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# Arctg table!

Started by asmcoder, Aug 03 2009 08:20 AM

19 replies to this topic

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#5
Members - Reputation: **100**

Posted 03 August 2009 - 09:36 AM

Quote:

Original post by alvaro

Do you mean a table with the tangent of each angle that is an integer number of degrees?

I mean the Arc tangent values for the selected angle entry, so ArcTg[0] will store the ArcTg value of angle 0, and ArcTg[359] will store the ArcTg value of angle 259.

See, I have a circle(x0,y0), a point in the circle(x,y).

What I want to do is to detrmine the angle with this formula:

Angle= ArcTg (y-y0/x-x0)

so with the lookup table I can simply do this to get the angle:

float Angle= ArcTgArray[(y-y0/x-x0)];

Thanks.

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#6
Crossbones+ - Reputation: **19059**

Posted 03 August 2009 - 09:50 AM

But that slope will not always be in [0,360]... You can't have a table that covers all the reals. You could have a table for values between 0 and 1 (in however many steps you want) and reduce all the other cases to this one. Could that be roughly what you want?

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#7
Crossbones+ - Reputation: **9041**

Posted 03 August 2009 - 10:12 AM

const int step = 361;

double arctan[step];

// Create a table that uses values from -1 to 1

for ( int i = 0; i < step; ++i )

arctan[i] = std::atan( (double)(i*2 - step) / (double)step );

// Then:

double angle = arctan[ std::min( step-1, std::max( 0, (int)( (test * step + step)/2 ) ) ) ];

You should be using

`atan2( y-y0, x-x0 )`anyways ...

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#8
Crossbones+ - Reputation: **19059**

Posted 03 August 2009 - 10:22 AM

If you don't have atan2, you can use something like this:

double atan2(double y, double x) {

double alpha=3.141592653589793238462643383279;

double gx=-1.0, gy=0.0, result=-alpha;

static double cosine_and_sine[32][2]={

{-1,0},

{0,1},

{0.70710678118654757274,0.70710678118654746172},

{0.92387953251128673848,0.38268343236508978178},

{0.98078528040323043058,0.19509032201612824808},

{0.99518472667219692873,0.098017140329560603629},

{0.99879545620517240501,0.049067674327418014935},

{0.99969881869620424997,0.024541228522912288124},

{0.99992470183914450299,0.012271538285719925387},

{0.99998117528260110909,0.0061358846491544752691},

{0.99999529380957619118,0.0030679567629659761432},

{0.99999882345170187925,0.0015339801862847655001},

{0.99999970586288222663,0.0007669903187427044855},

{0.99999992646571789212,0.00038349518757139556321},

{0.99999998161642933425,0.00019174759731070329153},

{0.99999999540410733356,9.5873799095977344669e-05},

{0.99999999885102686115,4.793689960306688131e-05},

{0.99999999971275665978,2.3968449808418219318e-05},

{0.99999999992818922046,1.1984224905069705298e-05},

{0.9999999999820472496,5.9921124526424275272e-06},

{0.9999999999955118124,2.9960562263346608352e-06},

{0.99999999999887800861,1.4980281131690111427e-06},

{0.99999999999971944664,7.490140565847157414e-07},

{0.9999999999999298339,3.7450702829238412872e-07},

{0.99999999999998245848,1.8725351414619534661e-07},

{0.99999999999999567013,9.3626757073098083589e-08},

{0.99999999999999888978,4.6813378536549088116e-08},

{0.99999999999999977796,2.3406689268274550676e-08},

{0.99999999999999988898,1.1703344634137276992e-08},

{1,5.8516723170686384961e-09},

{1,2.925836158534319248e-09},

{1,1.462918079267159624e-09}

};

for(int i=0;i<32;++i) {

double c=cosine_and_sine[i][0], s=cosine_and_sine[i][1];

double nx=gx*c-gy*s, ny=gy*c+gx*s;

if(x*ny<y*nx) {

result += alpha;

gx=nx;

gy=ny;

}

alpha*=.5;

}

return result;

}

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#9
Members - Reputation: **100**

Posted 03 August 2009 - 10:29 AM

**@alvaro:**I can have only 360 array's entry, and then check for the nearest array value to the value i got from calculating x-x0/y-y0.

**@_fastcall:**Could you please provide me with the output as you did in your first post? My environement compiler does not have a math library (no cos, sin... functions) and I cannot install other compilers.

Thanks.

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#10
Crossbones+ - Reputation: **9041**

Posted 03 August 2009 - 10:38 AM

Program:

The output:

Output.

You can use the binary interpreters that come with lua or python to generate your tables for you, as shown in my first post.

