Submissions are now closed for the first project and the panel, made up of Dimple, David C, Billy and myself will be announcing the first project in the next few days

In a previous post, I showed how to geometrically construct a sine-like function for a regular polygon.

I also pointed out how the shape of the function’s graph depends on the orientation of the polygon, since it isn’t perfectly symmetric like the circle.

This animation illustrates how the polygonal sine (dark curve) and polygonal cosines (clear curve) change as the generating polygon rotates.

DerivationFirst of all, it is important to point out these functions are not based on the perimeter of the shape, like it is for the unit circle.

We’re still sticking to the interior angle here. If we used the perimeter as a substitute for the angle we would just get a deformed linear spline of the sine function, which is rather useless and boring.In order to find these functions for an arbitrary polygon, we first need to write the polygon in polar form. That is, we want the radius for a given angle. In a circle, this is a constant value.

A general “Polar Polygon” function is:

PP

_{n}(x) = sec((2/n)·arcsin(sin((n/2)·x)))Where n is the number of sides of the polygon. If n is not an integer, the curve is not closed.

Armed with this function, we can quickly find the polygonal sine and polygonal cosine:

Psin

_{n}(x) = PP_{n}(x)·sin(x)

Pcos_{n}(x) = PP_{n}(x)·cos(x)As n grows, the functions approximate the circular ones, as expected. To rotate the polygon, just add an angle offset to the x in PP

_{n}.This technique is general for any polar curve. Here’s a heart’s sine function, for instance

So, what is it good for?I’ve used this several times when I wanted some smooth interpolation between a circle and a polygon, in such a way that the endpoints of the interpolation are a perfect circle and a perfect, pointy polygon. It’s useful in parametric surfaces, such as in this old avatar of mine:

Now you can also listen to what these waves sound like

The Art Center College of Design in Pasadena has compiled a document containing all of the gestures that our digital devices and RFID cards cause us to make.

Real People Are Different From Us

It turns out that the regular public don’t go on social networks or use mobile maps as much as us!

Gucci Unveils "Pinnable" Banner Ad

If you make a banner so beautiful your audience wants to pin it you are doing very well! Banners are naturally pinnable though adding the ‘Pin It’ button will encourage people to do this.

I recently presented a deck on the directions being taken (and opportunities) in HTML5 - here are the links I used, broken down by category.

**Fonts Script web fonts | Fontdeck Google Web Fonts Font Squirrel**

**Adobe TypeKit GREY GOOSE® Vodka**

**Forms HTML5 Contact Form**

**Responsive The Boston Globe ChoiceResponse → About Hiut Denim - Welcome**

**Reverse Büro Sony USA - Consumer Electronics Products, Movies, Music, Games and Services**

**ThemeLoom | Theme: Pure VIVID | Deep into theming with VIVID**

**Drag & Drop ZipDrop Preview - CodeCanyon Collapsible Drag Drop Panels - Web Developer Plus Demos gridster.js**

**Video/Audio HTML5 Video Player | Video.js**

**Canvas Shapecatcher: Draw the Unicode character you want!**

**The xx - Coexist Asteroids [Reloaded] - HTML5 Canvas JavaScript Game Demo by Kevin Roast js cloth**

**SVG http://svg-wow.org/camera/camera.xhtml Firefox 4’s inline SVG mask over HTML5 video | Atomic Robot Design 613 | The official site for James Anderson’s benefit year 2012. One Race, Every Medalist Ever - Interactive Graphic - NYTimes.com**

**FrameworksJQuery jQuery UI Javascript Slideshow Demo - Quiet Template - Rotate effect Seamco/ Building efficient bottling lines**

**iutopi - Creative Land / Branding, Graphic & Web Design | | | | | | | Mauro Macchiaroli + Javier González cultural solutions uk I Lincolnshire based cultural consultancy I research, planning & events management services**

**JQuery Tool Tips Radio 1 zoom tabs JQuery Drop Down Login**

**Raphael Raphaël · Playground Raphaël · Interactive Chart Raphaël · Analytics**

**Adobe Edge Mobile Browser Marketshare | Adobe Edge Animate Showcase | Edge Tools & Services | Adobe & HTML**

**Designer Spotlight | Adobe Edge Animate Showcase | Edge Tools & Services | Adobe & HTML**