openscad/BOSL2
1
0
Fork 0
mirror of https://github.com/revarbat/BOSL2.git synced 2025-08-12 02:44:25 +02:00
Code Issues Projects Releases Wiki Activity

Merge pull request #1657 from amatulic/general_dev

Browse Source 
Added v_round() to vectors.scad
This commit is contained in:
adrianVmariano
2025-04-28 18:54:26 -04:00
committed by GitHub
parent 7e89f0021e 699b109767
commit a053a0c332
1 changed files with 85 additions and 72 deletions
Download Patch File Download Diff File Expand all files Collapse all files

157
vectors.scad
View File

@@ -58,7 +58,7 @@ function is_vector(v, length, zero, all_nonzero=false, eps=EPSILON) =
// Function: add_scalar()
// Synopsis: Adds a scalar value to every item in a vector.
// Topics: Vectors, Math
// See Also: add_scalar(), v_mul(), v_div()
// See Also: v_mul(), v_div()
// Usage:
// v_new = add_scalar(v, s);
// Description:
@@ -69,35 +69,35 @@ function is_vector(v, length, zero, all_nonzero=false, eps=EPSILON) =
// Example:
// a = add_scalar([1,2,3],3); // Returns: [4,5,6]
function add_scalar(v,s) =
assert(is_vector(v), "Input v must be a vector")
assert(is_finite(s), "Input s must be a finite scalar")
assert(is_vector(v), "\nInput v must be a vector.")
assert(is_finite(s), "\nInput s must be a finite scalar.")
[for(entry=v) entry+s];
// Function: v_mul()
// Synopsis: Returns the element-wise multiplication of two equal-length vectors.
// Topics: Vectors, Math
// See Also: add_scalar(), v_mul(), v_div()
// See Also: add_scalar(), v_div()
// Usage:
// v3 = v_mul(v1, v2);
// Description:
// Element-wise multiplication. Multiplies each element of `v1` by the corresponding element of `v2`.
// Both `v1` and `v2` must be the same length. Returns a vector of the products. Note that
// the items in `v1` and `v2` can be anything that OpenSCAD will multiply.
// Both `v1` and `v2` must be the same length. Returns a vector of the products.
// The items in `v1` and `v2` can be anything that OpenSCAD can multiply together.
// Arguments:
// v1 = The first vector.
// v2 = The second vector.
// Example:
// v_mul([3,4,5], [8,7,6]); // Returns [24, 28, 30]
function v_mul(v1, v2) =
assert( is_list(v1) && is_list(v2) && len(v1)==len(v2), "Incompatible input")
assert( is_list(v1) && is_list(v2) && len(v1)==len(v2), "\nIncompatible input.")
[for (i = [0:1:len(v1)-1]) v1[i]*v2[i]];
// Function: v_div()
// Synopsis: Returns the element-wise division of two equal-length vectors.
// Topics: Vectors, Math
// See Also: add_scalar(), v_mul(), v_div()
// See Also: add_scalar(), v_mul()
// Usage:
// v3 = v_div(v1, v2);
// Description:
@@ -109,14 +109,14 @@ function v_mul(v1, v2) =
// Example:
// v_div([24,28,30], [8,7,6]); // Returns [3, 4, 5]
function v_div(v1, v2) =
assert( is_vector(v1) && is_vector(v2,len(v1)), "Incompatible vectors")
assert( is_vector(v1) && is_vector(v2,len(v1)), "\nIncompatible vectors.")
[for (i = [0:1:len(v1)-1]) v1[i]/v2[i]];
// Function: v_abs()
// Synopsis: Returns the absolute values of the given vector.
// Topics: Vectors, Math
// See Also: v_abs(), v_floor(), v_ceil()
// See Also: v_ceil(), v_floor(), v_round()
// Usage:
// v2 = v_abs(v);
// Description: Returns a vector of the absolute value of each element of vector `v`.
@@ -125,40 +125,53 @@ function v_div(v1, v2) =
// Example:
// v_abs([-1,3,-9]); // Returns: [1,3,9]
function v_abs(v) =
assert( is_vector(v), "Invalid vector" )
assert( is_vector(v), "\nInvalid vector." )
[for (x=v) abs(x)];
// Function: v_floor()
// Synopsis: Returns the values of the given vector, rounded down.
