| // Perform an affine transformation of matrix M on coordinate v.
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| //
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| // [Scale X] [Shear X along Y] [Shear X along Z] [Translate X]
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| // [Shear Y along X] [Scale Y] [Shear Y along Z] [Translate Y]
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| // [Shear Z along X] [Shear Z along Y] [Scale Z] [Translate Z]
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| // or rotation matrix [[cos,-sin],[sin,cos]] in the 2 axes for a plane.
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| function Affine(M, v) = M * [v[0], v[1], v[2], 1];
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|
|
|
|
| // Combine a list of affine transformation matrices into one.
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| function AffMerge(Mlist) = let(
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| AffMergeRec = function(Mlist, i) i >= len(Mlist) ?
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| [[1,0,0,0],[0,1,0,0],[0,0,1,0]] :
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| let (
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| rest = AffMergeRec(Mlist, i+1),
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| prod = Mlist[i] * [rest[0], rest[1], rest[2], [0,0,0,1]]
|
| )
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| [prod[0], prod[1], prod[2]]
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| )
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| AffMergeRec(Mlist, 0);
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|
|
|
|
| // Prepare a matrix to rotate around the x-axis.
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| function RotX(a) =
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| [[ 1, 0, 0, 0],
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| [ 0, cos(a), -sin(a), 0],
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| [ 0, sin(a), cos(a), 0]];
|
|
|
| // Prepare a matrix to rotate around the y-axis.
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| function RotY(a) =
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| [[ cos(a), 0, sin(a), 0],
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| [ 0, 1, 0, 0],
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| [-sin(a), 0, cos(a), 0]];
|
|
|
| // Prepare a matrix to rotate around the z-axis.
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| function RotZ(a) =
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| [[cos(a), -sin(a), 0, 0],
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| [sin(a), cos(a), 0, 0],
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| [ 0, 0, 1, 0]];
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|
|
| // Prepare a matrix to rotate around x, then y, then z.
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| function Rotate(rotvec) =
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| AffMerge([RotZ(rotvec[2]), RotY(rotvec[1]), RotX(rotvec[0])]);
|
|
|
| // Prepare a matrix to translate by vector v.
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| function Translate(v) =
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| [[1, 0, 0, v[0]],
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| [0, 1, 0, v[1]],
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| [0, 0, 1, v[2]]];
|
|
|
| // Prepare a matrix to scale by vector v.
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| function Scale(v) =
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| [[v[0], 0, 0, 0],
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| [ 0, v[1], 0, 0],
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| [ 0, 0, v[2], 0]];
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|
|
|
|
| $fn=64;ang1=45;ang2=15;rad1=4;rad2=10;
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| rotate([0,0,ang2]) translate([0,-rad2]){
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| %cylinder(h=.001,r=2);
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| rotate([0,0,ang1]) translate([0,-rad1]) cylinder(h=.001,r=2);
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| }
|
|
|
| M = AffMerge([Rotate([0,0,ang2]), Translate([0,-rad2,0]), Rotate([0,0,ang1]), Translate([0,-rad1,0])]);
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| p = Affine(M, [0,0,0]);
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| echo(p);
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| #translate([p[0]+2, p[1]<0 ? p[1] : 0, 0]) cube([6.95,abs(p[1]),.001]);
|