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Problems with buoyancy and multiple Gertsner-waves. Waves created using Shadergraph and equations recreated in code to try and simulate floatation

Quick summation:
I am attempting to create an ocean comprised of planes that can be easily loaded and unloaded based on distance. On this ocean I want a boat to sail with a player onboard in the first person, where I want them to experience the buoyancy of their boat relative to the surrounding waves.
I am new to shadergraph and have been following several tutorials to try and create the desired effect.
These tutorials include
Catlikecoding's Wave shader
https://catlikecoding.com/unity/tutorials/flow/waves/
Zicore's Gertsner wave
https://www.youtube.com/watch?v=Awd1hRpLSoI&ab_channel=Zicore
Tom Weiland's dynamic water physics
https://www.youtube.com/watch?v=eL_zHQEju8s&ab_channel=TomWeiland
These resources have gotten me a good chunk of the way there, but I've run into some issues regarding the boat physics specifically.
I understand the math behind simulating Gertsner waves, and have tried to set up a WaveManager that calculates the y-value of a "floater" at position (x,z).
Floater.cs
public Rigidbody rigidBody;
public float depthBeforeSubmerged = 1f;
public float displacementAmount = 3f;
public int floaterCount = 1;
public float waterDrag = 0.99f;
public float waterAngularDrag = 0.5f;
private void FixedUpdate()
{
rigidBody.AddForceAtPosition(Physics.gravity / floaterCount, transform.position, ForceMode.Acceleration);
float waveHeight = WaveManager.instance.GetWaveHeight(transform.position.x,transform.position.z);
if(transform.position.y < waveHeight)
{
float displacementMultiplier = Mathf.Clamp01((waveHeight-transform.position.y) / depthBeforeSubmerged) * displacementAmount;
rigidBody.AddForceAtPosition(new Vector3(0f, Mathf.Abs(Physics.gravity.y) * displacementMultiplier, 0f),transform.position, ForceMode.Acceleration);
rigidBody.AddForce(displacementMultiplier * -rigidBody.velocity * waterDrag * Time.fixedDeltaTime, ForceMode.VelocityChange);
rigidBody.AddTorque(displacementMultiplier * -rigidBody.angularVelocity * waterAngularDrag * Time.fixedDeltaTime, ForceMode.VelocityChange);
}
}
This is pretty much lifted directly from Tom Weiland's video. Basically, when my floatpoint dips below the calculated wave, it applies force to make it travel upwards. Following his instructions carefully yielded decent results, but the problem arose when I started using Shadergraph to create my ocean.
The main issue is I wanted the waves to be tileable across multiple planes, so I used the object position and transformed it to world position to do calculations, and then added it back to the object position before manipulating the vertices of the ocean plane.
I've tried to show it below here:
This makes the ocean plane tileable and looks great, but also enlarges it in the scene quite a bit. I've put a regular plane on top to show the difference. Both are 1x1 units in the inspector.
So this is the first problem. The calculations I do in my WaveManager aren't lining up properly with the actual visual representation of the waves.
The second problem is that I can't seem to make the calculations done in WaveManager give me the correct y-coordinates.
In the shader, the waves are animated using the Time-component.