// Topics: Vectors, Math
// See Also: v_abs(), v_floor(), v_ceil()
// Usage:
// v2 = v_floor(v);
// Description:
// Returns the given vector after performing a `floor()` on all items.
function v_floor(v) =
assert( is_vector(v), "Invalid vector" )
[for (x=v) floor(x)];
// Function: v_ceil()
// Synopsis: Returns the values of the given vector, rounded up.
// Topics: Vectors, Math
// See Also: v_abs(), v_floor(), v_ceil()
// See Also: v_abs(), v_floor(), v_round()
// Usage:
// v2 = v_ceil(v);
// Description:
// Returns the given vector after performing a `ceil()` on all items.
function v_ceil(v) =
assert( is_vector(v), "Invalid vector" )
assert(is_vector(v), "\nInvalid vector." )
[for (x=v) ceil(x)];
// Function: v_floor()
// Synopsis: Returns the values of the given vector, rounded down.
// Topics: Vectors, Math
// See Also: v_abs(), v_ceil(), v_round()
// Usage:
// v2 = v_floor(v);
// Description:
// Returns the given vector after performing a `floor()` on all items.
function v_floor(v) =
assert(is_vector(v), "\nInvalid vector." )
[for (x=v) floor(x)];
// Function: v_round()
// Synopsis: Returns the values of the given vector, rounded to the nearest whole number.
// Topics: Vectors, Math
// See Also: v_abs(), v_floor(), v_ceil()
// Usage:
// v2 = v_round(v);
// Description:
// Returns the given vector after performing a `round()` on all items.
function v_round(v) =
assert(is_vector(v), "\nInvalid vector." )
[for (x=v) round(x)];
// Function: v_lookup()
// Synopsis: Like `lookup()`, but it can interpolate between vector results.
// Topics: Vectors, Math
// See Also: v_abs(), v_floor(), v_ceil()
// See Also: v_abs(), v_floor(), v_ceil(), v_round()
// Usage:
// v2 = v_lookup(x, v);
// Description:
@@ -178,8 +191,8 @@ function v_lookup(x, v) =
hi = vhi[1]
)
assert(is_vector(lo) && is_vector(hi),
"Result values must all be numbers, or all be vectors.")
assert(len(lo) == len(hi), "Vector result values must be the same length")
"\nResult values must all be numbers, or all be vectors.")
assert(len(lo) == len(hi), "\nVector result values must be the same length.")
vlo.x == vhi.x? vlo[1] :
let( u = (x - vlo.x) / (vhi.x - vlo.x) )
lerp(lo,hi,u);
@@ -191,7 +204,7 @@ function v_lookup(x, v) =
// Function: unit()
// Synopsis: Returns the unit length of a given vector.
// Topics: Vectors, Math
// See Also: v_abs(), v_floor(), v_ceil()
// See Also: v_abs(), v_floor(), v_ceil(), v_round()
// Usage:
// v = unit(v, [error]);
// Description:
@@ -208,8 +221,8 @@ function v_lookup(x, v) =
// v5 = unit([0,0,0],[1,2,3]); // Returns: [1,2,3]
// v6 = unit([0,0,0]); // Asserts an error.
function unit(v, error=[[["ASSERT"]]]) =
assert(is_vector(v), "Invalid vector")
norm(v)<EPSILON? (error==[[["ASSERT"]]]? assert(norm(v)>=EPSILON,"Cannot normalize a zero vector") : error) :
assert(is_vector(v), "\nInvalid vector.")
norm(v)<EPSILON? (error==[[["ASSERT"]]]? assert(norm(v)>=EPSILON,"\nCannot normalize a zero vector.") : error) :
v/norm(v);
@@ -222,7 +235,7 @@ function unit(v, error=[[["ASSERT"]]]) =
// Description:
// Given a vector, returns the angle in degrees counter-clockwise from X+ on the XY plane.
function v_theta(v) =
assert( is_vector(v,2) || is_vector(v,3) , "Invalid vector")
assert( is_vector(v,2) || is_vector(v,3) , "\nInvalid vector.")
atan2(v.y,v.x);
@@ -255,19 +268,19 @@ function v_theta(v) =
function vector_angle(v1,v2,v3) =
assert( ( is_undef(v3) && ( is_undef(v2) || same_shape(v1,v2) ) )
|| is_consistent([v1,v2,v3]) ,
"Bad arguments.")
assert( is_vector(v1) || is_consistent(v1), "Bad arguments.")
