Hi all,

i try to rotate a vector using another vector
as the axis by a certain amount a.

both vectors are warped, so i cant use one
of those well-known matrices ... and i am
doing this with GLSL.

i found that i can rotate a vector using a
rotation matrix, created with

mat3 rotation( vector1 , cross(vector1,vector2) , vector2 )

and rotate my new vector using

vec3 new = old * rotation;

this will rotate around cross(vector1,vector2)
but ... where is the amount of my rotation?
is this the angle between vector1 and vector2?


thank you all for any hint,
hendrik

Hendrik Wendler wrote:
> 
> 
> Hi all,
> 
> i try to rotate a vector using another vector
> as the axis by a certain amount a.
> 

1. Make a transformation matrix using the axis vector
    x,y,z = axis vector
    angle = rotation angle in radians


GLfloat Mat[16];

// set identity matrix
memset(Mat, 0, sizeof(GLfloat) * 16);
Mat[0]  = 1;
Mat[5]  = 1;
Mat[10] = 1;
Mat[15] = 1;

float c = cos(angle);
float s = sin(angle);
float u = 1 - c;

Mat[0]  = (x * x * u) + c;
Mat[4]  = (y * x * u) - (z * s);
Mat[8]  = (z * x * u) + (y * s);

Mat[1]  = (x * y * u) + (z * s);
Mat[5]  = (y * y * u) + c;
Mat[9]  = (z * y * u) - (x * s);

Mat[2]  = (x * z * u) - (y * s);
Mat[6]  = (y * z * u) + (x * s);
Mat[10] = (z * z * u) + c;

2. Apply the matrix to the rotation vector
    rx,ry,rz = rotating vector
    dx,dy,dz = result vector

dx = (Mat[0] * rx) + (Mat[1] * ry) + (Mat[2] * rz);
dy = (Mat[4] * rx) + (Mat[5] * ry) + (Mat[6] * rz);
dz = (Mat[8] * rx) + (Mat[9] * ry) + (Mat[10] * rz);

Once you have build the rotation matrix, you can
rotate as many vectors as you want.

Hope that helps!
Best regards, Martin

hey thank you, martin!


i converted this to GLSL:

	float satangle = sat * 6.282;
	float csat = cos(satangle);
	float ssat = sin(satangle);
	float usat = 1.0 - chue;

	mat3 rotmat;
	rotmat[0][0] = satvec.x*satvec.x*usat + csat;			//	Mat[0]  = (x * x * 
u) + c;
	rotmat[1][0] = satvec.y*satvec.x*usat - (satvec.z*ssat);//	Mat[4]  = (y 
* x * u) - (z * s);
	rotmat[2][0] = satvec.z*satvec.x*usat + (satvec.y*ssat);//	Mat[8]  = (z 
* x * u) + (y * s);

	rotmat[0][1] = satvec.x*satvec.y*usat + (satvec.z*ssat);//	Mat[1]  = (x 
* y * u) + (z * s);
	rotmat[1][1] = satvec.y*satvec.y*usat + csat;			//	Mat[5]  = (y * y * 
u) + c;
	rotmat[2][1] = satvec.z*satvec.y*usat - (satvec.x*ssat);//	Mat[9]  = (z 
* y * u) - (x * s);

	rotmat[0][2] = satvec.x*satvec.z*usat - (satvec.y*ssat);//	Mat[2]  = (x 
* z * u) - (y * s);
	rotmat[1][2] = satvec.x*satvec.z*usat - (satvec.y*ssat);//	Mat[6]  = (y 
* z * u) + (x * s);
	rotmat[2][2] = satvec.z*satvec.z*usat + csat;			//	Mat[10] = (z * z * 
u) + c;
	col.xyz *=  rotmat;


All the best,
hendrik





Martin Steen schrieb:
> Hendrik Wendler wrote:
> 
>>
>>
>> Hi all,
>>
>> i try to rotate a vector using another vector
>> as the axis by a certain amount a.
>>
> 
> 1. Make a transformation matrix using the axis vector
>    x,y,z = axis vector
>    angle = rotation angle in radians
> 
> 
> GLfloat Mat[16];
> 
> // set identity matrix
> memset(Mat, 0, sizeof(GLfloat) * 16);
> Mat[0]  = 1;
> Mat[5]  = 1;
> Mat[10] = 1;
> Mat[15] = 1;
> 
> float c = cos(angle);
> float s = sin(angle);
> float u = 1 - c;
> 
> Mat[0]  = (x * x * u) + c;
> Mat[4]  = (y * x * u) - (z * s);
> Mat[8]  = (z * x * u) + (y * s);
> 
> Mat[1]  = (x * y * u) + (z * s);
> Mat[5]  = (y * y * u) + c;
> Mat[9]  = (z * y * u) - (x * s);
> 
> Mat[2]  = (x * z * u) - (y * s);
> Mat[6]  = (y * z * u) + (x * s);
> Mat[10] = (z * z * u) + c;
> 
> 2. Apply the matrix to the rotation vector
>    rx,ry,rz = rotating vector
>    dx,dy,dz = result vector
> 
> dx = (Mat[0] * rx) + (Mat[1] * ry) + (Mat[2] * rz);
> dy = (Mat[4] * rx) + (Mat[5] * ry) + (Mat[6] * rz);
> dz = (Mat[8] * rx) + (Mat[9] * ry) + (Mat[10] * rz);
> 
> Once you have build the rotation matrix, you can
> rotate as many vectors as you want.
> 
> Hope that helps!
> Best regards, Martin