mirror of
https://github.com/BelfrySCAD/BOSL2.git
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Revert "Review of geometry.scad for speed"
This reverts commit 49a3a166eb.
This commit is contained in:
RonaldoCMP
parent
49a3a166eb
commit
cdb68ad977
4 changed files with 52 additions and 95 deletions
12
arrays.scad
12
arrays.scad
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@ -42,7 +42,6 @@ function is_homogeneous(l, depth=10) =
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function is_homogenous(l, depth=10) = is_homogeneous(l, depth);
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function _same_type(a,b, depth) =
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(depth==0) ||
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(is_undef(a) && is_undef(b)) ||
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@ -98,6 +97,7 @@ function select(list, start, end) =
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// Function: slice()
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// Topics: List Handling
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// Usage:
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// list = slice(list,s,e);
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// Description:
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@ -476,7 +476,7 @@ function reverse(x) =
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// l9 = list_rotate([1,2,3,4,5],6); // Returns: [2,3,4,5,1]
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function list_rotate(list,n=1) =
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assert(is_list(list)||is_string(list), "Invalid list or string.")
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assert(is_int(n), "The rotation number should be integer")
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assert(is_finite(n), "Invalid number")
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let (
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ll = len(list),
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n = ((n % ll) + ll) % ll,
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@ -1332,8 +1332,6 @@ function permutations(l,n=2) =
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// pairs = zip(a,b);
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// triples = zip(a,b,c);
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// quads = zip([LIST1,LIST2,LIST3,LIST4]);
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// Topics: List Handling, Iteration
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// See Also: zip_long()
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// Description:
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// Zips together two or more lists into a single list. For example, if you have two
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// lists [3,4,5], and [8,7,6], and zip them together, you get [[3,8],[4,7],[5,6]].
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@ -1359,8 +1357,6 @@ function zip(a,b,c) =
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// pairs = zip_long(a,b);
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// triples = zip_long(a,b,c);
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// quads = zip_long([LIST1,LIST2,LIST3,LIST4]);
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// Topics: List Handling, Iteration
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// See Also: zip()
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// Description:
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// Zips together two or more lists into a single list. For example, if you have two
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// lists [3,4,5], and [8,7,6], and zip them together, you get [[3,8],[4,7],[5,6]].
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@ -1530,6 +1526,7 @@ function subindex(M, idx) =
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// [[4,2], 91, false],
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// [6, [3,4], undef]];
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// submatrix(A,[0,2],[1,2]); // Returns [[17, "test"], [[3, 4], undef]]
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function submatrix(M,idx1,idx2) =
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[for(i=idx1) [for(j=idx2) M[i][j] ] ];
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@ -1632,6 +1629,7 @@ function block_matrix(M) =
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assert(badrows==[], "Inconsistent or invalid input")
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bigM;
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// Function: diagonal_matrix()
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// Usage:
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// mat = diagonal_matrix(diag, <offdiag>);
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@ -1857,7 +1855,7 @@ function transpose(arr, reverse=false) =
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// A = matrix to test
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// eps = epsilon for comparing equality. Default: 1e-12
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function is_matrix_symmetric(A,eps=1e-12) =
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approx(A,transpose(A), eps);
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approx(A,transpose(A));
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// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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11
common.scad
11
common.scad
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@ -205,8 +205,7 @@ function is_func(x) = version_num()>20210000 && is_function(x);
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// Description:
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// Tests whether input is a list of entries which all have the same list structure
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// and are filled with finite numerical data. You can optionally specify a required
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// list structure with the pattern argument.
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// It returns `true` for the empty list regardless the value of the `pattern`.
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// list structure with the pattern argument. It returns `true` for the empty list.
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// Arguments:
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// list = list to check
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// pattern = optional pattern required to match
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@ -294,7 +293,7 @@ function default(v,dflt=undef) = is_undef(v)? dflt : v;
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// v = The list whose items are being checked.
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// recursive = If true, sublists are checked recursively for defined values. The first sublist that has a defined item is returned.
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// Examples:
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// val = first_defined([undef,7,undef,true]); // Returns: 7
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// val = first_defined([undef,7,undef,true]); // Returns: 1
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function first_defined(v,recursive=false,_i=0) =
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_i<len(v) && (
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is_undef(v[_i]) || (
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@ -606,15 +605,15 @@ function segs(r) =
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// Module: no_children()
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// Topics: Error Checking
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// Usage:
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// no_children($children);
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// Topics: Error Checking
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// See Also: no_function(), no_module()
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// Description:
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// Assert that the calling module does not support children. Prints an error message to this effect and fails if children are present,
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// as indicated by its argument.
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// Arguments:
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// $children = number of children the module has.
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// See Also: no_function(), no_module()
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// Example:
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// module foo() {
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// no_children($children);
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@ -677,7 +676,7 @@ function _valstr(x) =
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// expected = The value that was expected.
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// info = Extra info to print out to make the error clearer.
