grey/BOSL2
1
0
Fork 0
mirror of https://github.com/BelfrySCAD/BOSL2.git synced 2025-01-01 09:49:45 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions

Merge pull request #467 from adrianVmariano/master

Browse source 
fast_distance method for skin, regions for path_sweep & bug fixes
This commit is contained in:
Revar Desmera 2021-03-12 19:51:16 -08:00 committed by GitHub
commit 9c310d9c17
No known key found for this signature in database
GPG key ID: 4AEE18F83AFDEB23
7 changed files with 320 additions and 78 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

13
arrays.scad
View file

@ -1682,4 +1682,17 @@ function transpose(arr, reverse=false) =
arr;
// Function: is_matrix_symmetric()
// Usage:
// b = is_matrix_symmetric(A,<eps>)
// Description:
// Returns true if the input matrix is symmetric, meaning it equals its transpose.
// Matrix should have numerical entries.
// Arguments:
// A = matrix to test
// eps = epsilon for comparing equality. Default: 1e-12
function is_matrix_symmetric(A,eps=1e-12) =
approx(A,transpose(A));
// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap

134
math.scad
View file

@ -585,11 +585,11 @@ function lcm(a,b=[]) =
function sum(v, dflt=0) =
v==[]? dflt :
assert(is_consistent(v), "Input to sum is non-numeric or inconsistent")
is_vector(v) ? [for(i=[1:len(v)]) 1]*v :
_sum(v,v[0]*0);
function _sum(v,_total,_i=0) = _i>=len(v) ? _total : _sum(v,_total+v[_i], _i+1);
// Function: cumsum()
// Usage:
// sums = cumsum(v);
@ -1465,35 +1465,113 @@ function deriv3(data, h=1, closed=false) =
// Section: Complex Numbers
// Function: C_times()
// Function: complex()
// Usage:
// c = C_times(z1,z2)
// z = complex(list)
// Description:
// Multiplies two complex numbers represented by 2D vectors.
// Returns a complex number as a 2D vector [REAL, IMAGINARY].
// Converts a real valued number, vector or matrix into its complex analog
// by replacing all entries with a 2-vector that has zero imaginary part.
function complex(list) =
is_num(list) ? [list,0] :
[for(entry=list) is_num(entry) ? [entry,0] : complex(entry)];
// Function: c_mul()
// Usage:
// c = c_mul(z1,z2)
// Description:
// Multiplies two complex numbers, vectors or matrices, where complex numbers
// or entries are represented as vectors: [REAL, IMAGINARY]. Note that all
// entries in both arguments must be complex.
// Arguments:
// z1 = First complex number, given as a 2D vector [REAL, IMAGINARY]
// z2 = Second complex number, given as a 2D vector [REAL, IMAGINARY]
function C_times(z1,z2) =
assert( is_matrix([z1,z2],2,2), "Complex numbers should be represented by 2D vectors" )
// z1 = First complex number, vector or matrix
// z2 = Second complex number, vector or matrix
function _split_complex(data) =
is_vector(data,2) ? data
: is_num(data[0][0]) ? [data*[1,0], data*[0,1]]
: [
[for(vec=data) vec * [1,0]],
[for(vec=data) vec * [0,1]]
];
function _combine_complex(data) =
is_vector(data,2) ? data
: is_num(data[0][0]) ? [for(i=[0:len(data[0])-1]) [data[0][i],data[1][i]]]
: [for(i=[0:1:len(data[0])-1])
[for(j=[0:1:len(data[0][0])-1])
[data[0][i][j], data[1][i][j]]]];
function _c_mul(z1,z2) =
[ z1.x*z2.x - z1.y*z2.y, z1.x*z2.y + z1.y*z2.x ];
// Function: C_div()
function c_mul(z1,z2) =
is_matrix([z1,z2],2,2) ? _c_mul(z1,z2) :
_combine_complex(_c_mul(_split_complex(z1), _split_complex(z2)));
// Function: c_div()
// Usage:
// x = C_div(z1,z2)
// x = c_div(z1,z2)
// Description:
// Divides two complex numbers represented by 2D vectors.
// Returns a complex number as a 2D vector [REAL, IMAGINARY].
// Arguments:
// z1 = First complex number, given as a 2D vector [REAL, IMAGINARY]
// z2 = Second complex number, given as a 2D vector [REAL, IMAGINARY]
function C_div(z1,z2) =
function c_div(z1,z2) =
