mirror of
https://github.com/revarbat/BOSL2.git
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Standardize indention on spaces, not tabs.
This commit is contained in:
Revar Desmera
264
affine.scad
264
affine.scad
@@ -20,13 +20,13 @@ function ident(n) = [for (i = [0:1:n-1]) [for (j = [0:1:n-1]) (i==j)?1:0]];
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// Function: affine2d_to_3d()
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// Description: Takes a 3x3 affine2d matrix and returns its 4x4 affine3d equivalent.
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function affine2d_to_3d(m) = concat(
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[for (r = [0:2])
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concat(
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[for (c = [0:2]) m[r][c]],
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[0]
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)
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],
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[[0, 0, 0, 1]]
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[for (r = [0:2])
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concat(
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[for (c = [0:2]) m[r][c]],
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[0]
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)
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],
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[[0, 0, 0, 1]]
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);
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@@ -45,9 +45,9 @@ function affine2d_identity() = ident(3);
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// Arguments:
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// v = 2D Offset to translate by. [X,Y]
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function affine2d_translate(v) = [
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[1, 0, v.x],
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[0, 1, v.y],
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[0 ,0, 1]
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[1, 0, v.x],
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[0, 1, v.y],
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[0 ,0, 1]
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];
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@@ -57,9 +57,9 @@ function affine2d_translate(v) = [
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// Arguments:
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// v = 2D vector of scaling factors. [X,Y]
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function affine2d_scale(v) = [
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[v.x, 0, 0],
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[ 0, v.y, 0],
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[ 0, 0, 1]
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[v.x, 0, 0],
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[ 0, v.y, 0],
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[ 0, 0, 1]
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];
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@@ -69,9 +69,9 @@ function affine2d_scale(v) = [
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// Arguments:
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// ang = Number of degrees to rotate.
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function affine2d_zrot(ang) = [
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[cos(ang), -sin(ang), 0],
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[sin(ang), cos(ang), 0],
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[ 0, 0, 1]
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[cos(ang), -sin(ang), 0],
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[sin(ang), cos(ang), 0],
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[ 0, 0, 1]
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];
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@@ -83,12 +83,12 @@ function affine2d_zrot(ang) = [
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// Arguments:
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// v = The normal vector of the line to reflect across.
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function affine2d_mirror(v) =
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let(v=unit(point2d(v)), a=v.x, b=v.y)
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[
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[1-2*a*a, 0-2*a*b, 0],
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[0-2*a*b, 1-2*b*b, 0],
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[ 0, 0, 1]
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];
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let(v=unit(point2d(v)), a=v.x, b=v.y)
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[
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[1-2*a*a, 0-2*a*b, 0],
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[0-2*a*b, 1-2*b*b, 0],
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[ 0, 0, 1]
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];
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// Function: affine2d_skew()
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@@ -100,9 +100,9 @@ function affine2d_mirror(v) =
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// xa = Skew angle, in degrees, in the direction of the X axis.
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// ya = Skew angle, in degrees, in the direction of the Y axis.
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function affine2d_skew(xa, ya) = [
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[1, tan(xa), 0],
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[tan(ya), 1, 0],
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[0, 0, 1]
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[1, tan(xa), 0],
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[tan(ya), 1, 0],
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[0, 0, 1]
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];
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@@ -114,8 +114,8 @@ function affine2d_skew(xa, ya) = [
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// Arguments:
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// affines = A list of 3x3 affine2d matrices.
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function affine2d_chain(affines, _m=undef, _i=0) =
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(_i>=len(affines))? (is_undef(_m)? ident(3) : _m) :
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affine2d_chain(affines, _m=(is_undef(_m)? affines[_i] : affines[_i] * _m), _i=_i+1);
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(_i>=len(affines))? (is_undef(_m)? ident(3) : _m) :
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affine2d_chain(affines, _m=(is_undef(_m)? affines[_i] : affines[_i] * _m), _i=_i+1);
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@@ -133,10 +133,10 @@ function affine3d_identity() = ident(4);
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// Arguments:
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// v = 3D offset to translate by. [X,Y,Z]
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function affine3d_translate(v) = [
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[1, 0, 0, v.x],
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[0, 1, 0, v.y],
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[0, 0, 1, v.z],
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[0 ,0, 0, 1]
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[1, 0, 0, v.x],
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[0, 1, 0, v.y],
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[0, 0, 1, v.z],
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[0 ,0, 0, 1]
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];
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@@ -146,10 +146,10 @@ function affine3d_translate(v) = [
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// Arguments:
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// v = 3D vector of scaling factors. [X,Y,Z]
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function affine3d_scale(v) = [
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[v.x, 0, 0, 0],
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[ 0, v.y, 0, 0],
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[ 0, 0, v.z, 0],
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[ 0, 0, 0, 1]
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[v.x, 0, 0, 0],
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[ 0, v.y, 0, 0],
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[ 0, 0, v.z, 0],
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[ 0, 0, 0, 1]
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];
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@@ -159,10 +159,10 @@ function affine3d_scale(v) = [
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// Arguments:
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// ang = number of degrees to rotate.