I've found the documentation to be a bit sparse on Shadergraph components, probably because I'm self taught and have a hard time wrapping my head around some of these concepts.
I've had a hard time working out how to calculate the change in y-coordinates over time in the wavemanager-script. The different solutions I've tried have just made the y-coordinate slowly grow larger into the negative range. I just have no idea how to make my calculations match up with the ones done on the GPU.
It's no important that it be super accurate, just good enough to sell the effect with small waves.
The Wavemanager code, finally.
private void Start()
{
waveLengthA = waves.GetFloat("_WaveLengthA");
waveLengthB = waves.GetFloat("_WaveLengthB");
waveLengthC = waves.GetFloat("_WaveLengthC");
waveLengthD = waves.GetFloat("_WaveLengthD");
steepnessA = waves.GetFloat("_SteepnessA");
steepnessB = waves.GetFloat("_SteepnessB");
steepnessC = waves.GetFloat("_SteepnessC");
steepnessD = waves.GetFloat("_SteepnessD");
directionA = waves.GetVector("_DirectionA");
directionB = waves.GetVector("_DirectionB");
directionC = waves.GetVector("_DirectionC");
directionD = waves.GetVector("_DirectionD");
kA = (2 * Mathf.PI) / waveLengthA;
kB = (2 * Mathf.PI) / waveLengthB;
kC = (2 * Mathf.PI) / waveLengthC;
kD = (2 * Mathf.PI) / waveLengthD;
cA = Mathf.Sqrt(Mathf.Abs(Physics.gravity.y)/ kA);
cB = Mathf.Sqrt(Mathf.Abs(Physics.gravity.y) / kB);
cC = Mathf.Sqrt(Mathf.Abs(Physics.gravity.y) / kC);
cD = Mathf.Sqrt(Mathf.Abs(Physics.gravity.y) / kD);
}
private void Update()
{
offset += Time.deltaTime;
}
public float GetWaveHeight(float x,float z)
{
fA = kA*(directionA.x * x + directionA.y * z - cA * offset);
fB = kB * (directionB.x * x + directionB.y * z - cB * offset);
fC = kC * (directionC.x * x + directionC.y * z - cC * offset);
fD = kD * (directionD.x * x + directionD.y * z - cD * offset);
position += new Vector3(x + directionA.x * steepnessA / kA * Mathf.Cos(fA),steepnessA/kA*Mathf.Sin(fA),z+directionA.y*steepnessA/kA*Mathf.Cos(fA));
position += new Vector3(x + directionB.x * steepnessB / kB * Mathf.Cos(fB),steepnessB/kB*Mathf.Sin(fB),z+directionB.y*steepnessB/kB*Mathf.Cos(fB));
position += new Vector3(x + directionC.x * steepnessC / kC * Mathf.Cos(fC),steepnessC/kC*Mathf.Sin(fC),z+directionC.y*steepnessC/kC*Mathf.Cos(fC));
position += new Vector3(x + directionD.x * steepnessD / kD * Mathf.Cos(fD),steepnessC/kD*Mathf.Sin(fD),z+directionD.y*steepnessD/kD*Mathf.Cos(fD));
return position.y;
}
The code above is quite ugly with a lot of repetition, but my plan is to make a constructor at some point to make it easier to read.
I grab all the values used in my shader, to make sure they match even if I change the look of the waves. Then I do the calculations from Catlikecoding and plot in the x- and z-coordinates of my floating object.
As far as I can understand, it should work if I just combine alle the calculated vectors, but obviously I'm missing something.
From what I've seen others do, they often opt to create custom planes with more vertices, that can cover their entire gameworld and avoid the problem, but I'm making a larger world and am worried about performance. (Though I don't know if I should be even.) I really like the fact that my ocean planes are tileable.
Does anyone here know of any solutions or help me solve the issue of worldspace vs objectspace, or how to accurately recreate the time-progression as seen in the shader?
Any help would be much appreciated.

