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add exponential dist, IDENT constant
doc fixes
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3 changed files with 22 additions and 12 deletions
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@ -215,4 +215,9 @@ RAY = [true, false];
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LINE = [false, false];
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// Constant: IDENT
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// Description: Identity transformation matrix for three-dimensional transforms. Equal to `ident(4)`.
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IDENT=ident(4);
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// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
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21
math.scad
21
math.scad
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@ -567,17 +567,22 @@ function gaussian_rands(n=1, mean=0, cov=1, seed=undef) =
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move(mean,list_to_matrix(rdata,dim)*transpose(L));
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// Function: spherical_random_points()
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// Function: exponential_rands()
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// Usage:
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// points = spherical_random_points([n], [radius], [seed]);
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// See Also: random_polygon(), random_points()
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// Topics: Random, Points
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// arr = exponential_rands([n], [lambda], [seed])
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// Description:
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// Generate `n` 3D uniformly distributed random points lying on a sphere centered at the origin with radius equal to `radius`.
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// Returns random numbers with an exponential distribution with parameter lambda, and hence mean 1/lambda.
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// Arguments:
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// n = number of points to generate. Default: 1
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// radius = the sphere radius. Default: 1
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// seed = an optional seed for the random generation.
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// n = number of points to return. Default: 1
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// lambda = distribution parameter. The mean will be 1/lambda. Default: 1
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function exponential_rands(n=1, lambda=1, seed) =
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assert( is_int(n) && n>=1, "The number of points should be an integer greater than zero.")
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assert( is_num(lambda) && lambda>0, "The lambda parameter must be a positive number.")
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let(
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unif = is_def(seed) ? rands(0,1,n,seed=seed) : rands(0,1,n)
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)
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-(1/lambda) * [for(x=unif) ln(1-x)];
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// See https://mathworld.wolfram.com/SpherePointPicking.html
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function spherical_random_points(n=1, radius=1, seed) =
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@ -31,7 +31,7 @@ include <structs.scad>
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// .
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// For circular rounding you can use the `radius` or `r` parameter to set the rounding radius.
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// .
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// For chamfers you can use `length` to set the length of the chamfer.
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// For chamfers you can use `width` to set the width of the chamfer.
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// .
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// The "smooth" rounding method also has a parameter that specifies how smooth the curvature match is. This parameter, `k`,
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// ranges from 0 to 1, with a default of 0.5. Larger values gives a more
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@ -153,7 +153,7 @@ include <structs.scad>
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// away from the corner along the path where the roundover or chamfer should start. This makes it easy to ensure your roundover will fit,
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// so use it if you want the largest possible roundover.
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// * For circular rounding you can use the `radius` or `r` parameter to set the rounding radius.
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// * For chamfers you can use the `length` parameter, which sets the length of the chamfer edge.
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// * For chamfers you can use the `width` parameter, which sets the width of the chamfer edge.
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// .
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// As explained in [Types of Roundover](rounding.scad#subsection-types-of-roundover), the continuous curvature "smooth"
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// type of rounding also accepts the `k` parameter, between 0 and 1, which specifies how fast the curvature changes at
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@ -198,7 +198,7 @@ include <structs.scad>
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// radius/r = rounding radius, only compatible with `method="circle"`. Can be a number or vector.
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// cut = rounding cut distance, compatible with all methods. Can be a number or vector.
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// joint = rounding joint distance, compatible with `method="chamfer"` and `method="smooth"`. Can be a number or vector.
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// flat = length of the flat edge created by chamfering, compatible with `method="chamfer"`. Can be a number of vector.
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// width = width of the flat edge created by chamfering, compatible with `method="chamfer"`. Can be a number or vector.
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// k = continuous curvature smoothness parameter for `method="smooth"`. Can be a number or vector. Default: 0.5
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// closed = if true treat the path as a closed polygon, otherwise treat it as open. Default: true.
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// verbose = if true display rounding scale factors that show how close roundovers are to overlapping. Default: false
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@ -321,7 +321,7 @@ include <structs.scad>
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// path_len = path_segment_lengths(path,closed=true);
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// halflen = [for(i=idx(path)) min(select(path_len,i-1,i))/2];
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// polygon(round_corners(path,joint = halflen, method="circle",verbose=true));
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// Example(2D): Chamfering, specifying the chamfer length
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// Example(2D): Chamfering, specifying the chamfer width
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// path = star(5, step=2, d=100);
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// path2 = round_corners(path, method="chamfer", width=5);
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// polygon(path2);
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