Transformation matrices

[Sijan92]

Is there any easy way to find the transformation matrices rather than memorizing them or by finding the inverse?

 

[Zishi]

Is there any easy way to find the transformation matrices rather than memorizing them or by finding the inverse?

I don't think so. :geek:

 

[M.Usman Khan]

well there is an easier way...but it requires time to do it compared to learning them by heart....

its difficult to explain to ...i vill try explaing it when i get time....

 

[Zishi]

well there is an easier way...but it requires time to do it compared to learning them by heart....

its difficult to explain to ...i vill try explaing it when i get time....

That easier way is only the 'indirect way'. =/

 

[M.Usman Khan]

well there is an easier way...but it requires time to do it compared to learning them by heart....

its difficult to explain to ...i vill try explaing it when i get time....

That easier way is only the 'indirect way'. =/

Actually no.....if by the indirect way u mean taking inverse and trying to go backwards then absolutly no....

the way i m talking about requires concept of transformation(by concept i mean u most know all the formulas e.g.
shear factor=image distance to object/distance of object to invariant line)

 

[M.Usman Khan]

ok heres how u do it... :idea:

first make a small grid(graph grid with x and y axis...make it rough no need 2 b neat)
remember the identity matrix.




take the 1st row 2 b x-coordinates
take 2nd row 2 b y-cordinates

the first column of the identity matrix gives u the point A(1 0)..plot iton the small grid
2nd column gives the point B(0 1)..plot it 2

apply ur required transformation on these two points....make a new matrix with ur images

A` (the image of A) x-coordinate will become the 1row first column....y-coordinate 2nd row 1column
simalary, B` ....x-coordinate will go to the 1st row 2nd coloumn ....y - cordinate will do to 2nd row 2nd column

the new matrix will b ur required transformation matrix...

 

[umer khan]

ok heres how u do it... :idea:

first make a small grid(graph grid with x and y axis...make it rough no need 2 b neat)
remember the identity matrix.




take the 1st row 2 b x-coordinates
take 2nd row 2 b y-cordinates

the first column of the identity matrix gives u the point A(1 0)..plot iton the small grid
2nd column gives the point B(0 1)..plot it 2

apply ur required transformation on these two points....make a new matrix with ur images

A` (the image of A) x-coordinate will become the 1row first column....y-coordinate 2nd row 1column
simalary, B` ....x-coordinate will go to the 1st row 2nd coloumn ....y - cordinate will do to 2nd row 2nd column

the new matrix will b ur required transformation matrix...

ABSOLUTELY CORRECT thats hw i did it in my O levels paper :lol:

 

[Zishi]

ok heres how u do it... :idea:

first make a small grid(graph grid with x and y axis...make it rough no need 2 b neat)
remember the identity matrix.




take the 1st row 2 b x-coordinates
take 2nd row 2 b y-cordinates

the first column of the identity matrix gives u the point A(1 0)..plot iton the small grid
2nd column gives the point B(0 1)..plot it 2

apply ur required transformation on these two points....make a new matrix with ur images

A` (the image of A) x-coordinate will become the 1row first column....y-coordinate 2nd row 1column
simalary, B` ....x-coordinate will go to the 1st row 2nd coloumn ....y - cordinate will do to 2nd row 2nd column

the new matrix will b ur required transformation matrix...

That's what I was talking about! It is also an indirect way.

 

[M.Usman Khan]

ok heres how u do it... :idea:

first make a small grid(graph grid with x and y axis...make it rough no need 2 b neat)
remember the identity matrix.




take the 1st row 2 b x-coordinates
take 2nd row 2 b y-cordinates

the first column of the identity matrix gives u the point A(1 0)..plot iton the small grid
2nd column gives the point B(0 1)..plot it 2

apply ur required transformation on these two points....make a new matrix with ur images

A` (the image of A) x-coordinate will become the 1row first column....y-coordinate 2nd row 1column
simalary, B` ....x-coordinate will go to the 1st row 2nd coloumn ....y - cordinate will do to 2nd row 2nd column

the new matrix will b ur required transformation matrix...

That's what I was talking about! It is also an indirect way.

its not the INDIRECT WAY ....its the direct way....
thats how the transformation matrices r actually formed...

 

[hammadthepcgeek]

Well there is, as I learned lately. The matrices used to drive me mad and I was always confused about them. The trick applies however to only reflection and rotation from origin matrices. Now to craft the matrices, you need to keep in mind TWO points: (1.0) (1 on the x-axis) and (0,1) (1 on the y -axis). Now remember that you would always consider the X axis 1 first. Suppose there is a reflection in x axis. Now the (1,0) point would remain there, since it is actually on the reflection line and is thus an invariant point. The (0,1) point would however be reflected to (0,-1). Now arrange the results of the reflection. Always keep the X Axis 1 the first!!! Remember this. Now the matrix would be:

(1 0)
(0 -1)
Now I think you can work out the rest.

 

[FLRNAB]

Mnemonics