawBase = yawBase;
}
I need to shoot a ball from any height and make it bounce on a target position defined by the user. The angle of launch is also given. I've tried a couple of solutions so far:
Vector3 calcBallisticVelocityVector(Vector3 source, Vector3 target, float angle) {
Vector3 direction = target - source;
float h = direction.y;
direction.y = 0;
float distance = direction.magnitude;
float a = angle * Mathf.Deg2Rad;
direction.y = distance * Mathf.Tan(a);
distance += h/Mathf.Tan(a);
// calculate velocity
float velocity = Mathf.Sqrt(distance * Physics.gravity.magnitude / Mathf.Sin(2*a));
return velocity * direction.normalized;
}
Vector3 calcBallisticVelocityVector2(Vector3 source, Vector3 target, float angle) {
float distance = (target.Planar() - source.Planar()).magnitude;
float a = target.y - source.y - distance;
float halfGravity = -Physics.gravity.magnitude * 0.5f;
float distanceSquared = distance * distance;
float theta = Mathf.Deg2Rad * angle;
float cosSquared = Mathf.Cos(theta) * Mathf.Cos(theta);
float b = distanceSquared / cosSquared;
float speed = Mathf.Sqrt((halfGravity * b) / a);
Vector3 velocity = (target.Planar() - source.Planar()).normalized * Mathf.Cos(theta);
velocity.y = Mathf.Sin(theta);
return velocity * speed;
}
The results I'm getting is that even the ball does go into the direction is expected, it falls earlier than it should be so the speed calculated by these methods seems to be lower than what is actually required to hit the target position.
Rigidbody's mass is set to 1, Gravity is (0, -98, 0), rigid body's drag and angular drag is set to 0. What other variables could be affecting this behavior?
EDIT: One thing I forgot to mention is that I'm setting the resulting vector as rigid body's velocity, so I'm not using via the apply force method.
I adapted code gotten from here: https://answers.unity.com/questions/1131176/projectile-motion.html and now I'm getting the results I was expecting. I can always hit the target position at whatever angle I input.
private Vector3 calcBallisticVelocityVector(Vector3 initialPos, Vector3 finalPos, float angle)
{
var toPos = initialPos - finalPos;
var h = toPos.y;
toPos.y = 0;
var r = toPos.magnitude;
var g = -Physics.gravity.y;
var a = Mathf.Deg2Rad * angle;
var vI = Mathf.Sqrt (((Mathf.Pow (r, 2f) * g)) / (r * Mathf.Sin (2f * a) + 2f * h * Mathf.Pow (Mathf.Cos (a), 2f)));
Vector3 velocity = (finalPos.Planar() - initialPos.Planar()).normalized * Mathf.Cos(a);
velocity.y = Mathf.Sin(a);
return velocity * vI;
}
I am working on adding a helicopter to my 2d game and I need it to move in circular motion whilst moving on the x axis as well. Below you can find the code that I am using which uses the mathematical circle equation.
angle += speed * Time.deltaTime; //if you want to switch direction, use -= instead of +=
float x = startPoint.x + Mathf.Cos(angle) * radius;
float y = startPoint.y + Mathf.Sin(angle) * radius;
transform.position = new Vector2(x + 2, y);
The helicopter is rotating correctly but I can't figure out how I can make it move along the x axis. Concept image of how it should work below:
1) Make an empty game object
2) Parent your box to the empty game object
3) rotate the box around the empty game object
4) move the empty game object to the side
If you want to avoid adding an empty parent, you can keep track of the center of rotation separately, rotate around it, and move it over time.
public class hello_rotate : MonoBehaviour
{
float angle = 0;
float radius = 1;
float speed = 10;
float linear_speed = 1;
Vector2 centerOfRotation;
// Start is called before the first frame update
void Start()
{
centerOfRotation = transform.position;
}
// Update is called once per frame
void Update()
{
centerOfRotation.x = centerOfRotation.x + linear_speed * Time.deltaTime;
angle += speed * Time.deltaTime; //if you want to switch direction, use -= instead of +=
float x = centerOfRotation.x + Mathf.Cos(angle) * radius;
float y = centerOfRotation.y + Mathf.Sin(angle) * radius;
transform.position = new Vector2(x + 2, y);
}
}
I want to lerp between two rotations with different velocities on three different axis (yaw/pitch/roll) in unity3d, and tried to achieve that with Quaternion.LookRotation().
Quaternion.LookRotation() takes a direction Vector as first parameter, so i thought that i could lerp the direction first and then look at it with a lerped up-vector.
It should be no problem with Vector3.lerp(), but in this case i need to lerp the direction with different velocities on two axis (X and Y) relative to the initial direction.
So for example i have a camera facing a target, then the target moves up and right a bit, and now i want the camera to tilt slowly to the right too, but a bit faster up to the targets position (keeping its own position).