So, for anyone struggling with this, I found the answer.
When combining multiple waves together, the manipulated plane grows in size for every wave added.
In my above question, I had somehow messed up the formulas for calculating the waves. I redid them and got the correct result.
Now, the trick is to simply divide the resultant wave, by the number of waves that you are combining. This will make sure that the actual size of the plane won't change.
You of course need to do this in your waveManager code as well. It's important to keep in mind that you only need the y-coordinate, so you only have to calculate that. For each wave, calculate the y-coordinate and then divide the combined height by the number of waves. This will make the floatation code work as it should!
Hope this helps someone out there who struggled like me.

How can I ensure that an object using a cosine equation to determine speed meets its lowest valley at the same time it hits a waypoint?

I'm working on a game for game jam and part of it is to make platforms that move smoothly. They slow down at the ends of their movement before turning around. The platforms simply move side to side or up and down between two waypoints(which are just empty transforms). I have code that uses cosine to determine the speed which works well except it doesn't align with the waypoints, the platforms tend to slow and change direction before ever reaching the waypoints. I need a way to use the distance between the waypoints as a variable in determining how the cosine equation changes speed so that the platforms slow and reverse direction exactly at the waypoints.
Here is what I have so far:
void Side_to_side()
{
if (waypointIndex < horWaypoints.Length)
{
platformSpeed = (1f * (float)Mathf.Cos(2f * (float)Mathf.PI * 1f * totalTime));
Vector3 targetPosition = horWaypoints[waypointIndex].position;
float delta = platformSpeed * Time.deltaTime;
transform.position = Vector2.MoveTowards(transform.position, targetPosition, delta);
if (transform.position.x == targetPosition.x && transform.position.y == targetPosition.y)
{
if (waypointIndex + 1 == horWaypoints.Length)
waypointIndex = 0;
else
waypointIndex++;
}
}
else
{
waypointIndex = 0;
}
//Translate platform back and forth between two waypoints
}
As I have said this code moves the platforms in the motions i want but they don't use the waypoints as turn around points. I understand I could do away with the waypoints and just calculate how far I would like each platform to go before turning around individually but that would take time to do it for each platform whereas I'd like to quickly put down waypoint pairs for them to use and the script calculates what the perfect values would be to match the waypoint locations.

If I understand you correctly you want to move an object forth and back between exactly two positions and apply some smoothing to the movement.
I would rather use a combination of Vector2.Lerp with a Mathf.PingPong as factor and you can then apply ease in and out using additionally Mathf.SmoothStep.
This could look like e.g.
public Transform startPoint;
public Transform endPoint;
// Desired duration in seconds to go exactly one loop startPoint -> endPoint -> startPoint
public float duration = 1f;
private void Update ()
{
// This will move forth and back between 0 and 1 within "duration" seconds
var factor = Mathf.PingPong(Time.time / (2f * duration), 1f);
// This adds additional ease-in and -out near to 0 and 1
factor = Mathf.SmoothStep(0, 1, factor);
// This interpolates between the given positions according to the given factor
transform.position = Vector2.Lerp(startPoint, endPoint, factor);
}
you could of course still use cosine if necessary, basically any function that returns a value between 0 and 1. You just have to use the correct multiplier in order to achieve the desired duration in seconds.
Note: Typed on the phone and not 100% sure on the math but I hope the idea gets clear

Capture position and rotation of an object relative to another object

I have two identical objects and two cameras. What I'd like to achieve is the following:
1) Capture the position and rotation of Cube A relative to Camera A
2) Transfer that to a Cube B, so that in Camera B (which I cannot move), Cube B looks exactly as Cube A looks in Camera A
I was successful doing that with position with the following code:
positionDifference = CubeA.InverseTransformPoint(CameraA.transform.position);
To transfer it onto Cube B, I do:
cubeBpos = transform.InverseTransformPoint(CubeB.transform.localPosition);
while ( Mathf.Abs (cubeBpos.x + positionDifference.x) > 0.01f ) {
if (cubeBpos.x + positionDifference.x > 0) {
CubeB.transform.position += new Vector3(-0.01f, 0, 0);
}
else if (cubeBpos.x + positionDifference.x < 0) {
CubeB.transform.position += new Vector3(+0.01f, 0, 0);
}
cubeBpos = transform.InverseTransformPoint(CubeB.transform.position);
}
That's clunky, but works. However, when I try to transfer rotations, Cube B starts to pivot around the origin. Interestingly, when I move Cube A in world coordinates, Cube B moves in local, and vice versa. I suspect local-to-world coordinate translation is an issue, but I also think my rotation code is naive. I tried to capture rotation in two ways, first like this:
rotationDifference = Quaternion.Inverse(CubeA.transform.rotation) * CameraA.transform.rotation;
CubeB.transform.rotation = Quaternion.Inverse(rotationDifference);
Second attempt:
rotationDifference = new Vector3(transform.eulerAngles.x, transform.eulerAngles.y, transform.eulerAngles.z);
CubeB.transform.eulerAngles = rotationDifference;
Both approaches resulted in weird rotational offsets. I tried using localPosition and localEulerAngles, didn't help.
I'm hoping there's a smarter way to do this :)
EDIT:
Here's a Dropbox link to the project