assert( is_vector(z1,2) && is_vector(z2), "Complex numbers should be represented by 2D vectors." )
assert( !approx(z2,0), "The divisor `z2` cannot be zero." )
let(den = z2.x*z2.x + z2.y*z2.y)
[(z1.x*z2.x + z1.y*z2.y)/den, (z1.y*z2.x - z1.x*z2.y)/den];
// For the sake of consistence with Q_mul and vmul, C_times should be called C_mul
// Function: c_conj()
// Usage:
// w = c_conj(z)
// Description:
// Computes the complex conjugate of the input, which can be a complex number,
// complex vector or complex matrix.
function c_conj(z) =
is_vector(z,2) ? [z.x,-z.y] :
[for(entry=z) c_conj(entry)];
// Function: c_real()
// Usage:
// x = c_real(z)
// Description:
// Returns real part of a complex number, vector or matrix.
function c_real(z) =
is_vector(z,2) ? z.x
: is_num(z[0][0]) ? z*[1,0]
: [for(vec=z) vec * [1,0]];
// Function: c_imag()
// Usage:
// x = c_imag(z)
// Description:
// Returns imaginary part of a complex number, vector or matrix.
function c_imag(z) =
is_vector(z,2) ? z.y
: is_num(z[0][0]) ? z*[0,1]
: [for(vec=z) vec * [0,1]];
// Function: c_ident()
// Usage:
// I = c_ident(n)
// Description:
// Produce an n by n complex identity matrix
function c_ident(n) = [for (i = [0:1:n-1]) [for (j = [0:1:n-1]) (i==j)?[1,0]:[0,0]]];
// Function: c_norm()
// Usage:
// n = c_norm(z)
// Description:
// Compute the norm of a complex number or vector.
function c_norm(z) = norm_fro(z);
// Section: Polynomials
@ -1539,12 +1617,12 @@ function quadratic_roots(a,b,c,real=false) =
// where a_n is the z^n coefficient. Polynomial coefficients are real.
// The result is a number if `z` is a number and a complex number otherwise.
function polynomial(p,z,k,total) =
    is_undef(k)
    ?   assert( is_vector(p) , "Input polynomial coefficients must be a vector." )
        assert( is_finite(z) || is_vector(z,2), "The value of `z` must be a real or a complex number." )
        polynomial( _poly_trim(p), z, 0, is_num(z) ? 0 : [0,0])
    : k==len(p) ? total
    : polynomial(p,z,k+1, is_num(z) ? total*z+p[k] : C_times(total,z)+[p[k],0]);
is_undef(k)
? assert( is_vector(p) , "Input polynomial coefficients must be a vector." )
assert( is_finite(z) || is_vector(z,2), "The value of `z` must be a real or a complex number." )
polynomial( _poly_trim(p), z, 0, is_num(z) ? 0 : [0,0])
: k==len(p) ? total
: polynomial(p,z,k+1, is_num(z) ? total*z+p[k] : c_mul(total,z)+[p[k],0]);
// Function: poly_mult()
// Usage:
@ -1554,12 +1632,12 @@ function polynomial(p,z,k,total) =
// Given a list of polynomials represented as real coefficient lists, with the highest degree coefficient first,
// computes the coefficient list of the product polynomial.
function poly_mult(p,q) =
    is_undef(q) ?
        len(p)==2
is_undef(q) ?
len(p)==2
? poly_mult(p[0],p[1])
        : poly_mult(p[0], poly_mult(select(p,1,-1)))
    :
    assert( is_vector(p) && is_vector(q),"Invalid arguments to poly_mult")
: poly_mult(p[0], poly_mult(select(p,1,-1)))
:
assert( is_vector(p) && is_vector(q),"Invalid arguments to poly_mult")
p*p==0 || q*q==0
? [0]
: _poly_trim(convolve(p,q));
@ -1680,10 +1758,10 @@ function _poly_roots(p, pderiv, s, z, tol, i=0) =
svals = [for(zk=z) tol*polynomial(s,norm(zk))],
p_of_z = [for(zk=z) polynomial(p,zk)],
done = [for(k=[0:n-1]) norm(p_of_z[k])<=svals[k]],
newton = [for(k=[0:n-1]) C_div(p_of_z[k], polynomial(pderiv,z[k]))],
zdiff = [for(k=[0:n-1]) sum([for(j=[0:n-1]) if (j!=k) C_div([1,0], z[k]-z[j])])],
w = [for(k=[0:n-1]) done[k] ? [0,0] : C_div( newton[k],
[1,0] - C_times(newton[k], zdiff[k]))]
newton = [for(k=[0:n-1]) c_div(p_of_z[k], polynomial(pderiv,z[k]))],
zdiff = [for(k=[0:n-1]) sum([for(j=[0:n-1]) if (j!=k) c_div([1,0], z[k]-z[j])])],
w = [for(k=[0:n-1]) done[k] ? [0,0] : c_div( newton[k],
[1,0] - c_mul(newton[k], zdiff[k]))]
)
all(done) ? z : _poly_roots(p,pderiv,s,z-w,tol,i+1);

