Standard Utility Functions

Ranges

Step-Wise Range

$$ f\text{srange} \left( s\text{start}, s\text{stop}, s\text{step} \right) = \left[ \left(\right) \space \text{for} \space i = \left[ 0 \text{…} \text{floor}\left( \frac{s\text{stop}}{s\text{step}} \right) \right] \right] $$

Generate a list of numbers from $s\text{start}$ up to (and including) $s\text{stop}$ with difference $s_\text{step}$.

Step-Wise Exclusive Range

$$ f_\text{sxrange} \left( \right) $$

Generate a list of numbers from $s\text{start}$ up to (but excluding) $s\text{stop}$ with difference $s_\text{step}$.

Linearly Spaced Ranged

$$ f\text{nrange} \left( s\text{start}, s\text{stop}, n \right) = \left[ \left( s\text{start} + i \left( \frac {s\text{stop} - s\text{start}} {n} \right) \right) \space \text{for} \space i = \left[ 0 \text{…} n \right] \right] $$

Linearly Spaced Exclusive Range

$$ f\text{nxrange} \left( s\text{start}, s\text{stop}, n \right) = \left[ \left( s\text{start} + i \left( \frac {s\text{stop} - s\text{start}} {n} \right) \right) \space \text{for} \space i = \left[ 0 \text{…} n-1 \right] \right] $$

Generate a list of $n$ numbers evenly spaced apart between $s_start$ and $s_stop$ (inclusive).

$$ f_\text{nrange}(1, 10, 10) = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] \quad \text{(10 element list)} $$

List Range

$$ f_\text{lrange} \left( l \right) = \left[ 1 \text{…} \text{length}(l) \right] $$

Generate a list of integers corresponding to the indices of a list.

Step-Wise List Range

$$ f\text{lsrange} \left( l, s\text{period}, s\text{offset} \right) = \left[ \left( s\text{offset} + (i-1) \cdot s\text{period} \right) \space \text{for} \space i = \left[ 1 \text{…} \frac {\text{length}(l)} {s\text{period}} \right] \right] $$

Generate a list of integers corresponding to chunks of a list.

For instance, to iterate over every 3 items:

$$ L = [1 \text{…} 9] \quad \text{(9 element list)} $$

$$ I = f_\text{lsrange}(L, 3, 1) = [1, 4, 7] \quad \text{(3 element list)} $$

$$ [L[i] \space \text{for} \space i = I] = [1, 4, 7] \quad \text{(3 element list)} $$

Rendering

Line

$$ d_\text{line} $$

Circle

$$ d_\text{circle} $$

Rectangle

$$ d_\text{rect} $$

Regular Polygon

$$ d\text{polygon} \left( n, p_c, r, d \right) = \left[ \left( p_c\text{.}x + r \cos{\theta}, p_c\text{.}y + r \sin{\theta} \right) \space \text{for} \space \theta = f\text{nrange}\left( d, d + 2\pi, n \right) \right] $$

Grid

$$ d_\text{grid} $$

Spike

$$ d_\text{spike} $$