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SCSS/SASS module calculating sin/cos/tan using Taylor Expansion.
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/////////////////////////////////////////////////////////////////////////////////// | |
// Plain SASS Trigonometry Algorithm in Taylor Expansion // | |
// // | |
// Based on // | |
// http://japborst.net/posts/sass-sines-and-cosines // | |
// + http://thesassway.com/advanced/inverse-trigonometric-functions-with-sass // | |
/////////////////////////////////////////////////////////////////////////////////// | |
$pi: 3.14159265359; | |
$_precision: 10; | |
@function pow($base, $exp) { | |
$value: $base; | |
@if $exp > 1 { | |
@for $i from 2 through $exp { | |
$value: $value * $base; | |
} | |
} | |
@if $exp < 1{ | |
@for $i from 0 through -$exp { | |
$value: $value / $base; | |
} | |
} | |
@return $value; | |
} | |
@function fact($num) { | |
$fact: 1; | |
@if $num > 0{ | |
@for $i from 1 through $num { | |
$fact: $fact * $i; | |
} | |
} | |
@return $fact; | |
} | |
@function _to_unitless_rad($angle) { | |
@if unit($angle) == "deg" { | |
$angle: $angle / 180deg * $pi; | |
} | |
@if unit($angle) == "rad" { | |
$angle: $angle / 1rad; | |
} | |
@return $angle; | |
} | |
@function sin($angle){ | |
$a: _to_unitless_rad($angle); | |
$sin: $a; | |
@for $n from 1 through $_precision { | |
$sin: $sin + (pow(-1, $n) / fact(2 * $n + 1) ) * pow($a, (2 * $n + 1)); | |
} | |
@return $sin; | |
} | |
@function cos($angle){ | |
$a: _to_unitless_rad($angle); | |
$cos: 1; | |
@for $n from 1 through $_precision { | |
$cos: $cos + ( pow(-1,$n) / fact(2*$n) ) * pow($a,2*$n); | |
} | |
@return $cos; | |
} | |
@function tan($angle){ | |
@return sin($angle) / cos($angle); | |
} | |
$default-threshold: pi()/180/20; | |
@function convert-angle($value, $unit-name) { | |
$factors: ( | |
rad: 1rad, | |
deg: 180deg/pi(), | |
grad: 200grad/pi(), | |
turn: .5turn/pi() | |
); | |
@if not unitless($value) { | |
@warn '`#{$value}` should be unitless'; | |
@return false; | |
} | |
@if not map-has-key($factors, $unit-name) { | |
@warn 'unit `#{$unit-name}` is not a valid unit - please make sure it is either `deg`, `rad`, `grad` or `turn`'; | |
@return false; | |
} | |
@return $value*map-get($factors, $unit-name); | |
} | |
@function asin($z, $unit-name: deg, $threshold: $default-threshold) { | |
$sum: 0; | |
$complement: false; | |
$sign: if($z != 0, $z/abs($z), 1); | |
$z: abs($z); | |
@if $z > 1 { | |
@warn 'illegal `#{$z}` value for function'; | |
@return false; | |
} | |
@if $z > sin(pi()/4) { | |
$complement: true; | |
$z: sqrt(1 - pow($z, 2)); | |
} | |
$term: $z; | |
$i: 0; | |
$k: 1; | |
@while $term > $threshold { | |
$sum: $sum + $term; | |
$i: $i + 1; | |
$k: $k*(2*$i - 1)/(2*$i); | |
$j: 2*$i + 1; | |
$term: $k*pow($z, $j)/$j; | |
} | |
@return convert-angle($sign*(if($complement, pi()/2 - $sum, $sum)), $unit-name); | |
} | |
@function acos($z, $unit-name: deg, $threshold: $default-threshold) { | |
@return convert-angle(pi()/2, $unit-name) - asin($z, $unit-name, $threshold); | |
} | |
@function atan($z, $unit-name: deg, $threshold: $default-threshold) { | |
@return asin($z/sqrt(1 + pow($z, 2)), $unit-name, $threshold); | |
} |
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