Converting from 2D coordinate Systems

In summary, 2D coordinate systems have two axes and are used to represent points on a flat surface, while 3D coordinate systems have three axes and are used to represent points in space. Converting between 2D coordinate systems is necessary for accurate data sharing between different software or applications. The most common 2D coordinate systems used in science are Cartesian, polar, and spherical coordinates. To convert between 2D coordinate systems, specific mathematical equations are needed. There are limitations and considerations when converting between 2D coordinate systems, such as compatibility, differences in units or scales, and possible loss of precision.
  • #1
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I am trying to get from one 2D coordinate system to another 2D coordinate system. I found 2 corresponding points and each system. I did the following:

[a1 a2 ] * [ x1,y1 ] = [u1,v1]
[a3 a4] [ x2,y2] [u2,v2]

or A*x = u

if I use MATLAB to solve A = u*inv(x)

when will A be a valid transformation matrix?
Are there other methods to find transformation matrices?
 
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  • #2
This is not a homework question, I'm just doing some image processing and just need some help.
 
  • #3


Converting from one 2D coordinate system to another can be done using a transformation matrix. In this case, you have correctly identified the two corresponding points in each system and used them to create a 2x2 matrix A. However, it is important to note that for A to be a valid transformation matrix, it must be invertible.

In order for A to be invertible, its determinant must be non-zero. So, to answer your question, A will be a valid transformation matrix when its determinant is non-zero. This is because a non-zero determinant ensures that the matrix is non-singular and can be inverted.

There are also other methods to find transformation matrices, such as using rotation, translation, and scaling operations. These methods involve using geometric principles and equations to determine the transformation matrix.

Additionally, if you are using MATLAB, you can also use the built-in functions for transformation matrices, such as 'affine2d' or 'maketform'. These functions allow you to specify the type of transformation you want and provide the necessary inputs to generate the transformation matrix.

In summary, to ensure that A is a valid transformation matrix, its determinant must be non-zero. Other methods, such as using geometric principles or built-in functions, can also be used to find transformation matrices.
 

1. What is the difference between 2D and 3D coordinate systems?

2D coordinate systems have two axes (x and y) and are used to represent points on a flat surface, while 3D coordinate systems have three axes (x, y, and z) and are used to represent points in space.

2. Why do we need to convert between 2D coordinate systems?

Converting between 2D coordinate systems is necessary when working with different software or applications that use different coordinate systems. It allows for data to be accurately shared and used in various programs.

3. What are the most common 2D coordinate systems used in science?

The most common 2D coordinate systems used in science are Cartesian coordinates, polar coordinates, and spherical coordinates. Each system has its own advantages and is used in different applications.

4. How do you convert between 2D coordinate systems?

To convert between 2D coordinate systems, you will need to use mathematical equations specific to the two coordinate systems you are converting between. These equations will involve converting values for x and y (or r and θ) to their corresponding values in the new coordinate system.

5. Are there any limitations or considerations when converting between 2D coordinate systems?

Yes, there are a few limitations and considerations when converting between 2D coordinate systems. These include ensuring that the two coordinate systems are compatible, understanding any differences in units or scales between the systems, and possible loss of precision during the conversion process.

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