I'm using expression2 to program behavior in Garry's mod. Expression2 (archive link)
Okay so, to set the precedent. In Gmod I have a block and I am at a complete loss of how to get it to rotate around the 3 up, down and right vectors (Which are local. ie; if I pitch it 45 degrees the forward vector is 0.707, 0.707, 0). Essentially, From the 3 vectors I'd like to be able to get local Pitch/Roll/Yaw. By Local Pitch Roll Yaw I mean that they are completely independent of one another allowing true 3d rotation. So for example; if I place my craft so its nose is parallel to the floor the X,Y,Z would be 0,0,0. If I turn it parallel to the floor (World and Local Yaw) 90 degrees it's now 0, 0, 90. If I then pitch it (World Roll, Local Pitch) it 180 degrees it's now 180, 0, 90. I've already explored quaternions however I don't believe I should post my code here as I think I was re-inventing the wheel.
I know I didn't explain that well but I believe the problem is pretty generic. Any help anyone could offer is greatly appreciated.
Oh, I'd like to avoid gimblelock too.
Essentially calculating the rotation around each of the crafts up/forward/right vectors using the up/forward/right vectors.
To simply the question a generic implementation rather than one specific to Gmod is absolutely fine.
I'm not sure what the application you are looking forward to implementing, however, in this sort of situation, I would usually suggest applying angular force. Would that be sufficient for your needs in this regard?
Well if that is all that you need, then i have managed to perfect the angular force equation to having entities point at a given position.
EntityVector = Entity:massCenter()
Leverage = sqrt( ( Entity:inertia():length()^2 ) / 3 )
LookPos = EntityVector - Target:pos()
A = ang(
toDeg( atanr( LookPos:z() , sqrt( LookPos:x()^2 + LookPos:y()^2) ) ) ,
toDeg( atanr( -LookPos:y(), -LookPos:x() ) ) ,
0 )
EntityAngle = ( ( Entity:angles() - angnorm(A) ) * 5 + Entity:angVel() ) * 5
Entity:applyAngForce( -EntityAngle * Leverage )
This set of equations has helped me through countless projects
Related
I hope this is the right place to ask this question.
I have a curve that I'd like to fit, but I don't know exactly what kind of fitting would be appropriate.
The curve is the following:
y is converging towards 1 when x grows to infinity.
I tried something like f : x -> 1-k*exp(-l*x) but the result is far from convincing.
I have no clue where to start here, anyone has an idea?
Here are the data used to build the above figure. it takes me 1.5 minutes to compute one point of my function.
x = [0.04, 0.08, 0.12, 0.16, 0.2 , 0.24, 0.28, 0.32, 0.36, 0.4 ]
y = [0.71368682, 0.79734766, 0.83832184, 0.86394632, 0.8818312 ,
0.89515722, 0.90553446, 0.91387899, 0.92075551, 0.92653329]
Thanks a lot!
What make you assume that " y is converging towards 1 when x grows to infinity" ?
This doesn't match to the data. Or the data is in a too small range far from large x. Or the kind of function thay you choose might be not convenient.
For example assuming another exponential function :
Using the regression method shown pages 16-17 in : https://fr.scribd.com/doc/14674814/Regressions-et-equations-integrales the numerical calculus and result is :
If the limit at x infinit is definitively 1 you should look for another kind of function. Without clue from the origin of data one have to proceed by trial and error.
I am coming back since I am having this geometric problem that I am not familiar with on Unity.
For a f-zero style game, I have a collider box (white on the screen captures) which is the origin of my raycast, and is bound to the movement of the vehicle.
In the shown code, this is this.collider. I control its rotation via a traditional applymatrix and there is no problem.
Then, on top of that, I have the rendered body of the vehicle in this.meshes. It inherits the rotation of the collider box, but gets some extra rotation on its vertical axis to give a visual sliding dynamic during the hard turns.
It is separate from the collider to keep the vector.forward of the movement (and the raycast) not affected by the extra-rotation. This is purely visual.
My question is: what is the best way to implement it?
I tried different things, but, basically, if I copy the position and rotation of the collider, no problem. As soon as I try to add some extra rotation = this.driftRotation, my body flips when rotation.y value is less than -math.pi. I can adjust the value of the rotation by incrementing Math.PI (like in Unity), but it doesn't work here.