How to lerp the direction vector with different speeds on both axis to use it in Quaternion.LookRotation()?
EDIT:
Changed the title from "Lerp between Vector3 with different velocities on X/Y" to "Quaternion lerp with different velocities for yaw/pitch/roll" and modified the question to match the topic.
Thanks to minorlogic and the CjLib, i tried the following:
public Quaternion QuaternionLerpOn3Axis(
Quaternion rot1,
Quaternion rot2,
Vector3 lerpSpeed
) {
if (rot1 != rot2) {
float lerpSpeedPitch = lerpSpeed.x * Time.deltaTime;
float lerpSpeedYaw = lerpSpeed.y * Time.deltaTime;
float lerpSpeedRoll = lerpSpeed.z * Time.deltaTime;
// Lerp up direction
Vector3 vecUp = Vector3.Slerp(
rot1 * Vector3.up,
rot2 * Vector3.up,
lerpSpeedRoll
);
// Get new rotation with lerped yaw/pitch
Quaternion rotation = QuaternionUtil.Sterp(
rot1,
rot2,
rot1 * Vector3.right,
lerpSpeedYaw,
lerpSpeedPitch,
QuaternionUtil.SterpMode.Slerp
);
// Look at new direction and return rotation
return Quaternion.LookRotation(
rotation * rot1 * Vector3.forward,
vecUp
);
} else {
return rot1;
}
}
To try this without downloading CjLib, here is the whole code including the relevant parts for decoding the swing/twist:
public Quaternion QuaternionLerpOn3Axis(
Quaternion rot1,
Quaternion rot2,
Vector3 lerpSpeed
) {
if (rot1 != rot2) {
float lerpSpeedPitch = lerpSpeed.x * Time.deltaTime;
float lerpSpeedYaw = lerpSpeed.y * Time.deltaTime;
float lerpSpeedRoll = lerpSpeed.z * Time.deltaTime;
// Lerp up direction
Vector3 vecUp = Vector3.Slerp(
rot1 * Vector3.up,
rot2 * Vector3.up,
lerpSpeedRoll
);
// Get difference between two rotations
Quaternion q = rot2 * Quaternion.Inverse(rot1);
// Decompose quaternion into two axis
Quaternion rotYaw;
Quaternion rotPitch;
DecomposeSwingTwist(
q,
rot1 * Vector3.right,
out rotYaw,
out rotPitch
);
// Lerp yaw & pitch
rotYaw = Quaternion.Slerp(Quaternion.identity, rotYaw, lerpSpeedYaw);
rotPitch = Quaternion.Slerp(Quaternion.identity, rotPitch, lerpSpeedPitch);
// Look at new direction and return rotation
return Quaternion.LookRotation(
rotPitch * rotYaw * rot1 * Vector3.forward,
vecUp
);
} else {
return rot1;
}
}
public static void DecomposeSwingTwist(
Quaternion q,
Vector3 twistAxis,
out Quaternion swing,
out Quaternion twist
) {
Vector3 r = new Vector3(q.x, q.y, q.z); // (rotation axis) * cos(angle / 2)
float Epsilon = 1.0e-16f;
// Singularity: rotation by 180 degree
if (r.sqrMagnitude < Epsilon) {
Vector3 rotatedTwistAxis = q * twistAxis;
Vector3 swingAxis = Vector3.Cross(twistAxis, rotatedTwistAxis);
if (swingAxis.sqrMagnitude > Epsilon) {
float swingAngle = Vector3.Angle(twistAxis, rotatedTwistAxis);
swing = Quaternion.AngleAxis(swingAngle, swingAxis);
} else {
// More singularity: rotation axis parallel to twist axis
swing = Quaternion.identity; // no swing
}
// Always twist 180 degree on singularity
twist = Quaternion.AngleAxis(180.0f, twistAxis);
return;
}
// Formula & proof:
// http://www.euclideanspace.com/maths/geometry/rotations/for/decomposition/
Vector3 p = Vector3.Project(r, twistAxis);
twist = new Quaternion(p.x, p.y, p.z, q.w);
twist = Normalize(twist);
swing = q * Quaternion.Inverse(twist);
}
public static Quaternion Normalize(Quaternion q) {
float magInv = 1.0f / Magnitude(q);
return new Quaternion(magInv * q.x, magInv * q.y, magInv * q.z, magInv * q.w);
}
public static float Magnitude(Quaternion q) {
return Mathf.Sqrt(q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w);
}
By now this is the only way i could achieve a quaternion (s)lerp with different velocities on three different axis with a reasonably acceptable result.
But in my opinion it is not a real mathematical solution, it does not work really well if the lerp values are below ~1.5f (especially the Z/Roll-axis), and it has much overhead.
Any ideas how to solve this puzzle with less/better code?
