Arithmetic
Mathematical Functions
These @functions represent well-known classes of mathematical functions.
All parameters other than the first one define the concrete mathematical function,
while the first parameter always is the argument to that function instance.
@function identity()
Identity function (f(x) = x).
Parameters & Return
$x: (Number)
The argument to the function.
@return (Number)
$x.
@function linear()
Linear function (f(x) = mx + n).
Parameters & Return
$x: (Number)
The argument to the function.
$slope: (Number)
The slope of the function (m).
$initial: 0 (Number)
The initial value (y-intercept) of the function (n).
@return (Number)
The function value at $x.
@function polynomial()
Polynomial function (f(x) = c₀ + c₁x + c₂x² + … = ∑cᵢxⁱ).
Parameters & Return
$x: (Number)
The argument to the function.
$coefficients: (List)
The coefficients of the polynomial.
@return (Number)
The function value at $x.
Used By
@mixin palette()
@function exponential()
Exponential function (f(x) = abˣ).
Parameters & Return
$exponent: (Number)
The exponent (x).
$base: (Number)
The base (b).
$coefficient: (Number)
The coefficient (a).
@return (Number)
The coefficient times the base to the power of the exponent (abˣ).
Configuration Functions
Functions for processing configuration.
@function -map-aliases() [private]
Translate a map of aliases to values from a dictionary. Each alias is asigned the value of the aliased dictionary key.
Parameters & Return
$aliases: (Map)
Map of aliases.
$dict: (Map)
Dictionary to look up values.
@return (Map)
Map with aliases pointing to looked up values.
Used By
@function map-config()
@function -apply-domain-range() [private]
Apply a range to a given domain. If the domain doesn’t cover the range it will be repeated, adding the current lap count to each domain value and as a prefix to each key. This implies that with no domain given, we can easily use the set of integers (ℤ) as default domain.
Parameters & Return
$base: (Map)
Map of aliases.
$range: (Map)
Range limiting the domain.
@return (Map)
The domain limited by the range.
Used By
@function map-function()
@function map-function()
Translate a map of domain arguments to their values of a given function.
Parameters & Return
$domain: null (Map)
The domain on which to apply the function.
$range: null (Map)
Range limiting the domain.
$func: null (Function)
Function to apply.
$params: null (Map)
Parameters to the function.
@return (Map)
Map with domain symbols pointing to their function values.
@function map-config()
Translate a property configuration to a set of properties.
Parameters & Return
$conf: (Map)
Configuration map for this set of properties.
@return (Map)
A set of mapped, literal, and logical properties.
Geometry
Parametric Curves/Equations
Bézier Curves
Related
Wikipedia [external]
@function cubic()
Cubic Bézier curve, 1-dimensional.
Parameters & Return
$t: (Number)
The argument to the curve.
$p0: (Number)
First control point, P0.
$p1: (Number)
Second control point, P1.
$p2: (Number)
Third control point, P2.
$p3: (Number)
Fourth control point, P3.
@return (Number)
The curve value at $t.
Used By
@function cubic-2d()
@function cubic-2d()
Cubic Bézier curve, 2-dimensional.
Parameters & Return
$t: (Number)
The argument to the curve.
$x0: (Number)
Abscissa of first control point, P0.
$y0: (Number)
Ordinate of first control point, P0.
$x1: (Number)
Abscissa of second control point, P1.
$y1: (Number)
Ordinate of second control point, P1.
$x2: (Number)
Abscissa of third control point, P2.
$y2: (Number)
Ordinate of third control point, P2.
$x3: (Number)
Abscissa of fourth control point, P3.
$y3: (Number)
Ordinate of fourth control point, P3.
@return (Number)
The curve value at $t.
Meta Functions
Functions for working with function objects.
@function call-conditional()
Call a function with one argument and with or without additional parameters.
Parameters & Return
$func: (Function)
Mapping function.
$arg: (Number)
The argument to the function.
$params: null (Map)
Parameters to the function.
@return (*)
The return value of the function call.
Used By
@function map-function()
Typography
Typographical Rhythm
@function rlh()
Derive root line-height (rlh).
Parameters & Return
$scale-base: (Number<rem|em|%>)
Base font-size of the typographical scale.
$line-root: (Number)
Relative line-height of the document root.
@return (Number<rem>)
Root line height. Absolute value mimicking the experimental CSS unit [rlh][mdn:rlh].
@function grid-line()
Baseline grid compatible line height at a given font size.
Parameters & Return
$em: (Number<rem|em|%>)
Font size to fit.
$rlh: (Number<rem>)
Root line height.
$min: (Number)
Minimum line height ratio.
$sub: (Number)
The number of line sub-divisions the grid allows.
@return (Number<rem|unitless>)
The minimum line height that fits the font size.
For rem-based font sizes this is also in rem, otherwise a unit-less number.