No clean solution found with applyMatrix neither, and not a lot of google answers on "vertical rotation flip mesh"... though I'm pretty sure this pissue is common.
Some code:
this.meshes.position.set(
this.collider.position.x,
this.collider.position.y,
this.collider.position.z);
this.meshes.rotation.x = this.collider.rotation.x;
this.meshes.rotation.y = this.collider.rotation.y + this.driftRotation;
this.meshes.rotation.z = this.collider.rotation.z;
Enclosed more explicit pictures:
Thank you
Marquizzo, that's precisely the point: the 3rd px follows the 2nd one, so I'm still turning right but rotation suddenly flips (again, when rotation.y reaches -PI).
Anyway, I fixed it by not trying to directly change rotation.y value, but playing with matrix. Just takes time to understand what does what.
For those who may face a similar pb, here is my temp solution, until I find sthing more performant:
this.meshes.matrix.identity();
if (Math.abs(driftAmount) > 0)
{
this.driftAxis.copy(this.driftDirection);
this.driftValue = js.Utils.lerp(this.driftValue, Math.sign(driftAmount) * 0.4, 0.05);
this.meshes.matrix.makeRotationAxis(this.driftAxis, this.driftValue);
}
else if (Math.abs(this.driftValue) > 0)
{
this.driftAxis.copy(this.driftDirection);
this.driftValue = js.Utils.lerp(this.driftValue, 0, 0.1);
if (Math.abs(this.driftValue) < 0.001)
{
this.driftValue = 0;
}
this.meshes.matrix.makeRotationAxis(this.driftAxis, this.driftValue);
}
this.meshes.applyMatrix(this.collider.matrix);
I had to add a driftAxis along a driftDrection, which is my axis for my vertical rotation.
For ref. I think this subject is +/- bound to the issue I had:
https://github.com/mrdoob/three.js/issues/1460
Now I have another issue, how to add another rotation to this.meshes on another axis, the forward one, for a rolling effect, because if I just add another makeRotationAxis in this code it just skips the first one. But that sounds less difficult to figure out, there must exist the equivalent of combineMatrix something...
I'm using the blender game engine and python I made a script that makes an empty follow my cursor in 3D space. (I use the keyboard for height for now).
Now I wanted to implement a LookAt function for a general object rather than a camera, using python. I want the object to look exactly at the point I'm hovering (the empty position) at the screen. For now I'm using a cube so basically one face of the cube should always face the empty.
So, I thought of using matrices or quaternions but the problem is that All I have is a direction vector and I chose the x axis for the local look direction. So either way I need to calculate the euler angles and convert them to axis-rotation angles. (theta*[axis^]).
The resources I have in the Blender Game Engine is: mathutils (provide quarternions, euler based rotations (via axis-angles), matrices) - though it doesn't have any updated documentation which is just annyoingly horrible! I have to print help to get some sort of info!
Now I've been able to make the object look at the empty when I rotate only the Z axis. I used a little trick that handles the angle sign for me using simple trigonometry, so sign is handled and I don't need any matrix trickery or quarternions. The problem begins when I try to rotate once again - I want to rotate the Y axis for the up-down look (as known in 3D we need two sorts of rotations to face someone, the third is just for rotating the view upside-down - "rolling the camrea") since this rotation axis is the look direction vector.
Here's my script:
import bge
from mathutils import Vector, Matrix
import math
# Basic stuff
cont = bge.logic.getCurrentController()
own = cont.owner
scene = bge.logic.getCurrentScene()
c = scene.objects["Cube"]
e = scene.objects["Empty"]
# axises (we're using localOrientation)
x = Vector((1.0,0.0,0.0))
y = Vector((0.0,1.0,0.0))
z = Vector((0.0,0.0,1.0))
vec = Vector(e.worldPosition - c.worldPosition) # direction vector
# Converting direction vector into euler angles
# Using trigonometry we get: tan(psi) = cos(phi2)/cos(phi1)
# Where phi1 is the angle between x axises (euler angle)
# and phi2 is the euler of the y axises.
# psi is the z rotation angle.
# get cos(euler_angle)
phi1 = vec.dot(x)/vec.length # = cos p1
phi2 = vec.dot(y)/vec.length # = cos p2
phi3 = vec.dot(z)/vec.length # = cos p3
# get the rotation/steer angles
zAngle = math.atan(phi2/phi1)
yAngle = math.atan2(phi3,phi1)
xAngle = math.atan(phi2/phi3)
# use only 2 as the third must adapt (also: view concept - x is the looking direction, rotating it would make rolling)
r = c.localOrientation.to_euler()
r.z = zAngle
r.y = -yAngle
#r.x = xAngle
c.localOrientation = r
Seperately each axis works perfectly, but when combined, there are little jump glitches when I get through the global Y axis.