The problem is that you are treating position and rotation separately although they influence each other. Let's put both together and say we have model transforms for the two cameras and the two cubes (represented as homogeneous matrices; assuming column vectors). Then, we want to find the transform for cube B TCubeB, such that:
TCameraA^-1 * TCubeA = TCameraB^-1 * TCubeB
Note that TCamera is the model transform of the camera, not the view matrix. If you have the view matrix, simply leave the inverse away.
We can immediately solve for TCubeB:
TCameraB * TCameraA^-1 * TCubeA = TCubeB
I'm not too familiar with the Unity API but it seems like you cannot use transformation matrices directly. So let's split the transformation matrix T in a rotational part R and a translational part Tr:
TrCameraB * RCameraB * (TrCameraA * RCameraA)^-1 * TrCubeA * RCubeA = TrCubeB * RCubeB
TrCameraB * RCameraB * RCameraA^-1 * TrCameraA^-1 * TrCubeA * RCubeA = TrCubeB * RCubeB
If we care only about the rotation, we can calculate the respective quaternion by simply doing:
QCameraB * QCameraA^-1 * QCubeA = QCubeB
The translation becomes a bit more difficult. We need to find the translation transform, such that
TrCameraB * RCameraB * RCameraA^-1 * TrCameraA^-1 * TrCubeA * RCubeA * RCubeB^-1 = TrCubeB
To find the translation vector, simply multiply the origin to the left-hand side:
TrCameraB * RCameraB * RCameraA^-1 * TrCameraA^-1 * TrCubeA * RCubeA * RCubeB^-1 * (0, 0, 0, 1)
In pseudo-code, this boils down to (the matrices that appear stand for the respective translation vectors):
Vector4 translation = (0, 0, 0, 1)
translation += TrCubeA
translation -= TrCameraA
translation = RCameraA.Inverse().Transform(translation)
translation = RCameraB.Transform(translation)
translation += TrCameraB
Again, I barely know the Unity API and it might use some different conventions than I did (conventions in transformation math are especially tricky). But I am sure you can adapt the above derivations if something is not correct.

Nico's great answer solved my issue, but since code-formatting in the comment section wasn't built for this, here's the code that I wrote for Unity based on Nico's answer:
Vector3 translation = new Vector3(0,0,0);
translation += cubeA.transform.position;
translation -= cameraA.transform.position;
translation = cameraA.transform.InverseTransformPoint(translation);
translation = cameraB.transform.TransformPoint(translation/2);
cubeB.transform.position = translation;
Quaternion rotation = Quaternion.identity;
rotation = cameraB.transform.rotation * Quaternion.Inverse(cameraA.transform.rotation) * cubeA.transform.rotation;
cubeB.transform.rotation = rotation;
It's not one-to-one, but it achieves what I hoped: If Cube A is stationary and Camera A moves around it, then Cube B moves with respect to Camera B in such a way that Cube A and Cube B always have the exact same position and rotation in relation to their respective cameras.

