diff --git a/math.scad b/math.scad index 2297a29..9e4f73a 100644 --- a/math.scad +++ b/math.scad @@ -174,6 +174,31 @@ function lerp(a,b,u) = [for (v = u) (1-v)*a + v*b ]; +// Function: lerpn() +// Usage: +// x = lerpn(a, b, n); +// x = lerpn(a, b, n, ); +// Description: +// Returns exactly `n` values, linearly interpolated between `a` and `b`. +// If `endpoint` is true, then the last value will exactly equal `b`. +// If `endpoint` is false, then the last value will about `a+(b-a)*(1-1/n)`. +// Arguments: +// a = First value or vector. +// b = Second value or vector. +// n = The number of values to return. +// endpoint = If true, the last value will be exactly `b`. If false, the last value will be one step less. +// Examples: +// l = lerpn(-4,4,9); // Returns: [-4,-3,-2,-1,0,1,2,3,4] +// l = lerpn(-4,4,8,false); // Returns: [-4,-3,-2,-1,0,1,2,3] +// l = lerpn(0,1,6); // Returns: [0, 0.2, 0.4, 0.6, 0.8, 1] +// l = lerpn(0,1,5,false); // Returns: [0, 0.2, 0.4, 0.6, 0.8] +function lerpn(a,b,n,endpoint=true) = + assert(same_shape(a,b), "Bad or inconsistent inputs to lerp") + assert(is_int(n)) + assert(is_bool(endpoint)) + let( d = n - (endpoint? 1 : 0) ) + [for (i=[0:1:n-1]) let(u=i/d) (1-u)*a + u*b]; + // Section: Undef Safe Math @@ -434,32 +459,6 @@ function modang(x) = let(xx = posmod(x,360)) xx<180? xx : xx-360; -// Function: modrange() -// Usage: -// modrange(x, y, m, ) -// Description: -// Returns a normalized list of numbers from `x` to `y`, by `step`, modulo `m`. Wraps if `x` > `y`. -// Arguments: -// x = The start value to constrain. -// y = The end value to constrain. -// m = Modulo value. -// step = Step by this amount. -// Examples: -// modrange(90,270,360, step=45); // Returns: [90,135,180,225,270] -// modrange(270,90,360, step=45); // Returns: [270,315,0,45,90] -// modrange(90,270,360, step=-45); // Returns: [90,45,0,315,270] -// modrange(270,90,360, step=-45); // Returns: [270,225,180,135,90] -function modrange(x, y, m, step=1) = - assert( is_finite(x+y+step+m) && !approx(m,0), "Input must be finite numbers and the module value cannot be zero." ) - let( - a = posmod(x, m), - b = posmod(y, m), - c = step>0? (a>b? b+m : b) - : (a=len(l) || succ)? succ : - _any( - l, i+1, - succ = is_list(l[i]) ? _any(l[i]) : !(!l[i]) - ); +function _any_func(l, func, i=0, out=false) = + i >= len(l) || out? out : + _any_func(l, func, i=i+1, out=out || func(l[i])); + +function _any_bool(l, i=0, out=false) = + i >= len(l) || out? out : + _any_bool(l, i=i+1, out=out || l[i]); // Function: all() // Usage: // b = all(l); +// b = all(l,func); // Description: -// Returns true if all items in list `l` evaluate as true. -// If `l` is a lists of lists, `all()` is applied recursively to each sublist. +// Returns true if all items in list `l` evaluate as true. If `func` is given a function liteal +// of signature (x), returning bool, then that function literal is evaluated for each list item. // Arguments: // l = The list to test for true items. +// func = An optional function literal of signature (x), returning bool, to test each list item with. // Example: // all([0,false,undef]); // Returns false. // all([1,false,undef]); // Returns false. // all([1,5,true]); // Returns