93
regions.scad
View file

@ -58,35 +58,34 @@ module region(r)
// Function: check_and_fix_path()
// Usage:
// check_and_fix_path(path, [valid_dim], [closed])
// check_and_fix_path(path, [valid_dim], [closed], [name])
// Description:
// Checks that the input is a path. If it is a region with one component, converts it to a path.
// Note that arbitrary paths must have at least two points, but closed paths need at least 3 points.
// valid_dim specfies the allowed dimension of the points in the path.
// If the path is closed, removed duplicate endpoint if present.
// If the path is closed, removes duplicate endpoint if present.
// Arguments:
// path = path to process
// valid_dim = list of allowed dimensions for the points in the path, e.g. [2,3] to require 2 or 3 dimensional input. If left undefined do not perform this check. Default: undef
// closed = set to true if the path is closed, which enables a check for endpoint duplication
function check_and_fix_path(path, valid_dim=undef, closed=false) =
// name = parameter name to use for reporting errors. Default: "path"
function check_and_fix_path(path, valid_dim=undef, closed=false, name="path") =
let(
path = is_region(path)? (
assert(len(path)==1,"Region supplied as path does not have exactly one component")
path[0]
) : (
assert(is_path(path), "Input is not a path")
path
),
dim = array_dim(path)
path =
is_region(path)?
assert(len(path)==1,str("Region ",name," supplied as path does not have exactly one component"))
path[0]
:
assert(is_path(path), str("Input ",name," is not a path"))
path
)
assert(dim[0]>1,"Path must have at least 2 points")
assert(len(dim)==2,"Invalid path: path is either a list of scalars or a list of matrices")
assert(is_def(dim[1]), "Invalid path: entries in the path have variable length")
let(valid=is_undef(valid_dim) || in_list(dim[1],valid_dim))
assert(len(path)>(closed?2:1),closed?str("Closed path ",name," must have at least 3 points")
:str("Path ",name," must have at least 2 points"))
let(valid=is_undef(valid_dim) || in_list(len(path[0]),force_list(valid_dim)))
assert(
valid, str(
"The points on the path have length ",
dim[1], " but length must be ",
len(valid_dim)==1? valid_dim[0] : str("one of ",valid_dim)
"Input ",name," must has dimension ", len(path[0])," but dimension must be ",
is_list(valid_dim) ? str("one of ",valid_dim) : valid_dim
)
)
closed && approx(path[0],select(path,-1))? slice(path,0,-2) : path;
@ -223,6 +222,64 @@ function split_nested_region(region) =
) outs;
function find_first_approx(val, list, start=0, all=false, eps=EPSILON) =
all? [for (i=[start:1:len(list)-1]) if(approx(val, list[i], eps=eps)) i] :
__find_first_approx(val, list, eps=eps, i=start);
function __find_first_approx(val, list, eps, i=0) =
i >= len(list)? undef :
approx(val, list[i], eps=eps)? i :
__find_first_approx(val, list, eps=eps, i=i+1);
// Function: polygons_equal()
// Usage:
// b = polygons_equal(poly1, poly2, <eps>)
// Description:
// Returns true if the components of region1 and region2 are the same polygons
// within given epsilon tolerance.
// Arguments:
// poly1 = first polygon
// poly2 = second polygon
// eps = tolerance for comparison
// Example(NORENDER):
// polygons_equal(pentagon(r=4),
// rot(360/5, p=pentagon(r=4))); // returns true
// polygons_equal(pentagon(r=4),
// rot(90, p=pentagon(r=4))); // returns false
function polygons_equal(poly1, poly2, eps=EPSILON) =
let( l1 = len(poly1), l2 = len(poly2))
l1 != l2 ? false :
let( maybes = find_first_approx(poly1[0], poly2, eps=eps, all=true) )
maybes == []? false :
[for (i=maybes) if (__polygons_equal(poly1, poly2, eps, i)) 1] != [];
function __polygons_equal(poly1, poly2, eps, st) =
max([for(d=poly1-select(poly2,st,st-1)) d*d])<eps*eps;
// Function: regions_equal()
// Usage:
// b = regions_equal(region1, region2, <eps>)
// Description:
// Returns true if the components of region1 and region2 are the same polygons
// within given epsilon tolerance.
// Arguments:
// poly1 = first polygon
// poly2 = second polygon
// eps = tolerance for comparison
function regions_equal(region1, region2) =
assert(is_region(region1) && is_region(region2))
len(region1)==len(region2) &&
[
for (a=region1)
if (1!=sum(
[for(b=region2)
if (polygons_equal(path3d(a), path3d(b)))
1]
)
) 1
] == [];
// Section: Region Extrusion and VNFs