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function affine3d_xrot(ang) = [
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[1, 0, 0, 0],
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[0, cos(ang), -sin(ang), 0],
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[0, sin(ang), cos(ang), 0],
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[0, 0, 0, 1]
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[1, 0, 0, 0],
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[0, cos(ang), -sin(ang), 0],
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[0, sin(ang), cos(ang), 0],
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[0, 0, 0, 1]
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];
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@@ -172,10 +172,10 @@ function affine3d_xrot(ang) = [
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// Arguments:
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// ang = Number of degrees to rotate.
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function affine3d_yrot(ang) = [
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[ cos(ang), 0, sin(ang), 0],
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[ 0, 1, 0, 0],
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[-sin(ang), 0, cos(ang), 0],
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[ 0, 0, 0, 1]
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[ cos(ang), 0, sin(ang), 0],
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[ 0, 1, 0, 0],
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[-sin(ang), 0, cos(ang), 0],
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[ 0, 0, 0, 1]
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];
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@@ -187,10 +187,10 @@ function affine3d_yrot(ang) = [
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// Arguments:
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// ang = number of degrees to rotate.
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function affine3d_zrot(ang) = [
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[cos(ang), -sin(ang), 0, 0],
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[sin(ang), cos(ang), 0, 0],
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[ 0, 0, 1, 0],
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[ 0, 0, 0, 1]
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[cos(ang), -sin(ang), 0, 0],
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[sin(ang), cos(ang), 0, 0],
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[ 0, 0, 1, 0],
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[ 0, 0, 0, 1]
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];
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@@ -203,18 +203,18 @@ function affine3d_zrot(ang) = [
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// u = 3D axis vector to rotate around.
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// ang = number of degrees to rotate.
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function affine3d_rot_by_axis(u, ang) =
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approx(ang,0)? affine3d_identity() :
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let(
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u = unit(u),
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c = cos(ang),
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c2 = 1-c,
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s = sin(ang)
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) [
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[u.x*u.x*c2+c , u.x*u.y*c2-u.z*s, u.x*u.z*c2+u.y*s, 0],
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[u.y*u.x*c2+u.z*s, u.y*u.y*c2+c , u.y*u.z*c2-u.x*s, 0],
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[u.z*u.x*c2-u.y*s, u.z*u.y*c2+u.x*s, u.z*u.z*c2+c , 0],
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[ 0, 0, 0, 1]
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];
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approx(ang,0)? affine3d_identity() :
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let(
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u = unit(u),
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c = cos(ang),
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c2 = 1-c,
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s = sin(ang)
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) [
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[u.x*u.x*c2+c , u.x*u.y*c2-u.z*s, u.x*u.z*c2+u.y*s, 0],
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[u.y*u.x*c2+u.z*s, u.y*u.y*c2+c , u.y*u.z*c2-u.x*s, 0],
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[u.z*u.x*c2-u.y*s, u.z*u.y*c2+u.x*s, u.z*u.z*c2+c , 0],
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[ 0, 0, 0, 1]
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];
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// Function: affine3d_rot_from_to()
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@@ -226,22 +226,22 @@ function affine3d_rot_by_axis(u, ang) =
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// from = 3D axis vector to rotate from.
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// to = 3D axis vector to rotate to.
