I m having hard time to understand Quaternions and to use them in my engine for rotating object. I m looking for step by step explanation, actually a correction of my view of Quaternions.

Here is how I understand they work.

q = cos(40*) + sin(40)(i+j+k)

->what I understand is that i+j+k represents the axis of rotation. Basically if i = 1 that means we rotate object around X-axis.

Formula q * point * p-1, is what I dont quite understand. Lets for the sake say I understand why forumla goes like this. What I dont seems to get how would I apply this to my engine to rotate object.

What I tried is to create 3dVector with object position, example (0,0,-5). I would use quaternion that would rotate this vector around y axis, so q * ThisVector * q(conjugate), and then result I would put in translate matrix. But no work. I cant seem to find a way to implement them. I saw some articles on quaternion to matrices, But what do I put in that matrix, a result from qThisVectorq(conjugate) or it is just q that is transfromed in matrix?

EDIT What I want is to rotate object on Y-axis using quaternion. So far,because of lack of my understanding, I m failing to rotate. I created a class 3dVector ->three dimensional vector, and instantiate a new position (0,0,-5). This position I sent as translate matrix to opengl and multiplied with glPosition.

When I tried to rotate that object using quaternion. I just took that position (0,0,-5) and used it in formula q = q * p * q(conjugate). I manually calculated that but result I get didnt make object rotate on Y-axis around itself. Now I m not sure, but I think it actually rotated object but not around him self,he was moved to the right, so he was not in the same position anymore

I m having hard time to understand Quaternions and to use them in my engine for rotating object. I m looking for step by step explanation, actually a correction of my view of Quaternions.

Here is how I understand they work.

q = cos(40*) + sin(40)(i+j+k)

->what I understand is that i+j+k represents the axis of rotation. Basically if i = 1 that means we rotate object around X-axis.

Formula q * point * p-1, is what I dont quite understand. Lets for the sake say I understand why forumla goes like this. What I dont seems to get how would I apply this to my engine to rotate object.

What I tried is to create 3dVector with object position, example (0,0,-5). I would use quaternion that would rotate this vector around y axis, so q * ThisVector * q(conjugate), and then result I would put in translate matrix. But no work. I cant seem to find a way to implement them. I saw some articles on quaternion to matrices, But what do I put in that matrix, a result from qThisVectorq(conjugate) or it is just q that is transfromed in matrix?

EDIT What I want is to rotate object on Y-axis using quaternion. So far,because of lack of my understanding, I m failing to rotate. I created a class 3dVector ->three dimensional vector, and instantiate a new position (0,0,-5). This position I sent as translate matrix to opengl and multiplied with glPosition.

When I tried to rotate that object using quaternion. I just took that position (0,0,-5) and used it in formula q = q * p * q(conjugate). I manually calculated that but result I get didnt make object rotate on Y-axis around itself. Now I m not sure, but I think it actually rotated object but not around him self,he was moved to the right, so he was not in the same position anymore

EDIT_2:

I have cube that is on position [0,0,-5] and I want to rotate it around y-axis by some angle.

I tried to write code in python

poinToRotate = Quaternion(w=0,x=0,y=0,z=-5) angle =45 sinus = math.sin(math.radians(angle)); q=Quaternion( w=math.cos(math.radians(angle)), x=sinus*0, y=sinus*1, z=sinus*) newPoint = q.rotate(poinToRotate) 

Rotation is somewhere good but it cube does not rotate around it self but around some point. But when

 p = Quaternion(w=0,x=0,y=0,z=0) 

to make it to the center, result is all zeros.

I m having hard time to understand Quaternions and to use them in my engine for rotating object. I m looking for step by step explanation, actually a correction of my view of Quaternions.

Here is how I understand they work.

q = cos(40*) + sin(40)(i+j+k)

->what I understand is that i+j+k represents the axis of rotation. Basically if i = 1 that means we rotate object around X-axis.

Formula q * point * p-1, is what I dont quite understand. Lets for the sake say I understand why forumla goes like this. What I dont seems to get how would I apply this to my engine to rotate object.

What I tried is to create 3dVector with object position, example (0,0,-5). I would use quaternion that would rotate this vector around y axis, so q * ThisVector * q(conjugate), and then result I would put in translate matrix. But no work. I cant seem to find a way to implement them. I saw some articles on quaternion to matrices, But what do I put in that matrix, a result from qThisVectorq(conjugate) or it is just q that is transfromed in matrix?

I m having hard time to understand Quaternions and to use them in my engine for rotating object. I m looking for step by step explanation, actually a correction of my view of Quaternions.

Here is how I understand they work.

q = cos(40*) + sin(40)(i+j+k)

->what I understand is that i+j+k represents the axis of rotation. Basically if i = 1 that means we rotate object around X-axis.

Formula q * point * p-1, is what I dont quite understand. Lets for the sake say I understand why forumla goes like this. What I dont seems to get how would I apply this to my engine to rotate object.

What I tried is to create 3dVector with object position, example (0,0,-5). I would use quaternion that would rotate this vector around y axis, so q * ThisVector * q(conjugate), and then result I would put in translate matrix. But no work. I cant seem to find a way to implement them. I saw some articles on quaternion to matrices, But what do I put in that matrix, a result from qThisVectorq(conjugate) or it is just q that is transfromed in matrix?

EDIT What I want is to rotate object on Y-axis using quaternion. So far,because of lack of my understanding, I m failing to rotate. I created a class 3dVector ->three dimensional vector, and instantiate a new position (0,0,-5). This position I sent as translate matrix to opengl and multiplied with glPosition.

When I tried to rotate that object using quaternion. I just took that position (0,0,-5) and used it in formula q = q * p * q(conjugate). I manually calculated that but result I get didnt make object rotate on Y-axis around itself. Now I m not sure, but I think it actually rotated object but not around him self,he was moved to the right, so he was not in the same position anymore