User:LucasVB/Sandbox

Sandbox
This is a test page. Ignore whatever you see here :)

Polar polygon: sec(asin(sin(t*n/2))*2/n)

Hail anti-aliasing!

☢  Ҡ i∊ ff   ⌇  ↯  02:58, 9 February 2006 (UTC)

$$E_p = p \frac{a^2}{ed^3}$$

Radial line $$- \left ( x \frac{1}{\cos \theta} + y \frac{1}{\sin \theta } \right ) = 0$$

$$- 1 / (1 + 0.8 * cos(x))+cos(x) + 1$$

$$y = - \frac{1}{1 + e \cos(x)} + \cos(x)$$

$$\int_{-\pi}^\pi \cos(n x) \, dx = 0$$

$$\int_{-\pi}^\pi \sin(n x) \, dx = 0$$

$$\int_{-\pi}^\pi \sin(n x) \sin(m x) \, dx = \begin{cases} \pi, & n = m \\ 0, & n \ne m \end{cases} $$

Trapezoid functions

asin(sin(x))*3/pi * ((sgn(sin(x))*sgn(sin(3*x))) + 1)/2 + (1-(sgn(sin(x))*sgn(sin(3*x))))/2 * sgn(sin(x));

HSV trapezoid function: ((sgn(1-((x-floor(x/3)*3)-3/2)^2)+1)/2 - (sgn(1-(2*((x-floor(x/3)*3)-3/2))^2)+1)/2 ) * (abs(2*(x-floor(x/3)*3)-3)-1) + (1-(sgn(1-((x-floor(x/3)*3)-3/2)^2)+1)/2)