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Added some affine matrix generation optimizations.
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Revar Desmera
parent
b8e5171e3d
commit
e550909726
2 changed files with 70 additions and 54 deletions
120
affine.scad
120
affine.scad
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@ -202,17 +202,19 @@ function affine3d_zrot(ang) = [
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// Arguments:
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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) = 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[0]*u[0]*c2+c , u[0]*u[1]*c2-u[2]*s, u[0]*u[2]*c2+u[1]*s, 0],
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[u[1]*u[0]*c2+u[2]*s, u[1]*u[1]*c2+c , u[1]*u[2]*c2-u[0]*s, 0],
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[u[2]*u[0]*c2-u[1]*s, u[2]*u[1]*c2+u[0]*s, u[2]*u[2]*c2+c , 0],
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[ 0, 0, 0, 1]
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];
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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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// Function: affine3d_rot_from_to()
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@ -223,18 +225,23 @@ function affine3d_rot_by_axis(u, ang) = let(
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// Arguments:
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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) = 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[0]*u[0]*c2+c , u[0]*u[1]*c2-u[2]*s, u[0]*u[2]*c2+u[1]*s, 0],
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[u[1]*u[0]*c2+u[2]*s, u[1]*u[1]*c2+c , u[1]*u[2]*c2-u[0]*s, 0],
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[u[2]*u[0]*c2-u[1]*s, u[2]*u[1]*c2+u[0]*s, u[2]*u[2]*c2+c , 0],
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[ 0, 0, 0, 1]
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];
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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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// Function: affine_frame_map()
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@ -246,7 +253,7 @@ function affine3d_rot_from_to(from, to) = let(
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// Returns a transformation that maps one coordinate frame to another. You must specify two or three of `x`, `y`, and `z`. The specified
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// axes are mapped to the vectors you supplied. If you give two inputs, the third vector is mapped to the appropriate normal to maintain a right hand coordinate system.
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// If the vectors you give are orthogonal the result will be a rotation and the `reverse` parameter will supply the inverse map, which enables you
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// to map two arbitrary coordinate systems two each other by using the canonical coordinate system as an intermediary. You cannot use the `reverse` option
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// to map two arbitrary coordinate systems to each other by using the canonical coordinate system as an intermediary. You cannot use the `reverse` option
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// with non-orthogonal inputs.
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// Arguments:
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// x = Destination vector for x axis
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@ -259,30 +266,35 @@ function affine3d_rot_from_to(from, to) = let(
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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_def(x) ? unit(x) : undef,
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y = is_def(y) ? unit(y) : undef,
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z = is_def(z) ? unit(z) : undef,
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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( ocheck = approx(map[0]*map[1],0) && approx(map[0]*map[2],0) && approx(map[1]*map[2],0))
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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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:
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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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@ -294,8 +306,10 @@ 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(v=unit(point3d(v)), a=v.x, b=v.y, c=v.z)
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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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@ -437,8 +451,10 @@ function apply_list(points,transform_list) =
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// Function: is_2d_transform()
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// Usage: is_2d_transform(t)
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// Description: Checks if the input is a 3d transform that does not act on the z coordinate, except
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// Usage:
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// is_2d_transform(t)
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// Description:
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// Checks if the input is a 3d transform that does not act on the z coordinate, except
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// possibly for a simple scaling of z. Note that an input which is only a zscale returns false.
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function is_2d_transform(t) = // z-parameters are zero, except we allow t[2][2]!=1 so scale() works
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t[2][0]==0 && t[2][1]==0 && t[2][3]==0 && t[0][2] == 0 && t[1][2]==0 &&
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@ -8,7 +8,7 @@
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//////////////////////////////////////////////////////////////////////
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BOSL_VERSION = [2,0,210];
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BOSL_VERSION = [2,0,211];
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// Section: BOSL Library Version Functions
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