Radian LookUp Table

[Halsafar]

When working with quaternions/vectors/matrices/rotation of you require alot cos(angle)/sin(angle).

Now, it seems best to work in radians all the time and try to keep your numbers in radians; avoid converting into degree's.

Right now I have a lookup table which looks like this:
//----------------
//Generate Vector Circles
//----------------
void Camera::GenerateVectorCircle()
{
float Theta=0;
float Pi = 3.14159265358979f;
float ToRad = Pi / 180;

for (int i = 0;i < 360;i++)
{
Theta = i * ToRad;
m_VectorCircle[i].u = cosf(Theta);
m_VectorCircle[i].v = sinf(Theta);
}
}


This table seems to work fine but I'm sure it can't be 100% accurate unless...
Here is my question: between 0 --> 2pi (thus 0 --> 360)...Is there the same number of value's between 0 --> 2pi and 0 --> 360?

From a glance, obviously not.
So I must create a look up table to eliminate the use of sin and cos on a regular basis, but the look up table must have contain values for any angle in rads.

Is this possible? Between 0 and 2pi there are probably a quaddrillion values I would have to record for cos and sin on each angle.

So is accuracy lost if I just use that lookup table above and ALWAYS work in degree's?

Maybe this post is pointless.

[Halsafar]

The amount variable isa in degree.
Problem is..i convert it to rads the divide it by 2 then sin/cos it.
Because it is being divided by 2 means i cant use degree lookup table or i'll loose accuracy.
20 / 2 = 10...works
21 / 2 = 10.5 which could end up as 10 or 11
// Convert the angle degrees into radians.
float angle = GET_RADIANS(amount);

float sine = (float)sin(angle / 2.0f);

// Create the quaternion.
x = xAxis * sine;
y = yAxis * sine;
z = zAxis * sine;
w = (float)cos(angle / 2.0f);

[kebo]

I don't get it. Is this a trick question?
There are the same number of angles between 0 and 360 as there are between 0 and 2Pi. No matter what units you are working in (degrees/rads) you will still get increments of 1 degree based on how you are making your table. If you want better accuracy, you need to double the array size and

for (int i = 0;i < 720;i++)
{
Theta = i * ToRad * 0.5f;
m_VectorCircle[i].u = cosf(Theta);
m_VectorCircle[i].v = sinf(Theta);
}
}
just be sure to work with floats and becareful that (floatX/floatY) * floatY may not equal floatX
HTH kevin

[Halsafar]

I want to get sin and cos functions out of this function by using a lookup table.

Do you see the problem yet?

//-------------------
//Rotatef -- Thanks to Allen Sherrod for the idea/guideline
//-------------------
void Quaternion::Rotatef(float amount, float xAxis, float yAxis, float zAxis)
{
// Convert the angle degrees into radians.
float angle = DEGTORAD(amount);

// Call this once for optimization, just like using the if statement to determine if
// we should normalize.
float sine = sinf(angle / 2.0f);

// Create the quaternion.
x = xAxis * sine;
y = yAxis * sine;
z = zAxis * sine;
w = cosf(angle / 2.0f);

// Normalize the quaternion.
float length = 1 / (float)sqrt(x * x + y * y + z * z + w * w);
x *= length;
y *= length;
z *= length;
}

[kebo]

Do you see the problem yet?

no sorry

[Halsafar]

You can't have an array which takes floats. There is no such thing as VectorCircle[2.453564];

[kebo]

o, why didn't you say that to begin with You will obviously need to round the argument first. Then you need to decide whether you want 1 degree of accuracy or 1/2 degree or whatever. You then need to construct your array accordingly. If you want one degree accuracy then you array needs 360 points, if 1/2 degree accuracy, 720 points, etc. Then you need to adjust the argument to the function
kevin

[Halsafar]

Yah i guess thats all I can do eh.

Well thanks for your idea.

[NoteMe]

Just remember to not make it tooo big, then you will get to many cash misses, and it will be even slower then the sin function...

[Pixelgamer]

maybe you could make it like, when you want to look up radian [2.453564] you can defins VectorCircle as [2453564] or something? and then divide it with 1 000 000? Or would that make it a toooo big array (well I suppose you don't need so many decimals?)

[Halsafar]

This is a great idea and in fact may work to an extent.
Although, VectorCircle at the least has to be a struct of 2 floats, u and v to store the cos and sin values.
So its size in bytes would be at least 8...maybe 12 if you wrap it up in a class.

An array 2453564 big would be:
2,453,564 * 8 = 19,628,512 bytes = 19mb of ram zapped

Trimming it down to less decimal points would sure help.

Truly the problem I have is that I CANNOT run any trig functions in the main game loop...they are WAY to slow.
So I gotta compile a lookup table. I now loose the extreme precision of radians because I gotta go Pi * Angle/180 -- then the decimal point is cut off because it is stored in an int...
So I simply do a few things in degree's because of this.

[wossname]

Why not just wrap an array in a function and pass a float to that and do some internal processing.

Also: Default properties of classes can take floats as arguments (as well as anything else in fact.

[Halsafar]

Yes but:
Vector *m_VectorCircle
m_VectorCirlce = new Vector[360]
m_VectorCircle[2.56] <<-- error. You HAVE to use integers when diving through arrays. You can probably bitshift or increment the points by a float...but that probably won't do you any good.
delete [] m_VectorCircle

[opus]

Maybe I'm a bit easy minded, but:

I use only degrees in my prog.
I figured a lookup-table for every tenth of a degree gives enough accuracy.

So I use something like:
Create a LookUptable(array) for Sin(0 ...3599) and Cos(0 ..3599). The conversion from Rad is done in there.
Make a Function that takes degree as input and gives the Sinus/Cosinus as output. This Function uses the lookuptable and takes care of the multiplication from 1/10 degree to 1 degree.

So I only use a Sinus or Cosinus Function in my program that take degree as input!

[Halsafar]

Thats pretty what I'm doing but now I only get a 0-360 range of movement.
Its not a bad idea.
I suppose.


Also to clarify with my last post.
I believe you overload the [] operator in a class with a float.

[opus]

Sorry forgot to mention, when calling the sinus or Cosinus function, I take degree as input, but I only use it as an integer! In my application (where I'm using 1/10 degree resolution) I do something like

Sinus=SinusFromLookTableUpValue (Int(Degree*10))

the SinusFromLookupTable holds Values for each 1/10 degree.
That way I do not overload!!

[Halsafar]

Thats very intelligent.

Thanks for all the replies.

[opus]

Thats very intelligent.

I wish my math-teachers would have said that, back then..........

[A320-Daniel]

Hi folks,

how can I archieve the same result with asin,acos, atan and atan2 functions?
I have to use them quite a lot, of course those functions are quite slow...

Due to the fact VB6 doesn't have for example the atan2 function I look in the web for an alternative and found something with asin and acos.

Any ideas?

Thanks in advance!

Daniel

[opus]

We could use such LookUp tables since our input-values (the degrees) were equally distributed, so we could use them as the array-counter in the table.
In your case it would be more complicated.
If you use an equally distributed counter for the asin ( between -1 and 1 for example 400 values), your accuracy would not be the same for all output values.

I would use a lookup-table for sin and use it reverse, look thru all values in the table, the desired result is the indexof the closest value.
But I don't know if that would be faster than calculation!

[A320-Daniel]

Okay, I'll try that out. Thanks for your help! Really appreciated!!

Daniel