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// Example:
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// assert_approx(1/3, 0.333333333333333, str("number=",1,", demon=",3));
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// assert_approx(1/3, 0.333333333333333, str("numer=",1,", demon=",3));
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module assert_approx(got, expected, info) {
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no_children($children);
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if (!approx(got, expected)) {
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@ -889,57 +889,21 @@ function plane3pt_indexed(points, i1, i2, i3) =
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// plane_from_normal([0,0,1], [2,2,2]); // Returns the xy plane passing through the point (2,2,2)
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function plane_from_normal(normal, pt=[0,0,0]) =
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assert( is_matrix([normal,pt],2,3) && !approx(norm(normal),0),
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"Inputs `normal` and `pt` should be 3d vectors/points and `normal` cannot be zero." )
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"Inputs `normal` and `pt` should 3d vectors/points and `normal` cannot be zero." )
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concat(normal, normal*pt) / norm(normal);
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// Eigenvalues for a 3x3 symmetrical matrix in decreasing order
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// Based on: https://en.wikipedia.org/wiki/Eigenvalue_algorithm
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function _eigenvals_symm_3(M) =
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let( p1 = pow(M[0][1],2) + pow(M[0][2],2) + pow(M[1][2],2) )
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(p1<EPSILON)
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? -sort(-[ M[0][0], M[1][1], M[2][2] ]) // diagonal matrix: eigenvals in decreasing order
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: let( q = (M[0][0]+M[1][1]+M[2][2])/3,
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B = (M - q*ident(3)),
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dB = [B[0][0], B[1][1], B[2][2]],
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p2 = dB*dB + 2*p1,
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p = sqrt(p2/6),
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r = det3(B/p)/2,
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ph = acos(constrain(r,-1,1))/3,
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e1 = q + 2*p*cos(ph),
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e3 = q + 2*p*cos(ph+120),
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e2 = 3*q - e1 - e3 )
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[ e1, e2, e3 ];
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// i-th normalized eigenvector of 3x3 symmetrical matrix M from its eigenvalues
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// using Cayley–Hamilton theorem according to:
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// https://en.wikipedia.org/wiki/Eigenvalue_algorithm
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function _eigenvec_symm_3(M,evals,i=0) =
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let( A = (M - evals[(i+1)%3]*ident(3)) * (M - evals[(i+2)%3]*ident(3)) ,
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k = max_index( [for(i=[0:2]) norm(A[i]) ])
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)
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norm(A[k])<EPSILON ? ident(3)[k] : A[k]/norm(A[k]);
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// eigenvalues of the covariance matrix of points
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function _covariance_evals(points) =
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let( pm = sum(points)/len(points), // mean point
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Y = [ for(i=[0:len(points)-1]) points[i] - pm ],
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M = transpose(Y)*Y , // covariance matrix
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evals = _eigenvals_symm_3(M) )
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[pm, evals, M ];
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// Function: plane_from_points()
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// Usage:
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// plane_from_points(points, <fast>, <eps>);
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// Description:
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// Given a list of 3 or more coplanar 3D points, returns the coefficients of the normalized cartesian equation of a plane,
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// that is [A,B,C,D] where Ax+By+Cz=D is the equation of the plane where norm([A,B,C])=1.
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// If the points in the list are collinear or not coplanar, then `undef` is returned.
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// If `fast` is false and the points in the list are collinear or not coplanar, then `undef` is returned.
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// if `fast` is true, then the coplanarity test is skipped and a plane passing through 3 non-collinear arbitrary points is returned.
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// Arguments:
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// points = The list of points to find the plane of.
