Tranform a point another coordinate system

Hi,

I have a point matrix. How can I convert the definition of this point in one local coordinate system to another local coordinate system? I have 3 tranform matrices.

[William Rose]

@Furkan KORKMAZ,

Please provide more information. What are the three transform matrices you have? What transformations do they represent? Translate, rotate, perspective, etc?

A key question when you have multiple transformation matrices is the order in which to apply them. To answer that question, give a clear description, with words or equations or both, of how the coordinate systems are related.

[Furkan KORKMAZ]

Thank you William for your response.

Point_Sp, x1, x2 and x3 are my matrices. "Point_Sp" is explained in S1 (x1,y1) coordinate system. I want to transform "Point_Sp" firstly with x3 matrix, then with x1 matrix and finally transform to x2 matrix.

Point_Sp=[k1;k1*r;0,1];

Transform matrices:

x1=[[1,0,0,0];[0,1,0,-e];[0,0,1,0];[0,0,0,1]];

x2=[[cos(alfa2),sin(alfa2),0,0];[-sin(alfa2),cos(alfa2),0,0];[0,0,1,0];[0,0,0,1]];

x3=[[cos(alfa1),-sin(alfa1),0,0];[sin(alfa1),cos(alfa1),0,0];[0,0,1,0];[0,0,0,1]];

Answer 1

[William Rose]

@Furkan KORKMAZ,

Do you want a symbolic solution or a numerical solution?

If you want a numerical solution, then define the constants: k1, r, e, alfa1, alfa2, and then calculate

Sp2=x2*x1*x3*Sp;

If you want a symbolic solution, then define the variables symbolically:

syms k1 r e alfa1 alfa2
Sp=[k1;k1*r;0;1];

Transform matrices:

x1=[[1,0,0,0];[0,1,0,-e];[0,0,1,0];[0,0,0,1]];
x2=[[cos(alfa2),sin(alfa2),0,0];[-sin(alfa2),cos(alfa2),0,0];[0,0,1,0];[0,0,0,1]];
x3=[[cos(alfa1),-sin(alfa1),0,0];[sin(alfa1),cos(alfa1),0,0];[0,0,1,0];[0,0,0,1]];

Transform with x3, then x1, then x2:

Sp2=x2*x1*x3*Sp

Sp2 = 

[Furkan KORKMAZ]

Thank you, I need a numerical solution and this one is solved my problem. Thank you again.

[William Rose]

@Furkan KORKMAZ, you're welcome.