5
rounding.scad
View file

@ -75,7 +75,7 @@ include <structs.scad>
// circular roundovers. For continuous curvature roundovers `$fs` and `$fn` are used and `$fa` is
// ignored. Note that $fn is interpreted as the number of points on the roundover curve, which is
// not equivalent to its meaning for rounding circles because roundovers are usually small fractions
// of a circular arc. When doing continuous curvature rounding be sure to use lots of segments or the effect
// of a circular arc. As usual, $fn overrides $fs. When doing continuous curvature rounding be sure to use lots of segments or the effect
// will be hidden by the discretization. Note that if you use $fn with "smooth" then $fn points are added at each corner, even
// if the "corner" is flat, with collinear points, so this guarantees a specific output length.
//
@ -264,8 +264,7 @@ function round_corners(path, method="circle", radius, cut, joint, k, closed=true
let(
pathbit = select(path,i-1,i+1),
angle = approx(pathbit[0],pathbit[1]) || approx(pathbit[1],pathbit[2]) ? undef
: vector_angle(select(path,i-1,i+1))/2,
f=echo(angle=angle)
: vector_angle(select(path,i-1,i+1))/2
)
(!closed && (i==0 || i==len(path)-1)) ? [0] : // Force zeros at ends for non-closed
parm[i]==0 ? [0] : // If no rounding requested then don't try to compute parameters

2
shapes2d.scad
View file

@ -554,7 +554,7 @@ function arc(N, r, angle, d, cp, points, width, thickness, start, wedge=false, l
)
assert(is_vector(cp,2),"Centerpoint must be a 2d vector")
assert(angle!=0, "Arc has zero length")
assert(r>0, "Arc radius invalid")
assert(is_def(r) && r>0, "Arc radius invalid")
let(
N = max(3, is_undef(N)? ceil(segs(r)*abs(angle)/360) : N),
arcpoints = [for(i=[0:N-1]) let(theta = start + i*angle/(N-1)) r*[cos(theta),sin(theta)]+cp],

