Great intro to matrix node. Curious why rotation takes 6 (or 9) values whereas translation and scale take 3. I kind of see that it's the 3x3 matrix that represents the quaternion rotation, but how can the diagonal values be used for both rotation and scale? That's where I get confused. Or is it only 6 values used for rotation - not the whole 3x3 matrix (portion). Perhaps the scale and rotation need to be multiplied to fit both for using 1 matrix for rotation and scale. Sx⋅Rxx Sx⋅Rxy Sx⋅Rxz Sy⋅Ryx Sy⋅Ryy Sy⋅Ryz Sz⋅Rzx Sz⋅Rzy Sz⋅Rzz I'm not certain, but that might be what's needed to use both at the same time - but I may be way off. Otherwise, the 3 diagonal values would somehow have to be used for both rotation and scale. (if the rotation is defined by the 3x3 matrix - and not just 4 values (x,y,z,w) in that 3x3 matrix
Hello, It's a great question. You dive very deep. Sorry that I don't where to explain. I will try to explain by my learning process. The calculation rule of the matrix is the key to understand this. My method to comprehend that is to use a 4x4 matrix to multiply a 4x1 matrix(the position vector of the point is a 3x1 matrix, just add 1 in the fourth row to make it a 4x1 matrix). Then everything seems clear to me. When it comes to rotation, If one axis and angle are fixed (like the axis is (0,0,1)), we can figure out an equation about how to get the new position. Then reverse the calculation to get a 3x3 matrix which can be combined into a 4x4 matrix. I didn't calculate the equation thoroughly. I just comprehend the algorithm roughly. Hope I explained them well. If not, I suggest you find some Matrix tutorials of Houdini which are very detailed and much more powerful.
beautifull Zack, i hope you continue, nice to meet you. :)
@@nicolanarracci I appreciate your support. Thank you
Great intro to matrix node.
Curious why rotation takes 6 (or 9) values whereas translation and scale take 3.
I kind of see that it's the 3x3 matrix that represents the quaternion rotation, but how can the diagonal values be used for both rotation and scale? That's where I get confused.
Or is it only 6 values used for rotation - not the whole 3x3 matrix (portion).
Perhaps the scale and rotation need to be multiplied to fit both for using 1 matrix for rotation and scale.
Sx⋅Rxx Sx⋅Rxy Sx⋅Rxz
Sy⋅Ryx Sy⋅Ryy Sy⋅Ryz
Sz⋅Rzx Sz⋅Rzy Sz⋅Rzz
I'm not certain, but that might be what's needed to use both at the same time - but I may be way off.
Otherwise, the 3 diagonal values would somehow have to be used for both rotation and scale. (if the rotation is defined by the 3x3 matrix - and not just 4 values (x,y,z,w) in that 3x3 matrix
Hello, It's a great question. You dive very deep. Sorry that I don't where to explain. I will try to explain by my learning process.
The calculation rule of the matrix is the key to understand this. My method to comprehend that is to use a 4x4 matrix to multiply a 4x1 matrix(the position vector of the point is a 3x1 matrix, just add 1 in the fourth row to make it a 4x1 matrix). Then everything seems clear to me.
When it comes to rotation, If one axis and angle are fixed (like the axis is (0,0,1)), we can figure out an equation about how to get the new position. Then reverse the calculation to get a 3x3 matrix which can be combined into a 4x4 matrix.
I didn't calculate the equation thoroughly. I just comprehend the algorithm roughly.
Hope I explained them well. If not, I suggest you find some Matrix tutorials of Houdini which are very detailed and much more powerful.
@@zack-3d-animation - thanks
您好！我很想知道您是怎么给这些小方片上上不同的颜色的？
这是很简单的随机连接到渐变节点作为着色器颜色接入