Also, it seems that the "local" orientation in blender is just the same as the "worldOrientation" which is also annoying cause I'm not sure anymore in what frame of reference I'm working anymore. If anyone knows, please help !
Edit 1:
Appearantely there's a built in logic block that handles this for me and when I press "3D" it tracks AND succeeds on rotating BOTH axises. Though, I still want to know what's the problem with my script! What did the 3D button do that I didn't?
Edit 2:
I tried stop making trigo tricks and found out that when I use local orientation I ALWAYS get a gimbal lock in one axis. That's probably what happened behind the scenes. Thanks for anyone interested, if you have any good trick I'd still be glad to hear =]!
I have a youtube tutorial on how to make the camera look at specific objects. It may help.
https://www.youtube.com/watch?v=hwbObDkiJrE
But the concept, when using the gui, is to open the object->relations panel and for the object you want to be doing the LookAt, you make it the child of the object you want it to follow (the parent). You then select 'Vertex' as the relationship. This will then affect the rotation angles of the child object only.
Try this,
bpy.data.objects['child'].parent = bpy.data.objects['parent']
bpy.data.objects['child'].parent_type = 'VERTEX'
and actually there is more info here
https://blender.stackexchange.com/questions/26108/how-do-i-parent-objects
I have a point that moves (in one dimension), and I need it to move smoothly. So I think that it's velocity has to be a continuous function and I need to control the acceleration and then calculate it's velocity and position.
The algorithm doesn't seem something obvious to me, but I guess this must be a common problem, I just can't find the solution.
Notes:
The final destination of the object may change while it's moving and the movement needs to be smooth anyway.
I guess that a naive implementation would produce bouncing, and I need to avoid that.
This is a perfect candidate for using a "critically damped spring".
Conceptually you attach the point to the target point with a spring, or piece of elastic. The spring is damped so that you get no 'bouncing'. You can control how fast the system reacts by changing a constant called the "SpringConstant". This is essentially how strong the piece of elastic is.
Basically you apply two forces to the position, then integrate this over time. The first force is that applied by the spring, Fs = SpringConstant * DistanceToTarget. The second is the damping force, Fd = -CurrentVelocity * 2 * sqrt( SpringConstant ).
The CurrentVelocity forms part of the state of the system, and can be initialised to zero.
In each step, you multiply the sum of these two forces by the time step. This gives you the change of the value of the CurrentVelocity. Multiply this by the time step again and it will give you the displacement.
We add this to the actual position of the point.
In C++ code:
float CriticallyDampedSpring( float a_Target,
float a_Current,
float & a_Velocity,
float a_TimeStep )
{
float currentToTarget = a_Target - a_Current;
float springForce = currentToTarget * SPRING_CONSTANT;
float dampingForce = -a_Velocity * 2 * sqrt( SPRING_CONSTANT );
float force = springForce + dampingForce;
a_Velocity += force * a_TimeStep;
float displacement = a_Velocity * a_TimeStep;
return a_Current + displacement;
}
In systems I was working with a value of around 5 was a good point to start experimenting with the value of the spring constant. Set it too high will result in too fast a reaction, and too low the point will react too slowly.
Note, you might be best to make a class that keeps the velocity state rather than have to pass it into the function over and over.
I hope this is helpful, good luck :)
EDIT: In case it's useful for others, it's easy to apply this to 2 or 3 dimensions. In this case you can just apply the CriticallyDampedSpring independently once for each dimension. Depending on the motion you want you might find it better to work in polar coordinates (for 2D), or spherical coordinates (for 3D).