76
skin.scad
View file

@ -63,8 +63,8 @@
// Note that when dealing with continuous curves it is always better to adjust the
// sampling in your code to generate the desired sampling rather than using the `refine` argument.
// .
// You can choose from four methods for specifying alignment for incommensurate profiles.
// The available methods are `"distance"`, `"tangent"`, `"direct"` and `"reindex"`.
// You can choose from five methods for specifying alignment for incommensurate profiles.
// The available methods are `"distance"`, `"fast_distance"`, `"tangent"`, `"direct"` and `"reindex"`.
// It is useful to distinguish between continuous curves like a circle and discrete profiles
// like a hexagon or star, because the algorithms' suitability depend on this distinction.
// .
@ -87,14 +87,17 @@
// `sampling="segment"` may produce a more pleasing result. These two approaches differ only when
// the segments of your input profiles have unequal length.
// .
// The "distance" and "tangent" methods work by duplicating vertices to create
// The "distance", "fast_distance" and "tangent" methods work by duplicating vertices to create
// triangular faces. The "distance" method finds the global minimum distance method for connecting two
// profiles. This algorithm generally produces a good result when both profiles are discrete ones with
// a small number of vertices. It is computationally intensive (O(N^3)) and may be
// slow on large inputs. The resulting surfaces generally have curved faces, so be
// sure to select a sufficiently large value for `slices` and `refine`. Note that for
// this method, `sampling` must be set to `"segment"`, and hence this is the default setting.
// Using sampling by length would ignore the repeated vertices and ruin the alignment.
// Using sampling by length would ignore the repeated vertices and ruin the alignment.
// The "fast_distance" method is similar to "distance", but it makes the assumption that an edge should
// connect the first vertices of the two polygons. This reduces the run time to O(N^2) and makes
// the method usable on profiles with more points if you take care to index the inputs to match.
// .
// The `"tangent"` method generally produces good results when
// connecting a discrete polygon to a convex, finely sampled curve. It works by finding
@ -104,7 +107,9 @@
// polygon using triangular faces. Using `refine` with this method will have little effect on the model, so
// you should do it only for agreement with other profiles, and these models are linear, so extra slices also
// have no effect. For best efficiency set `refine=1` and `slices=0`. As with the "distance" method, refinement
// must be done using the "segment" sampling scheme to preserve alignment across duplicated points.
// must be done using the "segment" sampling scheme to preserve alignment across duplicated points.
// Note that the "tangent" method produces similar results to the "distance" method on curved inputs. If this
// method fails due to concavity, "fast_distance" may be a good option.
// .
// It is possible to specify `method` and `refine` as arrays, but it is important to observe
// matching rules when you do this. If a pair of profiles is connected using "tangent" or "distance"
@ -119,11 +124,11 @@
// profiles = list of 2d or 3d profiles to be skinned. (If 2d must also give `z`.)
// slices = scalar or vector number of slices to insert between each pair of profiles. Set to zero to use only the profiles you provided. Recommend starting with a value around 10.
// ---
// refine = resample profiles to this number of points per edge. Can be a list to give a refinement for each profile. Recommend using a value above 10 when using the "distance" method. Default: 1.
// sampling = sampling method to use with "direct" and "reindex" methods. Can be "length" or "segment". Ignored if any profile pair uses either the "distance" or "tangent" methods. Default: "length".
// refine = resample profiles to this number of points per edge. Can be a list to give a refinement for each profile. Recommend using a value above 10 when using the "distance" or "fast_distance" methods. Default: 1.