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// fast = If true, don't verify that all points in the list are coplanar. Default: false
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// eps = Tolerance in geometric comparisons. Default: `EPSILON` (1e-9)
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// Example(3D):
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// xyzpath = rot(45, v=[-0.3,1,0], p=path3d(star(n=6,id=70,d=100), 70));
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@ -950,18 +914,17 @@ function _covariance_evals(points) =
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function plane_from_points(points, fast=false, eps=EPSILON) =
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assert( is_path(points,dim=3), "Improper 3d point list." )
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assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
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len(points) == 3
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? let( plane = plane3pt(points[0],points[1],points[2]) )
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plane==[] ? undef : plane
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: let(
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cov_evals = _covariance_evals(points),
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pm = cov_evals[0],
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evals = cov_evals[1],
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M = cov_evals[2],
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evec = _eigenvec_symm_3(M,evals,i=2) )
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// echo(error_points_plane= abs(max(points*evec)-pm*evec), limit=eps)
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!fast && abs(max(points*evec)-pm*evec)>eps*evals[0] ? undef :
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[ each evec, pm*evec] ;
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let(
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indices = noncollinear_triple(points,error=false)
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)
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indices==[] ? undef :
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let(
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p1 = points[indices[0]],
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p2 = points[indices[1]],
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p3 = points[indices[2]],
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plane = plane3pt(p1,p2,p3)
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)
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fast || points_on_plane(points,plane,eps=eps) ? plane : undef;
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// Function: plane_from_polygon()
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@ -985,11 +948,12 @@ function plane_from_points(points,fast=false, eps=EPSILON) =
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function plane_from_polygon(poly, fast=false, eps=EPSILON) =
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assert( is_path(poly,dim=3), "Invalid polygon." )
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assert( is_finite(eps) && (eps>=0), "The tolerance should be a non-negative value." )
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len(poly)==3 ? plane3pt(poly[0],poly[1],poly[2]) :
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let( triple = sort(noncollinear_triple(poly,error=false)) )
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triple==[] ? [] :
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let( plane = plane3pt(poly[triple[0]],poly[triple[1]],poly[triple[2]]))
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fast? plane: points_on_plane(poly, plane, eps=eps)? plane: [];
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let(
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poly = deduplicate(poly),
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n = polygon_normal(poly),
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plane = [n.x, n.y, n.z, n*poly[0]]
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)
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fast? plane: coplanar(poly,eps=eps)? plane: [];
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// Function: plane_normal()
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@ -1288,11 +1252,9 @@ function coplanar(points, eps=EPSILON) =
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len(points)<=2 ? false
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: let( ip = noncollinear_triple(points,error=false,eps=eps) )
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ip == [] ? false :
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let(
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plane = plane3pt(points[ip[0]],points[ip[1]],points[ip[2]]),
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normal = point3d(plane),
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pt_nrm = points*normal )
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abs(max(max(pt_nrm)-plane[3], -min(pt_nrm)+plane[3])) < eps;
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let( plane = plane3pt(points[ip[0]],points[ip[1]],points[ip[2]]),
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normal = point3d(plane) )
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max( points*normal ) - plane[3]< eps*norm(normal);
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// Function: points_on_plane()
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@ -1703,7 +1665,7 @@ function noncollinear_triple(points,error=true,eps=EPSILON) =
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n = (pb-pa)/nrm,
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distlist = [for(i=[0:len(points)-1]) _dist2line(points[i]-pa, n)]
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)
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max(distlist)<eps*nrm
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max(distlist)<eps
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? assert(!error, "Cannot find three noncollinear points in pointlist.")
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[]
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: [0,b,max_index(distlist)];
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@ -1784,8 +1746,8 @@ function polygon_area(poly, signed=false) =
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v1 = poly[i] - poly[0],
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v2 = poly[i+1] - poly[0]
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)
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cross(v1,v2)
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])* n/2
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cross(v1,v2) * n
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])/2
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)
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signed ? total : abs(total);
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@ -1958,7 +1920,7 @@ function centroid(poly, eps=EPSILON) =
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let(
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n = len(poly[0])==2 ? 1 :
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let(
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plane = plane_from_points(poly) )
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plane = plane_from_points(poly, fast=true) )
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assert( !is_undef(plane), "The polygon must be planar." )
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plane_normal(plane),
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v0 = poly[0] ,
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@ -2046,7 +2008,7 @@ function point_in_polygon(point, poly, nonzero=true, eps=EPSILON) =
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// poly = The list of 2D path points for the perimeter of the polygon.
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function polygon_is_clockwise(poly) =
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assert(is_path(poly,dim=2), "Input should be a 2d path")
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polygon_area(poly, signed=true)<-EPSILON;
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polygon_area(poly, signed=true)<0;
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// Function: clockwise_polygon()
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@ -705,7 +705,7 @@ module test_plane3pt_indexed() {
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module test_plane_from_points() {
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assert_std(plane_from_points([[0,0,20], [0,10,10], [0,0,0], [0,5,3]]), [1,0,0,0]);
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assert_approx(plane_from_points([[2,0,20], [2,10,10], [2,0,0], [2,3,4]]), [1,0,0,2]);
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assert_std(plane_from_points([[2,0,20], [2,10,10], [2,0,0], [2,3,4]]), [1,0,0,2]);
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assert_std(plane_from_points([[0,0,0], [10,0,10], [0,0,20], [5,0,7]]), [0,1,0,0]);
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assert_std(plane_from_points([[0,2,0], [10,2,10], [0,2,20], [4,2,3]]), [0,1,0,2]);
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assert_std(plane_from_points([[0,0,0], [10,10,0], [20,0,0], [8,3,0]]), [0,0,1,0]);
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@ -836,9 +836,7 @@ module test_cleanup_path() {
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module test_polygon_area() {
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assert(approx(polygon_area([[1,1],[-1,1],[-1,-1],[1,-1]]), 4));
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assert(approx(polygon_area(circle(r=50,$fn=1000),signed=true), -PI*50*50, eps=0.1));
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assert(approx(polygon_area(rot([13,27,75],
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p=path3d(circle(r=50,$fn=1000),fill=23)),
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signed=true), -PI*50*50, eps=0.1));
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assert(approx(polygon_area(rot([13,27,75],p=path3d(circle(r=50,$fn=1000),fill=23)),signed=true), PI*50*50, eps=0.1));
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}
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*test_polygon_area();
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