Leap Motion Get Finger Bending (C#)

Hello I tried a lot diffrent ways to get bending angle in Leap Motion. But I couldn't get true values. I used this method for reading. Thanks in advance.
Bone bone1 = finger.Bone(Bone.BoneType.TYPE_INTERMEDIATE);
Bone bone2 = finger.Bone(Bone.BoneType.TYPE_PROXIMAL);
double angle = 180 - ((bone1.Direction.AngleTo(bone2.Direction) / Math.PI) * 180) * 2;

In this example I'll use array accessors as a quicker way of accessing bones from Finger objects.
For reference, bone indices are: 0 = metacarpal, 1 = proximal, 2 = intermediate, 3 = distal. You can validate this by looking at the definition of BoneType.
(Careful, the thumb has one fewer bone than the other fingers.)
Vector3 bone0Dir = finger.bones[0].Direction.ToVector3();
Vector3 bone1Dir = finger.bones[1].Direction.ToVector3();
float angle = Vector3.Angle(bone0Dir, bone1Dir);
This example retrieves the angle in degrees between the metacarpal bone and the proximal bone of the finger object.
Note that Vector3.Angle returns the unsigned angle between the two bones; if you desire a signed angle, you can use the SignedAngle function instead. You'll need to pass it a reference axis; Vector3.Cross(hand.PalmarAxis(), hand.DistalAxis()) would be suitable for this.
EDIT: Ah, apologies, the answer is a bit different if you're outside of the Unity engine. In that case, Leap.Vector.AngleTo is sufficient, but there's a simpler way to convert radians to degrees:
Vector bone0Dir = finger.bones[0].Direction;
Vector bone1Dir = finger.bones[1].Direction;
float angle = bone0Dir.AngleTo(bone1Dir) * Vector.RAD_TO_DEG;
Again, this will return the unsigned angle, but fingers don't usually bend backwards, so this should be sufficient for your use-case. You can also use Math.Asin((bone0Dir.Cross(bone1Dir).Magnitude)) * RAD_TO_DEG to get a (right-handed) signed angle.

Creating a jump function

I am trying to create a jump method in XNA, but I am facing a lot of problems, it doesn't work for me, I've been trying doing it for like 2 hours long and still no "luck". Can anybody give me a code sample, or at least a direction?
Note: I want the jump to be realistic, using gravity and such.
Thank you!
I erased all my work but here's the latest I tried, I know it shouldn't work for sure, but still..
public void Jump(GameTime gameTime)
{
float currentTime = (float)0.1;
if (position.Y == 200)
{
position.Y += velocity.Y*currentTime -gravity * (float)(Math.Pow(currentTime,2)) / 2;
}
if (position.Y == 200 + jumpHeight)
{
position.Y -= velocity.Y * currentTime - gravity * (float)(Math.Pow(currentTime, 2)) / 2;
}
}

I see that you've learned the equations of motion from your code (which I don't think was in place when I made my comment). However you're a little off, your issue is with your time variable. You're passing in your game time, but then using .1f for your time variable. What you really want for your time variable is the time since you started the jump. Further, position.Y is unlikely to ever be exactly equal to 200 or 200 + jumpHeight. It's a float (I assume), so you can never trust that it'll be a nice round number. If you want to specify an exact maximum jump height, you'll have to perform some equations before and set your velocity.Y accordingly (solve for when velocity equals 0 i.e. the top of your jump).
So, to fix your original code I think something like this will work, albeit totally untested:
public void Jump(GameTime gameTime)
{
if(jumping && position.Y > groundLevelAtPlayer) {
//Get the total time since the jump started
float currentTime = gameTime.totalTime - character.timeofjumpStart;
//gravity should be a negative number, so add it
position.Y += (velocity.Y * currentTime)
+ (gravity * ((float)(Math.Pow(currentTime, 2)) / 2));
}
else
{
jumping = false;
}
}

How exactly do you want to make your player jump? Since you mentioned realism I am assuming that you want your player to jump and move across both the X and Y axis, so that it will move along an arc(parabola if you will).
If that is what you are after, you will need to replicate projectile motion. This previous SO thread contains various methods in which you could implement such motion.
Edit:
You should be able to use the same equations presented. For vertical jumps, the angle will be 90 degrees, or pi/2 if you are working with radians. If you are pressing your direction keys, you will have to use the same equations. The angle at which you want your player to start the jump will have to be selected by yourself. Usually maximum range is obtained at an angle of 45 degrees (pi/4) assuming that the same force is used, so your option is really between 0 and 45 degrees.