// sampling = sampling method to use with "direct" and "reindex" methods. Can be "length" or "segment". Ignored if any profile pair uses either the "distance", "fast_distance", or "tangent" methods. Default: "length".
// closed = set to true to connect first and last profile (to make a torus). Default: false
// caps = true to create endcap faces when closed is false. Can be a length 2 boolean array. Default is true if closed is false.
// method = method for connecting profiles, one of "distance", "tangent", "direct" or "reindex". Default: "direct".
// method = method for connecting profiles, one of "distance", "fast_distance", "tangent", "direct" or "reindex". Default: "direct".
// z = array of height values for each profile if the profiles are 2d
// convexity = convexity setting for use with polyhedron. (module only) Default: 10
// anchor = Translate so anchor point is at the origin. (module only) Default: "origin"
@ -374,7 +379,7 @@ function skin(profiles, slices, refine=1, method="direct", sampling, caps, close
assert(len(bad)==0, str("Profiles ",bad," are not a paths or have length less than 3"))
let(
profcount = len(profiles) - (closed?0:1),
legal_methods = ["direct","reindex","distance","tangent"],
legal_methods = ["direct","reindex","distance","fast_distance","tangent"],
caps = is_def(caps) ? caps :
closed ? false : true,
capsOK = is_bool(caps) || (is_list(caps) && len(caps)==2 && is_bool(caps[0]) && is_bool(caps[1])),
@ -402,7 +407,7 @@ function skin(profiles, slices, refine=1, method="direct", sampling, caps, close
assert(methodlistok==[], str("method list contains invalid method at ",methodlistok))
assert(len(method) == profcount,"Method list is the wrong length")
assert(in_list(sampling,["length","segment"]), "sampling must be set to \"length\" or \"segment\"")
assert(sampling=="segment" || (!in_list("distance",method) && !in_list("tangent",method)), "sampling is set to \"length\" which is only allowed iwith methods \"direct\" and \"reindex\"")
assert(sampling=="segment" || (!in_list("distance",method) && !in_list("fast_distance",method) && !in_list("tangent",method)), "sampling is set to \"length\" which is only allowed with methods \"direct\" and \"reindex\"")
assert(capsOK, "caps must be boolean or a list of two booleans")
assert(!closed || !caps, "Cannot make closed shape with caps")
let(
@ -449,6 +454,7 @@ function skin(profiles, slices, refine=1, method="direct", sampling, caps, close
let(
pair =
method[i]=="distance" ? _skin_distance_match(profiles[i],select(profiles,i+1)) :
method[i]=="fast_distance" ? _skin_aligned_distance_match(profiles[i], select(profiles,i+1)) :
method[i]=="tangent" ? _skin_tangent_match(profiles[i],select(profiles,i+1)) :
/*method[i]=="reindex" || method[i]=="direct" ?*/
let( p1 = subdivide_path(profiles[i],max_list[i], method=sampling),
@ -720,6 +726,23 @@ function _skin_distance_match(poly1,poly2) =
)
swap ? [newbig, newsmall] : [newsmall,newbig];
// This function associates vertices but with the assumption that index 0 is associated between the
// two inputs. This gives only quadratic run time. As above, output is pair of polygons with
// vertices duplicated as suited to use as input to skin().
function _skin_aligned_distance_match(poly1, poly2) =
let(
result = _dp_distance_array(poly1, poly2, abort_thresh=1/0),
map = _dp_extract_map(result[1]),
shift0 = len(map[0]) - max(max_index(map[0],all=true))-1,
shift1 = len(map[1]) - max(max_index(map[1],all=true))-1,
new0 = polygon_shift(repeat_entries(poly1,unique_count(map[0])[1]),shift0),
new1 = polygon_shift(repeat_entries(poly2,unique_count(map[1])[1]),shift1)
)
[new0,new1];
//////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// Internal Function: _skin_tangent_match()
/// Usage:
@ -927,7 +950,7 @@ module sweep(shape, transforms, closed=false, caps, convexity=10,
// path_sweep(shape, path, <method>, <normal=>, <closed=>, <twist=>, <twist_by_length=>, <symmetry=>, <last_normal=>, <tangent=>, <relaxed=>, <caps=>, <convexity=>, <transforms=>, <anchor=>, <cp=>, <spin=>, <orient=>, <extent=>) <attachments>;