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function affine3d_rot_from_to(from, to) =
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let(
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from = unit(point3d(from)),
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to = unit(point3d(to))
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) approx(from,to)? affine3d_identity() :
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let(
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u = vector_axis(from,to),
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ang = vector_angle(from,to),
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c = cos(ang),
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c2 = 1-c,
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s = sin(ang)
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) [
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[u.x*u.x*c2+c , u.x*u.y*c2-u.z*s, u.x*u.z*c2+u.y*s, 0],
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[u.y*u.x*c2+u.z*s, u.y*u.y*c2+c , u.y*u.z*c2-u.x*s, 0],
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[u.z*u.x*c2-u.y*s, u.z*u.y*c2+u.x*s, u.z*u.z*c2+c , 0],
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[ 0, 0, 0, 1]
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];
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let(
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from = unit(point3d(from)),
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to = unit(point3d(to))
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) approx(from,to)? affine3d_identity() :
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let(
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u = vector_axis(from,to),
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ang = vector_angle(from,to),
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c = cos(ang),
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c2 = 1-c,
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s = sin(ang)
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) [
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[u.x*u.x*c2+c , u.x*u.y*c2-u.z*s, u.x*u.z*c2+u.y*s, 0],
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[u.y*u.x*c2+u.z*s, u.y*u.y*c2+c , u.y*u.z*c2-u.x*s, 0],
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[u.z*u.x*c2-u.y*s, u.z*u.y*c2+u.x*s, u.z*u.z*c2+c , 0],
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[ 0, 0, 0, 1]
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];
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// Function: affine_frame_map()
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@@ -266,35 +266,35 @@ function affine3d_rot_from_to(from, to) =
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// // The next map sends [1,1,0] to [0,1,1] and [-1,1,0] to [0,-1,1]
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// T = affine_frame_map(x=[0,1,1], y=[0,-1,1]) * affine_frame_map(x=[1,1,0], y=[-1,1,0],reverse=true);
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function affine_frame_map(x,y,z, reverse=false) =
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assert(num_defined([x,y,z])>=2, "Must define at least two inputs")
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let(
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xvalid = is_undef(x) || (is_vector(x) && len(x)==3),
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yvalid = is_undef(y) || (is_vector(y) && len(y)==3),
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zvalid = is_undef(z) || (is_vector(z) && len(z)==3)
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)
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assert(xvalid,"Input x must be a length 3 vector")
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assert(yvalid,"Input y must be a length 3 vector")
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assert(zvalid,"Input z must be a length 3 vector")
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let(
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x = is_undef(x)? undef : unit(x),
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y = is_undef(y)? undef : unit(y),
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z = is_undef(z)? undef : unit(z),
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map = is_undef(x)? [cross(y,z), y, z] :
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is_undef(y)? [x, cross(z,x), z] :
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is_undef(z)? [x, y, cross(x,y)] :
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[x, y, z]
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)
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reverse? (
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let(
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ocheck = (
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approx(map[0]*map[1],0) &&
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approx(map[0]*map[2],0) &&
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approx(map[1]*map[2],0)
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)
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)
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assert(ocheck, "Inputs must be orthogonal when reverse==true")
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affine2d_to_3d(map)
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) : affine2d_to_3d(transpose(map));
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assert(num_defined([x,y,z])>=2, "Must define at least two inputs")
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let(
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xvalid = is_undef(x) || (is_vector(x) && len(x)==3),
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yvalid = is_undef(y) || (is_vector(y) && len(y)==3),
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zvalid = is_undef(z) || (is_vector(z) && len(z)==3)
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)
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assert(xvalid,"Input x must be a length 3 vector")
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assert(yvalid,"Input y must be a length 3 vector")
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assert(zvalid,"Input z must be a length 3 vector")
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let(
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x = is_undef(x)? undef : unit(x),
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y = is_undef(y)? undef : unit(y),
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z = is_undef(z)? undef : unit(z),
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map = is_undef(x)? [cross(y,z), y, z] :
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is_undef(y)? [x, cross(z,x), z] :
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is_undef(z)? [x, y, cross(x,y)] :
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[x, y, z]
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)
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reverse? (
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let(
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ocheck = (
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approx(map[0]*map[1],0) &&
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approx(map[0]*map[2],0) &&
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approx(map[1]*map[2],0)
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)
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)
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assert(ocheck, "Inputs must be orthogonal when reverse==true")
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affine2d_to_3d(map)
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) : affine2d_to_3d(transpose(map));
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@@ -306,15 +306,15 @@ function affine_frame_map(x,y,z, reverse=false) =
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// Arguments:
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// v = The normal vector of the plane to reflect across.
