Processing 1.0 - Processing Discourse - 3D Rotation around an arbitrary axxis

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Index › Programming Questions & Help › Syntax Questions › 3D Rotation around an arbitrary axxis

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3D Rotation around an arbitrary axxis (Read 2960 times)

leds

3D Rotation around an arbitrary axxis
Dec 4^th, 2008, 11:48am

Hello,

i want to rotate an object around a point into the position of another object in 3d.
the angle i´m calculating, is the angleBetween the two normals of the two facing faces.

So, now i have the angle and i have an arbitrary axxis arround my object should rotate. But which technique/class i can use, to rotate my object?

I used to script in mel, and this is the way how i would make it there (e.g. rot command..). Or should i think in processing in a totally different way/concept?
I would be very pleased, if somebody could help me..

PVector v1 = new PVector(10, 20, 30);
PVector v2 = new PVector(60, 80, 33);

//calculate the angle between
float a = PVector.angleBetween(v1, v2);

//rotation around the axxis:
PVector v3 = v1.cross(v2);

//but how to rotate a vector around an arbitrary axxis?

JohnG

Re: 3D Rotation around an arbitrary axxis
Reply #1 - Dec 4^th, 2008, 12:09pm

Here's some code I wrote to rotate a point (v) around an arbitrary axis(passing through the origin) by a given angle:

This doesn't use processing's new PVector class, but should give you the steps you need. nx/ny/nz are normalised values of the x/y/z values.

Vector rotate(Vector v, Vector _axis,float ang)
{
Vector axis=new Vector(_axis.nx(),_axis.ny(),_axis.nz());
Vector vnorm=new Vector(v.nx(),v.ny(),v.nz());
float _parallel=Dot(axis,v);
Vector parallel=multiply(axis,_parallel);
Vector perp=subtract(parallel,v);
Vector Cross=cross(v,axis);
Vector result=add(parallel,add(multiply(Cross,sin(-ang)),multiply(perp,cos(-ang))));
return result;
}

leds

Re: 3D Rotation around an arbitrary axxis
Reply #2 - Dec 4^th, 2008, 12:32pm

ok, thank you very much. Now i understand, how to rotate one point around any axis.

But in my case, i already know the resulting vector and i want to rotate an object with the calculated angle around the calc. axis. so i need some code/techique how to transfer angle+axis in x,y,z rotation for the object..
Is this possible? Where i can look how?
..and thank you for answering..

esperanc

Re: 3D Rotation around an arbitrary axxis
Reply #3 - Mar 28^th, 2009, 9:50am

I think you would probably need a function similar to the one below.
I got the math from the OpenGL "red book". It's a shame the processing guys didn't include it in the set of transformation functions.
Code:


// Applies a general rotation of r radians around axis x,y,z 
void rotate (float r, float x, float y, float z) {
  float d = sqrt(x*x+y*y+z*z);
  float a = x/d, b = y/d, c = z/d;
  float t[][]={{a*a,a*b,a*c},{b*a,b*b,b*c},{c*a,c*b,c*c}};
  float s[][]={{0,-c,b},{c,0,-a},{-b,a,0}};
  float cosr=cos(r);
  float sinr=sin(r);
  float m[][]={{1,0,0},{0,1,0},{0,0,1}};
  for (int i=0; i<3; i++)
     for (int j=0; j<3; j++)
	  m[i][j] = t[i][j] + cosr*(m[i][j]-t[i][j])+sinr*s[i][j];
  applyMatrix (m[0][0],m[0][1],m[0][2],0,
		   m[1][0],m[1][1],m[1][2],0,
		   m[2][0],m[2][1],m[2][2],0,
		   0,0,0,1);
}

Cheers,

--Claudio

gll

Re: 3D Rotation around an arbitrary axxis
Reply #4 - Oct 26^th, 2009, 2:18am

I think it is there: http://dev.processing.org/source/index.cgi/trunk/processing/core/src/processing/core/PMatrix3D.java?rev=4997&view=markup
Code:

  public void rotate(float angle, float v0, float v1, float v2) {
    // TODO should make sure this vector is normalized

    float c = cos(angle);
    float s = sin(angle);
    float t = 1.0f - c;

    apply((t*v0*v0) + c, (t*v0*v1) - (s*v2), (t*v0*v2) + (s*v1), 0,
	(t*v0*v1) + (s*v2), (t*v1*v1) + c, (t*v1*v2) - (s*v0), 0,
	(t*v0*v2) - (s*v1), (t*v1*v2) + (s*v0), (t*v2*v2) + c, 0,
	 0, 0, 0, 1);
  }

I think it's undocumented because rotate(Float) is already used for 2D XY rotations. rotate(Float,FloatFloat,Float) should work everywhere, it's in the PGraphics.

LaBelle / ANAR.ch / LaBelle.spaceKIT.ca

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