// vnf = path_sweep(shape, path, <method>, <normal=>, <closed=>, <twist=>, <twist_by_length=>, <symmetry=>, <last_normal=>, <tangent=>, <relaxed=>, <caps=>, <convexity=>, <transforms=>);
// Description:
// Takes as input a 2D polygon path or region, and a 2d or 3d path and constructs a polyhedron by sweeping the shape along the path.
// Takes as input a 2D polygon path, and a 2d or 3d path and constructs a polyhedron by sweeping the shape along the path.
// When run as a module returns the polyhedron geometry. When run as a function returns a VNF by default or if you set `transforms=true`
// then it returns a list of transformations suitable as input to `sweep`.
// .
@ -1206,6 +1229,18 @@ module sweep(shape, transforms, closed=false, caps, convexity=10,
// outside = [for(i=[0:len(trans)-1]) trans[i]*scale(lerp(1,1.5,i/(len(trans)-1)))];
// inside = [for(i=[len(trans)-1:-1:0]) trans[i]*scale(lerp(1.1,1.4,i/(len(trans)-1)))];
// sweep(shape, concat(outside,inside),closed=true);
// Example: Using path_sweep on a region
// rgn1 = [for (d=[10:10:60]) circle(d=d,$fn=8)];
// rgn2 = [square(30,center=false)];
// rgn3 = [for (size=[10:10:20]) move([15,15],p=square(size=size, center=true))];
// mrgn = union(rgn1,rgn2);
// orgn = difference(mrgn,rgn3);
// path_sweep(orgn,arc(r=40,angle=180));
// Example: A region with a twist
// region = [for(i=pentagon(5)) move(i,p=circle(r=2,$fn=25))];
// path_sweep(region,
// circle(r=16,$fn=75),closed=true,
// twist=360/5*2,symmetry=5);
module path_sweep(shape, path, method="incremental", normal, closed=false, twist=0, twist_by_length=true,
symmetry=1, last_normal, tangent, relaxed=false, caps, convexity=10,
anchor="origin",cp,spin=0, orient=UP, extent=false)
@ -1225,7 +1260,7 @@ function path_sweep(shape, path, method="incremental", normal, closed=false, twi
assert(!closed || twist % (360/symmetry)==0, str("For a closed sweep, twist must be a multiple of 360/symmetry = ",360/symmetry))
assert(closed || symmetry==1, "symmetry must be 1 when closed is false")
assert(is_integer(symmetry) && symmetry>0, "symmetry must be a positive integer")
assert(is_path(shape,2) || is_region(shape), "shape must be a 2d path or region.")
// let(shape = check_and_fix_path(shape,valid_dim=2,closed=true,name="shape"))
assert(is_path(path), "input path is not a path")
assert(!closed || !approx(path[0],select(path,-1)), "Closed path includes start point at the end")
let(
@ -1301,15 +1336,15 @@ function path_sweep(shape, path, method="incremental", normal, closed=false, twi
translate(path[i%L])*rotation*zrot(-twist*pathfrac[i])
] :
assert(false,"Unknown method or no method given")[], // unknown method
ends_match = !closed ? true :
let(
start = apply(transform_list[0],path3d(shape)),
end = reindex_polygon(start, apply(transform_list[L],path3d(shape)))
)
all([for(i=idx(start)) approx(start[i],end[i])]),
ends_match = !closed ? true
: let( rshape = is_path(shape) ? [path3d(shape)]
: [for(s=shape) path3d(s)]
)
regions_equal(apply(transform_list[0], rshape),
apply(transform_list[L], rshape)),
dummy = ends_match ? 0 : echo("WARNING: ***** The points do not match when closing the model *****")
)
transforms ? transform_list : sweep(clockwise_polygon(shape), transform_list, closed=false, caps=fullcaps);
transforms ? transform_list : sweep(is_path(shape)?clockwise_polygon(shape):shape, transform_list, closed=false, caps=fullcaps);
// Function&Module: path_sweep2d()
@ -1361,7 +1396,8 @@ function path_sweep2d(shape, path, closed=false, caps, quality=1) =
caps = is_def(caps) ? caps
: closed ? false : true,
capsOK = is_bool(caps) || (is_list(caps) && len(caps)==2 && is_bool(caps[0]) && is_bool(caps[1])),
fullcaps = is_bool(caps) ? [caps,caps] : caps
fullcaps = is_bool(caps) ? [caps,caps] : caps,
shape = check_and_fix_path(shape,valid_dim=2,closed=true,name="shape")
)
assert(capsOK, "caps must be boolean or a list of two booleans")
assert(!closed || !caps, "Cannot make closed shape with caps")