I'd do something like Alex Deem's answer for trajectory planning, but with limits on force and velocity:
In pseudocode:
xtarget: target position
vtarget: target velocity*
x: object position
v: object velocity
dt: timestep
F = Ki * (xtarget-x) + Kp * (vtarget-v);
F = clipMagnitude(F, Fmax);
v = v + F * dt;
v = clipMagnitude(v, vmax);
x = x + v * dt;
clipMagnitude(y, ymax):
r = magnitude(y) / ymax
if (r <= 1)
return y;
else
return y * (1/r);
where Ki and Kp are tuning constants, Fmax and vmax are maximum force and velocity. This should work for 1-D, 2-D, or 3-D situations (magnitude(y) = abs(y) in 1-D, otherwise use vector magnitude).
It's not quite clear exactly what you're after, but I'm going to assume the following:
There is some maximum acceleration;
You want the object to have stopped moving when it reaches the destination;
Unlike velocity, you do not require acceleration to be continuous.
Let A be the maximum acceleration (by which I mean the acceleration is always between -A and A).
The equation you want is
v_f^2 = v_i^2 + 2 a d
where v_f = 0 is the final velocity, v_i is the initial (current) velocity, and d is the distance to the destination (when you switch from acceleration A to acceleration -A -- that is, from speeding up to slowing down; here I'm assuming d is positive).
Solving:
d = v_i^2 / (2A)
is the distance. (The negatives cancel).
If the current distance remaining is greater than d, speed up as quickly as possible. Otherwise, begin slowing down.
Let's say you update the object's position every t_step seconds. Then:
new_position = old_position + old_velocity * t_step + (1/2)a(t_step)^2
new_velocity = old_velocity + a * t_step.
If the destination is between new_position and old_position (i.e., the object reached its destination in between updates), simply set new_position = destination.
You need an easing formula, which you would call at a set interval, passing in the time elapsed, start point, end point and duration you want the animation to be.
Doing time-based calculations will account for slow clients and other random hiccups. Since it calculates on time elapsed vs. the time in which it has to compkete, it will account for slow intervals between calls when returning how far along your point should be in the animation.
The jquery.easing plugin has a ton of easing functions you can look at:
http://gsgd.co.uk/sandbox/jquery/easing/
I've found it best to pass in 0 and 1 as my start and end point, since it will return a floating point between the two, you can easily apply it to the real value you are modifying using multiplication.
i'm developing a game.
How can i "fade in" the audio volume for a sound, based on the "distance" of a sprite from the current render scene ?
Suppose i've a world:
WIDTH_WORLD = 10000
HEIGHT_WORLD = 10000
Current Scene
xCurrent = 800 ( + Width Res. = 800 + 1024 = 1824)
yCurrent = 400 ( + Height Res. = 400 + 768 =... )
Far Sprite
xSprite = 7000
ySprite = 3000
What is a good algorithm to "calculate" audio volume (and maybe left/right pan channel ratio) ?
Thanks in advance!
Total Volumn
There are several approaches for the attenuation of the volume. E.g. you could use a linear damping function, like volume = max( 0, max_volume - max_volume/max_distance * distance ), or a function with inverse distance fall off, like volume = min( max_volume, max_volume / distance ).
Balance Ratio
Again, there are several approaches to realize an adequate functionality. In your case, you could say, if the object is at or beyond the left screen border, pan to the left, if the object is at or beyond the right screen border, pan to the right, otherwise use an interpolation function, e.g. balance = (object_x-camera_x) / screen_half_width with values between -1: left, +1: right, and 0: center.
When combining these approaches you have to think about what is suitable for your case: For example only damp the volume if the object is out of screen bounds, what ever...
Use the distance (Dsquared = xdist^2 + ydist ^2) as a scaling factor to downscale your volume. Invert this distance squared value to apply directly to your volume (volume falls off as a square of distance, and distance is easily calculated as a squared value anyway).
Left / right channel ratio is done simply by defining two different points for the left and right channels (to the left and right, respectively, of your render location), perform the above calculation, and find the ratios of your channels that way. Because the above calculation is just a sum of two squares, it's very computationally simple.
Well, the volume of a sound degrades as the square of the distance from the sound source, so that would give you a good place to start.
Knowing what library you are using for your game would be helpful though - many game libraries will have this sort of functionality built in already.