There are many magical properties in matrix computation, such as:

AB != BA
A != 0, B != 0, but maybe AB = 0.
AB = AC, A != 0, but we can’t get that B = C.

People couldn’t understand why it was so different from ordinary numerical calculations when it was born. It was like a rebellious child who occasionally slipped out of his father’s control and did something that surprised everyone. For example, the physicist Heisenberg’s matrix mechanics and his uncertainty principle, Diff = AB – BA != 0.

In fact, the matrix computation can be associated with path planning and graphical transformations in the real world.

For example, Rotate an object around the Z axis, Rotate(Angle, zDir0, zDir1, zDir2), it can be represented as a matrix.

Move the item along a vector , Move(vec0, vec1, vec2), can also be presented as a matrix:

    \[\begin{pmatrix} 1 & 0 & 0 & vec0 \\ 0 & 1 & 0 & vec1 \\ 0 & 0 & 1 & vec2 \\ 0 & 0 & 0 & 1 \end{pmatrix}\]

Similarly, Scale(fac0, fac1, fac2) is:

    \[\begin{pmatrix} fac0 & 0 & 0 & 0 \\ 0 & fac1 & 0 & 0 \\ 0 & 0 & fac2 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}\]

We add the module linear transform tester in 3d Model Edtior. Users can input simple commands to control the linear transformation of the model and observe the matrix in real time.

Simple commands, for example:
Translate the object along vector (2, 4, 6) ~ M(2, 4, 6)
Rotate the object 45 degrees about the Z axis ~ R(45, 0, 0, 1)
Scale the object in the X direction by 2 ~ S(2, 1, 1)
Specify the transformation matrix directly ~

    \[\begin{matrix} a & b & c & 0 \\ b & c & a & 1 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}\]

Demo video:

Service address: 3d Model Edtior


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[…] For more information on how to use the web app 3D Model Editor to do linear transformation, you can refer to the post 3D Model Editor – Linear Transform Tester. […]

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