75
tests/test_math.scad
View file

@ -824,19 +824,78 @@ module test_lcm() {
test_lcm();
module test_C_times() {
assert_equal(C_times([4,5],[9,-4]), [56,29]);
assert_equal(C_times([-7,2],[24,3]), [-174, 27]);
module test_c_mul() {
assert_equal(c_mul([4,5],[9,-4]), [56,29]);
assert_equal(c_mul([-7,2],[24,3]), [-174, 27]);
assert_equal(c_mul([3,4], [[3,-7], [4,9], [4,8]]), [[37,-9],[-24,43], [-20,40]]);
assert_equal(c_mul([[3,-7], [4,9], [4,8]], [[1,1],[3,4],[-3,4]]), [-58,31]);
M = [
[ [3,4], [9,-1], [4,3] ],
[ [2,9], [4,9], [3,-1] ]
];
assert_equal(c_mul(M, [ [3,4], [4,4],[5,5]]), [[38,91], [-30, 97]]);
assert_equal(c_mul([[4,4],[9,1]], M), [[5,111],[67,117], [32,22]]);
assert_equal(c_mul(M,transpose(M)), [ [[80,30], [30, 117]], [[30,117], [-134, 102]]]);
assert_equal(c_mul(transpose(M),M), [ [[-84,60],[-42,87],[15,50]], [[-42,87],[15,54],[60,46]], [[15,50],[60,46],[15,18]]]);
}
test_C_times();
test_c_mul();
module test_C_div() {
assert_equal(C_div([56,29],[9,-4]), [4,5]);
assert_equal(C_div([-174,27],[-7,2]), [24,3]);
module test_c_div() {
assert_equal(c_div([56,29],[9,-4]), [4,5]);
assert_equal(c_div([-174,27],[-7,2]), [24,3]);
}
test_C_div();
test_c_div();
module test_c_conj(){
assert_equal(c_conj([3,4]), [3,-4]);
assert_equal(c_conj( [ [2,9], [4,9], [3,-1] ]), [ [2,-9], [4,-9], [3,1] ]);
M = [
[ [3,4], [9,-1], [4,3] ],
[ [2,9], [4,9], [3,-1] ]
];
Mc = [
[ [3,-4], [9,1], [4,-3] ],
[ [2,-9], [4,-9], [3,1] ]
];
assert_equal(c_conj(M), Mc);
}
test_c_conj();
module test_c_real(){
M = [
[ [3,4], [9,-1], [4,3] ],
[ [2,9], [4,9], [3,-1] ]
];
assert_equal(c_real(M), [[3,9,4],[2,4,3]]);
assert_equal(c_real( [ [3,4], [9,-1], [4,3] ]), [3,9,4]);
assert_equal(c_real([3,4]),3);
}
test_c_real();
module test_c_imag(){
M = [
[ [3,4], [9,-1], [4,3] ],
[ [2,9], [4,9], [3,-1] ]
];
assert_equal(c_imag(M), [[4,-1,3],[9,9,-1]]);
assert_equal(c_imag( [ [3,4], [9,-1], [4,3] ]), [4,-1,3]);
assert_equal(c_imag([3,4]),4);
}
test_c_imag();
module test_c_ident(){
assert_equal(c_ident(3), [[[1, 0], [0, 0], [0, 0]], [[0, 0], [1, 0], [0, 0]], [[0, 0], [0, 0], [1, 0]]]);
}
test_c_ident();
module test_c_norm(){
assert_equal(c_norm([3,4]), 5);
assert_approx(c_norm([[3,4],[5,6]]), 9.273618495495704);
}
test_c_norm();
module test_back_substitute(){
R = [[12,4,3,2],