"\nBad arguments.")
assert( is_vector(v1) || is_consistent(v1), "\nBad arguments.")
let( vecs = ! is_undef(v3) ? [v1-v2,v3-v2] :
! is_undef(v2) ? [v1,v2] :
len(v1) == 3 ? [v1[0]-v1[1], v1[2]-v1[1]]
: v1
)
assert(is_vector(vecs[0],2) || is_vector(vecs[0],3), "Bad arguments.")
assert(is_vector(vecs[0],2) || is_vector(vecs[0],3), "\nBad arguments.")
let(
norm0 = norm(vecs[0]),
norm1 = norm(vecs[1])
)
assert(norm0>0 && norm1>0, "Zero length vector.")
assert(norm0>0 && norm1>0, "\nZero length vector.")
// NOTE: constrain() corrects crazy FP rounding errors that exceed acos()'s domain.
acos(constrain((vecs[0]*vecs[1])/(norm0*norm1), -1, 1));
@@ -299,16 +312,16 @@ function vector_angle(v1,v2,v3) =
// axis6 = vector_axis([[10,0,10], [0,0,0], [-10,10,0]]); // Returns: [-0.57735, -0.57735, 0.57735]
function vector_axis(v1,v2=undef,v3=undef) =
is_vector(v3)
? assert(is_consistent([v3,v2,v1]), "Bad arguments.")
? assert(is_consistent([v3,v2,v1]), "\nBad arguments.")
vector_axis(v1-v2, v3-v2)
: assert( is_undef(v3), "Bad arguments.")
: assert( is_undef(v3), "\nBad arguments.")
is_undef(v2)
? assert( is_list(v1), "Bad arguments.")
? assert( is_list(v1), "\nBad arguments.")
len(v1) == 2
? vector_axis(v1[0],v1[1])
: vector_axis(v1[0],v1[1],v1[2])
: assert( is_vector(v1,zero=false) && is_vector(v2,zero=false) && is_consistent([v1,v2])
, "Bad arguments.")
, "\nBad arguments.")
let(
eps = 1e-6,
w1 = point3d(v1/norm(v1)),
@@ -331,9 +344,9 @@ function vector_axis(v1,v2=undef,v3=undef) =
function vector_bisect(v1,v2) =
assert(is_vector(v1))
assert(is_vector(v2))
assert(!approx(norm(v1),0), "Zero length vector.")
assert(!approx(norm(v2),0), "Zero length vector.")
assert(len(v1)==len(v2), "Vectors are of different sizes.")
assert(!approx(norm(v1),0), "\nZero length vector.")
assert(!approx(norm(v2),0), "\nZero length vector.")
assert(len(v1)==len(v2), "\nVectors are of different sizes.")
let( v1 = unit(v1), v2 = unit(v2) )
approx(v1,-v2)? undef :
let(
@@ -360,7 +373,7 @@ function vector_bisect(v1,v2) =
// stroke([[0,0],w],endcap2="arrow2",color="red");
// stroke([[0,0],vector_perp(v,w)], endcap2="arrow2", color="blue");
function vector_perp(v,w) =
assert(is_vector(v) && is_vector(w) && len(v)==len(w), "Invalid or mismatched inputs")
assert(is_vector(v) && is_vector(w) && len(v)==len(w), "\nInvalid or mismatched inputs")
w - w*v*v/(v*v);
@@ -370,7 +383,7 @@ function vector_perp(v,w) =
// Function: pointlist_bounds()
// Synopsis: Returns the min and max bounding coordinates for the given list of points.
// Topics: Geometry, Bounding Boxes, Bounds
// See Also: closest_point(), vnf_bounds()
// See Also: closest_point(), furthest_point(), vnf_bounds()
// Usage:
// pt_pair = pointlist_bounds(pts);
// Description:
@@ -380,7 +393,7 @@ function vector_perp(v,w) =
// Arguments:
// pts = List of points.
function pointlist_bounds(pts) =
assert(is_path(pts,dim=undef,fast=true) , "Invalid pointlist." )
assert(is_path(pts,dim=undef,fast=true) , "\nInvalid pointlist." )
let(
select = ident(len(pts[0])),
spread = [
@@ -395,7 +408,7 @@ function pointlist_bounds(pts) =
// Function: closest_point()
// Synopsis: Finds the closest point in a list of points.