true. -// all([[0,0], [0,0]]); // Returns false. -// all([[0,0], [1,0]]); // Returns false. +// all([[0,0], [0,0]]); // Returns true. +// all([[0,0], [1,0]]); // Returns true. // all([[1,1], [1,1]]); // Returns true. -function all(l) = - assert( is_list(l), "The input is not a list." ) - _all(l); +function all(l, func) = + assert(is_list(l), "The input is not a list.") + assert(func==undef || is_func(func)) + is_func(func) + ? _all_func(l, func) + : _all_bool(l); -function _all(l, i=0, fail=false) = - (i>=len(l) || fail)? !fail : - _all( - l, i+1, - fail = is_list(l[i]) ? !_all(l[i]) : !l[i] - ) ; +function _all_func(l, func, i=0, out=true) = + i >= len(l) || !out? out : + _all_func(l, func, i=i+1, out=out && func(l[i])); + +function _all_bool(l, i=0, out=true) = + i >= len(l) || !out? out : + _all_bool(l, i=i+1, out=out && l[i]); // Function: count_true() // Usage: -// n = count_true(l) +// n = count_true(l,) +// n = count_true(l,func,) // Description: // Returns the number of items in `l` that evaluate as true. // If `l` is a lists of lists, this is applied recursively to each @@ -1289,24 +1301,38 @@ function _all(l, i=0, fail=false) = // in all recursive sublists. // Arguments: // l = The list to test for true items. -// nmax = If given, stop counting if `nmax` items evaluate as true. +// func = An optional function literal of signature (x), returning bool, to test each list item with. +// --- +// nmax = Max number of true items to count. Default: `undef` (no limit) // Example: // count_true([0,false,undef]); // Returns 0. // count_true([1,false,undef]); // Returns 1. // count_true([1,5,false]); // Returns 2. // count_true([1,5,true]); // Returns 3. -// count_true([[0,0], [0,0]]); // Returns 0. -// count_true([[0,0], [1,0]]); // Returns 1. -// count_true([[1,1], [1,1]]); // Returns 4. -// count_true([[1,1], [1,1]], nmax=3); // Returns 3. -function _count_true_rec(l, nmax, _cnt=0, _i=0) = - _i>=len(l) || (is_num(nmax) && _cnt>=nmax)? _cnt : - _count_true_rec(l, nmax, _cnt=_cnt+(l[_i]?1:0), _i=_i+1); +// count_true([[0,0], [0,0]]); // Returns 2. +// count_true([[0,0], [1,0]]); // Returns 2. +// count_true([[1,1], [1,1]]); // Returns 2. +// count_true([[1,1], [1,1]], nmax=1); // Returns 1. +function count_true(l, func, nmax) = + assert(is_list(l)) + assert(func==undef || is_func(func)) + is_func(func) + ? _count_true_func(l, func, nmax) + : _count_true_bool(l, nmax); -function count_true(l, nmax) = - is_undef(nmax)? len([for (x=l) if(x) 1]) : - !is_list(l) ? ( l? 1: 0) : - _count_true_rec(l, nmax); +function _count_true_func(l, func, nmax, i=0, out=0) = + i >= len(l) || (nmax!=undef && out>=nmax) ? out : + _count_true_func( + l, func, nmax, i = i + 1, + out = out + (func(l[i])? 1:0) + ); + +function _count_true_bool(l, nmax, i=0, out=0) = + i >= len(l) || (nmax!=undef && out>=nmax) ? out : + _count_true_bool( + l, nmax, i = i + 1, + out = out + (l[i]? 1:0) + ); @@ -1573,6 +1599,7 @@ function c_ident(n) = [for (i = [0:1:n-1]) [for (j = [0:1:n-1]) (i==j)?[1,0]:[0, function c_norm(z) = norm_fro(z); + // Section: Polynomials // Function: quadratic_roots() @@ -1624,6 +1651,7 @@ function polynomial(p,z,k,total) = : 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: // x = polymult(p,q)