#include <iterator>

#include <fstream>

#include <iomanip>

#include <cmath>

int main()

{

const int step = 361;

double arctan[step];

// Note: Range is from -1 to 1 inclusive.

for ( int i = 0; i < step; ++i )

arctan[i] = std::atan( (double)(i*2 - step) / (double)(step-1) );

std::ofstream fs( "out.txt" );

fs.precision( 16 );

std::copy( arctan, arctan + step, std::ostream_iterator<double>( fs, " " ) );

fs.flush();

}

The output:

Output.

You can use the binary interpreters that come with lua or python to generate your tables for you, as shown in my first post.

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#11
Members - Reputation: **980**

Posted 03 August 2009 - 11:00 AM

1. Your use of the abbreviation "ArcTg" for "arctangent" is unusual. The standard abbreviation is "atan" or occasionally "arctan;" you will see either this or "tan

2. You say you have no math libraries? You can compute your table using the series expansion,

which I have taken from the Wikipedia article. Note that the return value is in radians.

[Edited by - Emergent on August 3, 2009 6:00:36 PM]

^{-1}" in math texts.2. You say you have no math libraries? You can compute your table using the series expansion,

which I have taken from the Wikipedia article. Note that the return value is in radians.

[Edited by - Emergent on August 3, 2009 6:00:36 PM]

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#12
Members - Reputation: **510**

Posted 03 August 2009 - 11:17 AM

What alvaro is saying is that you have tangent and arctangent mixed up. Arctangent takes in the ratio of sides on the triangle, which could be anything, and then returns the angle, which is between 0 and 360. It is regular tangent that takes the angle as input.

Tangent:[0,360]->[-inf,inf]

Arctangent:[-inf,inf]->[-90,90]

So it sounds like you want tangent(x) for x from 0 to 360, right?

Tangent:[0,360]->[-inf,inf]

Arctangent:[-inf,inf]->[-90,90]

So it sounds like you want tangent(x) for x from 0 to 360, right?

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#13
Members - Reputation: **100**

Posted 03 August 2009 - 12:31 PM

Quote:

Original post by Maze Master

What alvaro is saying is that you have tangent and arctangent mixed up. Arctangent takes in the ratio of sides on the triangle, which could be anything, and then returns the angle, which is between 0 and 360. It is regular tangent that takes the angle as input.

Tangent:[0,360]->[-inf,inf]

Arctangent:[-inf,inf]->[-90,90]

So it sounds like you want tangent(x) for x from 0 to 360, right?

Actually, I want something to

**return the angle**from the diference between

the point in the circle and the center of the circle. I believe this fromula applies in this case:

Angle= arctangen (PointY-CenterY/PointX-CenterX)

Cheers.

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#14
Crossbones+ - Reputation: **19059**

Posted 04 August 2009 - 01:42 AM

Quote:

Original post by asmcoder@alvaro:I can have only 360 array's entry, and then check for the nearest array value to the value i got from calculating x-x0/y-y0.

You mean you will search for the value in the table? Then you need a table of tangent, not arc-tangent, as we have been saying from the beginning.

Quote:

[...]My environement compiler does not have a math library (no cos, sin... functions) and I cannot install other compilers.

Can you use the code I posted above?

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#18
Crossbones+ - Reputation: **19059**

Posted 04 August 2009 - 12:38 PM

Quote:

Original post by asmcoder

I've done that using this formula: Degree=Radian*180/Pi

Btw, why don't you recommend getting degree answers?

1) It's a more natural choice. Dividing the circle in 360 degrees is a completely arbitrary decision, although it's a familiar one. The length of a circle measured in radii is 2*pi, so it would be natural to measure angles by specifying the length of the arc determined by the angle, measured in radii, and that's what radians are.

2) It makes derivatives simple. The derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x), if you measure angles in radians.

3) Libraries (except for OpenGL) and hardware use radians.

4) exp(i*x) = cos(x) + i*sin(x), as long as x is in radians (if this doesn't make sense, I won't try to explain it).

I've been meaning to write a little article advocating the use of the most natural representation in several types of variables. In short, it would say:

* Prefer vectors to angles.

* Prefer radians to degrees (if you have to use angles at all, which you probably don't).

* Start counting from 0.

* Use ranges of the form [x,y), which include the bottom element and don't include the top element.

* Use a 24-hour format for time, instead of am/pm.

* Use fractions, not percentages.

If you follow those simple pieces of advice, your code will have fewer special cases and many formulas will be simpler.

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#20
Members - Reputation: **202**

Posted 05 August 2009 - 01:47 AM

Quote:

I'm very interested on your article. Could you please point me a link to it?

Quote:

I've been meaning to writea little article advocating the use of the most natural representation in several types of variables. In short,it would say

;)