Help chaining together 3D rotations
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I’m a 3D newbie and I used the AXECUBE example to get x and y rotations working independently, but I can’t figure out how to chain them together in axe syntax and I’m not sure what I’m doing wrong. If anybody could point me in the right direction or give me an example program with composite rotations it would be greatly appreciated.
Techno wrote:
I’m a 3D newbie and I used the AXECUBE example to get x and y rotations working independently, but I can’t figure out how to chain them together in axe syntax and I’m not sure what I’m doing wrong. If anybody could point me in the right direction or give me an example program with composite rotations it would be greatly appreciated.

What do you mean by "chain them together" exactly? do you mean applying the rotations to the model vertices? (P.S. if you could post example code with your questions so we know the context that would make it easier to diagnose and fix.)
Funny Math guy
Thanks for replying so quickly, the code below contains two independent rotations that were taken from the AXECUBE example, just in a form I found easier to read. I could only get them to work on their own. By "chain them together" I mean I want to be able to rotate the vertices of the cube in two axes at once, if that makes sense.

SourceCoder 3 (AXECUBE) wrote:
:.CUBE
:[F7F7F7F7F708]->GDB1
:[F7F7F7F708F7]
:[F7F7F708F7F7]
:[F70808F708F7]
:[F70808F7F708]
:[F70808080808]
:[08F70808F7F7]
:[08F708080808]
:[08F708F7F708]
:[0808F7080808]
:[0808F708F7F7]
:[0808F7F708F7]
:
:0->theta
:0->T
:DiagnosticOff
:Repeat getKey(15)
: theta+1->theta
: . T+1->T
: ClrDraw
: sin(theta)->S
: cos(theta)->C
: sin(theta)->M
: cos(theta)->N
:
: For(A,0,11)
: A*6+GDB1->B
:
: .X ROTATION
: sign{B+1)->G
: sign{B+2)->Z
: . y' = y * cos(angle) - z * sin(angle);
: G*N-(Z*M)->Y
: . z' = z * cos(angle) + y * sin(angle);
: Z*N+(G*M)->Z
: sign{B)*128->X
:
: sign{B+4)->G
: sign{B+5)->W
: . y' = y * cos(angle) - z * sin(angle);
: G*N-(W*M)->V
: . z' = z * cos(angle) + y * sin(angle);
: W*N+(G*M)->W
: sign{B+3)*128->U
:
: .Y ROTATION
: sign{B)->G
: sign{B+2)->Z
: . x' = x * cos(angle) + z * sin(angle);
: G*C+(Z*S)->X
: . z' = z * cos(angle) - x * sin(angle);
: Z*C-(G*S)->Z
: sign{B+1)*128->Y
:
: sign{B+3)->G
: sign{B+5)->W
: . x' = x * cos(angle) + z * sin(angle);
: G*C+(W*S)->U
: . z' = z * cos(angle) - x * sin(angle);
: W*C-(G*S)->W
: sign{B+4)*128->V
:
: Z+4500/64->Z
: W+4500/64->W
: Line(X//Z+48,Y//Z+32,U//W+48,V//W+32)
: End
: DispGraph
:End
Looks like you are using 2d rotations on 2 different axes.

You can do a 3d rotation: https://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions
I am using the 3D rotation equations for x:
y' = y * cos(angle) - z * sin(angle)
z' = z * cos(angle) + y * sin(angle)
x' = x
And for y:
x' = x * cos(angle) + z * sin(angle)
z' = z * cos(angle) - x * sin(angle)
y' = y
I think then to chain then together, you would actually need to do the Y rotation on the output of the X rotation. So when doing the Y rotation, instead of pulling G, Z, etc. from B, use the result of the X rotation's calculation for the input.

Sorry, I don't know Axe syntax, so just going by what think I see happening.
I switched to using composite rotation by multiplying the X and Y rotation matrices and using them together to transform the vertices, but it produces the same output of random spinning lines.