// Topics: Geometry, Points, Distance
// See Also: pointlist_bounds(), furthest_point(), closest_point()
// See Also: pointlist_bounds(), furthest_point()
// Usage:
// index = closest_point(pt, points);
// Description:
@@ -404,15 +417,15 @@ function pointlist_bounds(pts) =
// pt = The point to find the closest point to.
// points = The list of points to search.
function closest_point(pt, points) =
assert( is_vector(pt), "Invalid point." )
assert(is_path(points,dim=len(pt)), "Invalid pointlist or incompatible dimensions." )
assert( is_vector(pt), "\nInvalid point." )
assert(is_path(points,dim=len(pt)), "\nInvalid pointlist or incompatible dimensions." )
min_index([for (p=points) norm(p-pt)]);
// Function: furthest_point()
// Synopsis: Finds the furthest point in a list of points.
// Topics: Geometry, Points, Distance
// See Also: pointlist_bounds(), furthest_point(), closest_point()
// See Also: pointlist_bounds(), closest_point()
// Usage:
// index = furthest_point(pt, points);
// Description:
@@ -421,8 +434,8 @@ function closest_point(pt, points) =
// pt = The point to find the farthest point from.
// points = The list of points to search.
function furthest_point(pt, points) =
assert( is_vector(pt), "Invalid point." )
assert(is_path(points,dim=len(pt)), "Invalid pointlist or incompatible dimensions." )
assert( is_vector(pt), "\nInvalid point." )
assert(is_path(points,dim=len(pt)), "\nInvalid pointlist or incompatible dimensions." )
max_index([for (p=points) norm(p-pt)]);
@@ -436,7 +449,7 @@ function furthest_point(pt, points) =
// Given a list of query points `query` and a `target` to search,
// finds the points in `target` that match each query point. A match holds when the
// distance between a point in `target` and a query point is less than or equal to `r`.
// The returned list will have a list for each query point containing, in arbitrary
// The returned list contains a list for each query point containing, in arbitrary
// order, the indices of all points that match that query point.
// The `target` may be a simple list of points or a search tree.
// When `target` is a large list of points, a search tree is constructed to
@@ -444,8 +457,8 @@ function furthest_point(pt, points) =
// For small point lists, a direct search is done dispensing a tree construction.
// Alternatively, `target` may be a search tree built with `vector_search_tree()`.
// In that case, that tree is parsed looking for matches.
// An empty list of query points will return a empty output list.
// An empty list of target points will return a output list with an empty list for each query point.
// An empty list of query points returns a empty output list.
// An empty list of target points returns a output list with an empty list for each query point.
// Arguments:
// query = list of points to find matches for.
// r = the search radius.
@@ -485,7 +498,7 @@ function vector_search(query, r, target) =
query==[] ? [] :
is_list(query) && target==[] ? is_vector(query) ? [] : [for(q=query) [] ] :
assert( is_finite(r) && r>=0,
"The query radius should be a positive number." )
"\nThe query radius should be a positive number." )
let(
tgpts = is_matrix(target), // target is a point list
tgtree = is_list(target) // target is a tree
@@ -495,13 +508,13 @@ function vector_search(query, r, target) =
&& (len(target[1])==4 || (len(target[1])==1 && is_list(target[1][0])) )
)
assert( tgpts || tgtree,
"The target should be a list of points or a search tree compatible with the query." )
"\nThe target should be a list of points or a search tree compatible with the query." )
let(
dim = tgpts ? len(target[0]) : len(target[0][0]),
simple = is_vector(query, dim)
)
assert( simple || is_matrix(query,undef,dim),
"The query points should be a list of points compatible with the target point list.")
"\nThe query points should be a list of points compatible with the target point list.")
tgpts
? len(target)<=400
? simple ? [for(i=idx(target)) if(norm(target[i]-query)<=r) i ] :
@@ -518,9 +531,9 @@ function _bt_search(query, r, points, tree) =
assert( is_list(tree)
&& ( ( len(tree)==1 && is_list(tree[0]) )
|| ( len(tree)==4 && is_num(tree[0]) && is_num(tree[1]) ) ),
"The tree is invalid.")