...another approach:
Now i tried to extend the concept of decomposing the swing/twist to decomposing yaw/pitch/roll.
This works fine (?) if the target does not flip over 180°, and it still needs some input/feedback from someone who really knows how to deal with quaternion rotations.
public Quaternion QuaternionLerpYawPitchRoll(
Quaternion rot1,
Quaternion rot2,
Vector3 lerpSpeed
) {
if (rot1 != rot2) {
float lerpSpeedPitch = lerpSpeed.x * Time.deltaTime;
float lerpSpeedYaw = lerpSpeed.y * Time.deltaTime;
float lerpSpeedRoll = lerpSpeed.z * Time.deltaTime;
// Decompose quaternion into yaw/pitch/roll
Quaternion rotYaw;
Quaternion rotPitch;
Quaternion rotRoll;
DecomposeYawPitchRoll(rot1, rot2, out rotYaw, out rotPitch, out rotRoll);
// Lerp swing & twist
rotYaw = Quaternion.Slerp(Quaternion.identity, rotYaw, lerpSpeedYaw);
rotPitch = Quaternion.Slerp(Quaternion.identity, rotPitch, lerpSpeedPitch);
rotRoll = Quaternion.Slerp(Quaternion.identity, rotRoll, lerpSpeedRoll);
// Combine yaw/pitch/roll with current rotation
return Quaternion.LookRotation(
rotPitch * rotYaw * rot1 * Vector3.forward,
rotRoll * rot1 * Vector3.up
);
} else {
return rot1;
}
}
public static void DecomposeYawPitchRoll(
Quaternion rot1,
Quaternion rot2,
out Quaternion yaw,
out Quaternion pitch,
out Quaternion roll
) {
Vector3 pitchAxis = rot1 * Vector3.right;
Vector3 rollAxis = rot1 * Vector3.forward;
Vector3 yawAxis = rot1 * Vector3.up;
// Get difference between two rotations
Quaternion diffQ = rot2 * Quaternion.Inverse(rot1);
Vector3 r = new Vector3(diffQ.x, diffQ.y, diffQ.z); // (rotation axis) * cos(angle / 2)
float Epsilon = 1.0e-16f;
// Singularity: rotation by 180 degree
if (r.sqrMagnitude < Epsilon) {
Vector3 rotatedPitchAxis = diffQ * pitchAxis;
Vector3 rotatedYawAxis = Vector3.Cross(pitchAxis, rotatedPitchAxis);
Vector3 rotatedRollAxis = diffQ * rollAxis;
if (rotatedYawAxis.sqrMagnitude > Epsilon) {
float yawAngle = Vector3.Angle(pitchAxis, rotatedPitchAxis);
yaw = Quaternion.AngleAxis(yawAngle, rotatedYawAxis);
} else {
// More singularity: yaw axis parallel to pitch axis
yaw = Quaternion.identity; // No yaw
}
if (rotatedRollAxis.sqrMagnitude > Epsilon) {
float rollAngle = Vector3.Angle(yawAxis, rotatedYawAxis);
roll = Quaternion.AngleAxis(rollAngle, rotatedRollAxis);
} else {
// More singularity: roll axis parallel to yaw axis
roll = Quaternion.identity; // No roll
}
// Always twist 180 degree on singularity
pitch = Quaternion.AngleAxis(180.0f, pitchAxis);
} else {
// Formula & proof:
// http://www.euclideanspace.com/maths/geometry/rotations/for/decomposition/
pitch = GetProjectedRotation(diffQ, pitchAxis);
roll = GetProjectedRotation(diffQ, rollAxis);
yaw = diffQ * Quaternion.Inverse(pitch);
}
}
public static Quaternion GetProjectedRotation(Quaternion rotation, Vector3 direction) {
Vector3 r = new Vector3(rotation.x, rotation.y, rotation.z);
Vector3 proj = Vector3.Project(r, direction);
rotation = new Quaternion(proj.x, proj.y, proj.z, rotation.w);
return Normalize(rotation);
}
public static Quaternion Normalize(Quaternion q) {
float magInv = 1.0f / Magnitude(q);
return new Quaternion(magInv * q.x, magInv * q.y, magInv * q.z, magInv * q.w);
}
public static float Magnitude(Quaternion q) {
return Mathf.Sqrt(q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w);
}
Author of CjLib here.
It sounds like you actually don't need swing-twist decomposition.
I'd say just get the decomposed yaw/pitch/row for the current quaternion and desired quaternion. And then update the yaw/pitch/row values depending on how fast you want them to individually track the target value, and generate an updated quaternion from that set of yaw/pitch/row values.
Lerping with a maximum speed cap (which I refer to as "seeking") might be fine, but it would not look smooth. I recommend using critically-damped numeric springing. And here's a shameless placement of a 3-part series I wrote on this topic.