Finding a transformation matrix: map the unit cube to the displayed parallelogram

lgc1007

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Dec 12, 2023
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Screen Shot 2023-12-12 at 11.38.07 AM.png
Hi all, I'm struggling quite a lot with this problem. I can find the null space of a matrix, but I don't know where to start with finding the matrix that transforms the object on the left to the object on the right. From what I think, the unit cube (in R3) was mapped to the x-y plane (in R3) as z=0 for all the coordinates of the parallelogram.
The transformation matrix that maps/projects objects to the x-y plane is: Screen Shot 2023-12-12 at 11.47.48 AM.png but I think that the 1s in the matrix would be a & b (variables). Since the vertices aren't labeled, I'm finding it difficult to know which specific points of the unit cube correspond to specific points in the parallelogram. I tried having a=2 and b= 1/2 in the x-y projection matrix but it doesn't work for all points. I was wondering if anyone has suggestions on how I could approach this problem : )
 
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View attachment 36813
Hi all, I'm struggling quite a lot with this problem. I can find the null space of a matrix, but I don't know where to start with finding the matrix that transforms the object on the left to the object on the right. From what I think, the unit cube (in R3) was mapped to the x-y plane (in R3) as z=0 for all the coordinates of the parallelogram.
The transformation matrix that maps/projects objects to the x-y plane is: View attachment 36814 but I think that the 1s in the matrix would be a & b (variables). Since the vertices aren't labeled, I'm finding it difficult to know which specific points of the unit cube correspond to specific points in the parallelogram. I tried having a=2 and b= 1/2 in the x-y projection matrix but it doesn't work for all points. I was wondering if anyone has suggestions on how I could approach this problem : )
I'd probably start with your projection (into a square on the xy-plane), and then find a second transformation from that to the parallelogram. Then multiply the matrices.
 
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