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function affine3d_mirror(v) =
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let(
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v=unit(point3d(v)),
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a=v.x, b=v.y, c=v.z
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) [
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[1-2*a*a, -2*a*b, -2*a*c, 0],
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[ -2*b*a, 1-2*b*b, -2*b*c, 0],
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[ -2*c*a, -2*c*b, 1-2*c*c, 0],
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[ 0, 0, 0, 1]
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];
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let(
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v=unit(point3d(v)),
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a=v.x, b=v.y, c=v.z
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) [
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[1-2*a*a, -2*a*b, -2*a*c, 0],
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[ -2*b*a, 1-2*b*b, -2*b*c, 0],
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[ -2*c*a, -2*c*b, 1-2*c*c, 0],
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[ 0, 0, 0, 1]
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];
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// Function: affine3d_skew()
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@@ -330,10 +330,10 @@ function affine3d_mirror(v) =
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// szx = Skew factor multiplier for skewing along the Z axis as you get farther from the X axis. Default: 0
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// szy = Skew factor multiplier for skewing along the Z axis as you get farther from the Y axis. Default: 0
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function affine3d_skew(sxy=0, sxz=0, syx=0, syz=0, szx=0, szy=0) = [
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[ 1, sxy, sxz, 0],
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[syx, 1, syz, 0],
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[szx, szy, 1, 0],
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[ 0, 0, 0, 1]
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[ 1, sxy, sxz, 0],
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[syx, 1, syz, 0],
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[szx, szy, 1, 0],
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[ 0, 0, 0, 1]
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];
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@@ -346,10 +346,10 @@ function affine3d_skew(sxy=0, sxz=0, syx=0, syz=0, szx=0, szy=0) = [
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// xa = Skew angle, in degrees, in the direction of the X axis.
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// ya = Skew angle, in degrees, in the direction of the Y axis.
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function affine3d_skew_xy(xa, ya) = [
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[1, 0, tan(xa), 0],
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[0, 1, tan(ya), 0],
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[0, 0, 1, 0],
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[0, 0, 0, 1]
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[1, 0, tan(xa), 0],
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[0, 1, tan(ya), 0],
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[0, 0, 1, 0],
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[0, 0, 0, 1]
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];
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@@ -362,10 +362,10 @@ function affine3d_skew_xy(xa, ya) = [
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// xa = Skew angle, in degrees, in the direction of the X axis.
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// za = Skew angle, in degrees, in the direction of the Z axis.
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function affine3d_skew_xz(xa, za) = [
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[1, tan(xa), 0, 0],
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[0, 1, 0, 0],
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[0, tan(za), 1, 0],
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[0, 0, 0, 1]
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[1, tan(xa), 0, 0],
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[0, 1, 0, 0],
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[0, tan(za), 1, 0],
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[0, 0, 0, 1]
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];
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@@ -378,10 +378,10 @@ function affine3d_skew_xz(xa, za) = [
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// ya = Skew angle, in degrees, in the direction of the Y axis.
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// za = Skew angle, in degrees, in the direction of the Z axis.
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function affine3d_skew_yz(ya, za) = [
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[ 1, 0, 0, 0],
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[tan(ya), 1, 0, 0],
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[tan(za), 0, 1, 0],
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[ 0, 0, 0, 1]
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[ 1, 0, 0, 0],
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[tan(ya), 1, 0, 0],
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[tan(za), 0, 1, 0],
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[ 0, 0, 0, 1]
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];
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||||
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@@ -393,8 +393,8 @@ function affine3d_skew_yz(ya, za) = [
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||||
// Arguments:
|
||||
// affines = A list of 4x4 affine3d matrices.
|
||||
function affine3d_chain(affines, _m=undef, _i=0) =
|
||||
(_i>=len(affines))? (is_undef(_m)? ident(4) : _m) :
|
||||
affine3d_chain(affines, _m=(is_undef(_m)? affines[_i] : affines[_i] * _m), _i=_i+1);
|
||||
(_i>=len(affines))? (is_undef(_m)? ident(4) : _m) :
|
||||
affine3d_chain(affines, _m=(is_undef(_m)? affines[_i] : affines[_i] * _m), _i=_i+1);
|
||||
|
||||
|
||||
// Function: apply()
|
||||
@@ -464,4 +464,4 @@ function is_2d_transform(t) = // z-parameters are zero, except we allow t[2][
|
||||
|
||||
|
||||
|
||||
// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
|
||||
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
|
||||
|
||||
Reference in New Issue
Block a user