"\nThe tree is invalid.")
len(tree)==1
? assert( tree[0]==[] || is_vector(tree[0]), "The tree is invalid." )
? assert( tree[0]==[] || is_vector(tree[0]), "\nThe tree is invalid." )
[for(i=tree[0]) if(norm(points[i]-query)<=r) i ]
: norm(query-points[tree[0]]) > r+tree[1] ? [] :
concat(
@@ -541,14 +554,14 @@ function _bt_search(query, r, points, tree) =
// search process. The tree construction stops branching when
// a tree node represents a number of points less or equal to `leafsize`.
// Search trees are ball trees. Constructing the
// tree should be O(n log n) and searches should be O(log n), though real life
// performance depends on how the data is distributed, and it will deteriorate
// for high data dimensions. This data structure is useful when you will be
// tree should be O(n log n) and searches should be O(log n), although real life
// performance depends on how the data is distributed, and it deteriorates
// for high data dimensions. This data structure is useful when you are
// performing many searches of the same data, so that the cost of constructing
// the tree is justified. (See https://en.wikipedia.org/wiki/Ball_tree)
// For a small lists of points, the search with a tree may be more expensive
// than direct comparisons. The argument `treemin` sets the minimum length of
// point set for which a tree search will be done by `vector_search`.
// the point set for which a tree search will be done by `vector_search`.
// For an empty list of points it returns an empty list.
// Arguments:
// points = list of points to store in the search tree.
@@ -568,9 +581,9 @@ function _bt_search(query, r, points, tree) =
// }
function vector_search_tree(points, leafsize=25, treemin=400) =
points==[] ? [] :
assert( is_matrix(points), "The input list entries should be points." )
assert( is_matrix(points), "\nThe input list entries should be points." )
assert( is_int(leafsize) && leafsize>=1,
"The tree leaf size should be an integer greater than zero.")
"\nThe tree leaf size should be an integer greater than zero.")
len(points)<treemin ? points :
[ points, _bt_tree(points, count(len(points)), leafsize) ];
@@ -621,7 +634,7 @@ function _bt_tree(points, ind, leafsize=25) =
// }
function vector_nearest(query, k, target) =
assert(is_int(k) && k>0)
assert(is_vector(query), "Query must be a vector.")
assert(is_vector(query), "\nQuery must be a vector.")
let(
tgpts = is_matrix(target,undef,len(query)), // target is a point list
tgtree = is_list(target) // target is a tree
@@ -630,9 +643,9 @@ function vector_nearest(query, k, target) =
&& (len(target[1])==4 || (len(target[1])==1 && is_list(target[1][0])) )
)
assert( tgpts || tgtree,
"The target should be a list of points or a search tree compatible with the query." )
"\nThe target should be a list of points or a search tree compatible with the query." )
assert((tgpts && (k<=len(target))) || (tgtree && (k<=len(target[0]))),
"More results are requested than the number of points.")
"\nMore results are requested than the number of points.")
tgpts
? let( tree = _bt_tree(target, count(len(target))) )
column(_bt_nearest( query, k, target, tree),0)
@@ -644,7 +657,7 @@ function _bt_nearest(p, k, points, tree, answers=[]) =
assert( is_list(tree)
&& ( ( len(tree)==1 && is_list(tree[0]) )
|| ( len(tree)==4 && is_num(tree[0]) && is_num(tree[1]) ) ),
"The tree is invalid.")
"\nThe tree is invalid.")
len(tree)==1
? _insert_many(answers, k, [for(entry=tree[0]) [entry, norm(points[entry]-p)]])
: let( d = norm(p-points[tree[0]]) )
@@ -669,7 +682,7 @@ function _insert_sorted(list, k, new) =
function _insert_many(list, k, newlist,i=0) =
i==len(newlist)
? list
: assert(is_vector(newlist[i],2), "The tree is invalid.")
: assert(is_vector(newlist[i],2), "\nThe tree is invalid.")
_insert_many(_insert_sorted(list,k,newlist[i]),k,newlist,i+1);