SourceCoder 3 (AXECUBE) wrote:
:.CUBE
:[F7F7F7F7F708]->GDB1
:[F7F7F7F708F7]
:[F7F7F708F7F7]
:[F70808F708F7]
:[F70808F7F708]
:[F70808080808]
:[08F70808F7F7]
:[08F708080808]
:[08F708F7F708]
:[0808F7080808]
:[0808F708F7F7]
:[0808F7F708F7]
:
:0->theta
:0->T
:DiagnosticOff
:Repeat getKey(15)
: T+1->T
: . T+1->T
: ClrDraw
: sin(theta)->S
: cos(theta)->C
: sin(T)->M
: cos(T)->N
:
: For(A,0,11)
: A*6+GDB1->B
:
: . Rotation
: sign{B)->J
: sign{B+1)->G
: sign{B+2)->I
: . G is a placeholder for y
: . J is a placeholder for x
: . I is a placeholder for z
: . x' = cosBX + sinB * sinaY + sinB * cosaZ;
: (N*J)+(M*M*G)+(M*N*I)->X
: . y' = cosaY - sinaZ
: G*N-(I*M)->Y
: . z' = -sinBX + cosB * sinaY + cosB * cosaZ
: (-1*M*J)+(N*M*G)+(N*N*I)->Z
:
: sign{B+3)->J
: sign{B+4)->G
: sign{B+5)->R
: . G is a placeholder for y
: . J is a placeholder for x
: . R is a placeholder for w(which is z of the second vertex)
: . x' = cosBX + sinB * sinaY + sinB * cosaZ;
: (N*J)+(M*M*G)+(M*N*R)->U
: . y' = cosaY - sinaZ
: G*N-(R*M)->V
: . z' = -sinBX + cosB * sinaY + cosB * cosaZ
: (-1*M*J)+(N*M*G)+(N*N*R)->W
:
: Z+4500/64->Z
: W+4500/64->W
: Line(X//Z+48,Y//Z+32,U//W+48,V//W+32)
: End
: DispGraph
:End
I got the rotation code to work but I'm having trouble with precision as my cube keeps wiggling:

SourceCoder 3 (AXECUBE) wrote:
:.CUBE
:[F7F7F7F7F708]->GDB1
:[F7F7F7F708F7]
:[F7F7F708F7F7]
:[F70808F708F7]
:[F70808F7F708]
:[F70808080808]
:[08F70808F7F7]
:[08F708080808]
:[08F708F7F708]
:[0808F7080808]
:[0808F708F7F7]
:[0808F7F708F7]
:
:0->theta
:0->T
:DiagnosticOff
:FnOn
:Repeat getKey(15)
: theta+1->theta
: T+1->T
: ClrDraw
: sin(theta)->S
: cos(theta)->C
: sin(T)->M
: cos(T)->N
:
: For(A,0,11)
: A*6+GDB1->B
: sign{B}->X->G
: sign{B+1}->Y->O
: sign{B+2}->Z->R
: sign{B+3}->U->P
: sign{B+4}->V->F
: sign{B+5}->W->J
:
: . ----\-X ROTATION----\-
: . G acts as a placeholder for the Y variable, since we're performing operations on the actual Y variable and it cannot change.
: . y' = y * cos(angle) - z * sin(angle);
: O*N-(Z*M)->Y//31->Y
: . z' = z * cos(angle) + y * sin(angle);
: Z*N+(O*M)->Z//31->Z
: X*4->X
:
: . y' = y * cos(angle) - z * sin(angle);
: F*N-(J*M)->V//31->V
: . z' = z * cos(angle) + y * sin(angle);
: J*N+(F*M)->W//31->W
: U*4->U
:
: . ----\-Y ROTATION----\-
: . G acts as a placeholder for the X variable, since we're performing operations on the actual X variable and should change.
: . x' = x * cos(angle) + z * sin(angle);
: X->G
: G*C+(Z*S)->X//31->X
: . z' = z * cos(angle) - x * sin(angle);
: Z*C-(G*S)->Z//31->Z
: Y*4->Y
:
: U->G
: . x' = x * cos(angle) + z * sin(angle);
: G*C+(W*S)->U//31->U
: . z' = z * cos(angle) - x * sin(angle);
: W*C-(G*S)->W//31->W
: V*4->V
:
: ...
: If V>=127
: Disp 5
: End
: ...
:
: Z+700/64->Z
: W+700/64->W
: Line(X//Z+48,Y//Z+32,U//W+48,V//W+32)
: End
: DispGraph
:End
It's probably the division that's wriggling. I just don't know how to fix it.
try always rounding down the last 4 bits.
  
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