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Moved path functions from geometry.scad to paths.scad
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Revar Desmera
154
paths.scad
154
paths.scad
@@ -252,6 +252,71 @@ function path_closest_point(path, pt) =
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) [min_seg, pts[min_seg]];
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// Function: path_tangents()
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// Usage: path_tangents(path, [closed])
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// Description:
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// Compute the tangent vector to the input path. The derivative approximation is described in deriv().
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// The returns vectors will be normalized to length 1.
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function path_tangents(path, closed=false) =
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assert(is_path(path))
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[for(t=deriv(path)) normalize(t)];
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// Function: path_normals()
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// Usage: path_normals(path, [tangents], [closed])
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// Description:
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// Compute the normal vector to the input path. This vector is perpendicular to the
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// path tangent and lies in the plane of the curve. When there are collinear points,
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// the curve does not define a unique plane and the normal is not uniquely defined.
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function path_normals(path, tangents, closed=false) =
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assert(is_path(path))
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assert(is_bool(closed))
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let( tangents = default(tangents, path_tangents(path,closed)) )
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assert(is_path(tangents))
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[
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for(i=idx(path)) let(
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pts = i==0? (closed? select(path,-1,1) : select(path,0,2)) :
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i==len(path)-1? (closed? select(path,i-1,i+1) : select(path,i-2,i)) :
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select(path,i-1,i+1)
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) normalize(cross(
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cross(pts[1]-pts[0], pts[2]-pts[0]),
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tangents[i]
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))
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];
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// Function: path_curvature()
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// Usage: path_curvature(path, [closed])
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// Description:
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// Numerically estimate the curvature of the path (in any dimension).
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function path_curvature(path, closed=false) =
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let(
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d1 = deriv(path, closed=closed),
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d2 = deriv2(path, closed=closed)
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) [
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for(i=idx(path))
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sqrt(
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sqr(norm(d1[i])*norm(d2[i])) -
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sqr(d1[i]*d2[i])
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) / pow(norm(d1[i]),3)
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];
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// Function: path_torsion()
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// Usage: path_torsion(path, [closed])
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// Description:
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// Numerically estimate the torsion of a 3d path.
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function path_torsion(path, closed=false) =
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let(
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d1 = deriv(path,closed=closed),
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d2 = deriv2(path,closed=closed),
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d3 = deriv3(path,closed=closed)
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) [
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for (i=idx(path)) let(
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crossterm = cross(d1[i],d2[i])
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) crossterm * d3[i] / sqr(norm(crossterm))
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];
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// Function: path3d_spiral()
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// Description:
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@@ -1091,12 +1156,14 @@ function _path_cuts_dir(path, cuts, closed=false, eps=1e-2) =
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// and passing the rounding error forward to the next entry.
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// This will generally distribute the error in a uniform manner.
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function _sum_preserving_round(data, index=0) =
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index == len(data)-1 ? list_set(data, len(data)-1, round(data[len(data)-1])) :
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let(
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newval = round(data[index]),
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error = newval - data[index]
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)
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_sum_preserving_round(list_set(data, [index,index+1], [newval, data[index+1]-error]), index+1);
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index == len(data)-1 ? list_set(data, len(data)-1, round(data[len(data)-1])) :
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let(
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newval = round(data[index]),
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error = newval - data[index]
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) _sum_preserving_round(
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list_set(data, [index,index+1], [newval, data[index+1]-error]),
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index+1
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);
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// Function: subdivide_path()
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@@ -1155,31 +1222,37 @@ function _sum_preserving_round(data, index=0) =
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// mypath = subdivide_path([[0,0,0],[2,0,1],[2,3,2]], 12);
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// place_copies(mypath)sphere(r=.1,$fn=32);
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function subdivide_path(path, N, closed=true, exact=true, method="length") =
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assert(is_path(path))
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assert(method=="length" || method=="segment")
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assert((is_num(N) && N>0) || is_vector(N),"Parameter N to subdivide_path must be postive number or vector")
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let(
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count = len(path) - (closed?0:1),
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add_guess =
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method=="segment" ?
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(is_list(N) ? assert(len(N)==count,"Vector parameter N to subdivide_path has the wrong length")
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add_scalar(N,-1)
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: replist((N-len(path)) / count, count))
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: // method=="length"
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assert(is_num(N),"Parameter N to subdivide path must be a number when method=\"length\"")
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let(
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path_lens = concat([for (i = [0:1:len(path)-2]) norm(path[i+1]-path[i])],
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closed?[norm(path[len(path)-1]-path[0])]:[]),
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add_density = (N - len(path)) / sum(path_lens)
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)
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path_lens * add_density,
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add = exact ? _sum_preserving_round(add_guess) : [for (val=add_guess) round(val)]
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)
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concat(
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[for (i=[0:1:count])
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each [for(j=[0:1:add[i]]) lerp(path[i],select(path,i+1), j/(add[i]+1))]],
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closed ? [] : [select(path,-1)]
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);
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assert(is_path(path))
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assert(method=="length" || method=="segment")
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assert((is_num(N) && N>0) || is_vector(N),"Parameter N to subdivide_path must be postive number or vector")
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let(
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count = len(path) - (closed?0:1),
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add_guess = method=="segment"? (
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is_list(N)? (
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assert(len(N)==count,"Vector parameter N to subdivide_path has the wrong length")
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add_scalar(N,-1)
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) : replist((N-len(path)) / count, count)
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) : // method=="length"
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assert(is_num(N),"Parameter N to subdivide path must be a number when method=\"length\"")
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let(
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path_lens = concat(
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[ for (i = [0:1:len(path)-2]) norm(path[i+1]-path[i]) ],
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closed? [norm(path[len(path)-1]-path[0])] : []
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),
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add_density = (N - len(path)) / sum(path_lens)
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)
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path_lens * add_density,
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add = exact? _sum_preserving_round(add_guess) :
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[for (val=add_guess) round(val)]
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) concat(
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[
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for (i=[0:1:count]) each [
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for(j=[0:1:add[i]])
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lerp(path[i],select(path,i+1), j/(add[i]+1))
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]
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],
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closed? [] : [select(path,-1)]
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);
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// Function: path_length_fractions()
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@@ -1190,14 +1263,17 @@ function subdivide_path(path, N, closed=true, exact=true, method="length") =
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// will have one extra point because of the final connecting segment that connects the last
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// point of the path to the first point.
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function path_length_fractions(path, closed=false) =
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assert(is_path(path))
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assert(is_bool(closed))
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let(
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lengths = [0, for(i=[0:1:len(path)-(closed?1:2)]) norm(select(path,i+1)-path[i])],
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partial_len = cumsum(lengths),
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total_len = select(partial_len,-1)
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)
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partial_len / total_len;
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assert(is_path(path))
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assert(is_bool(closed))
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let(
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lengths = [
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0,
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for (i=[0:1:len(path)-(closed?1:2)])
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norm(select(path,i+1)-path[i])
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],
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partial_len = cumsum(lengths),
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total_len = select(partial_len,-1)
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) partial_len / total_len;
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