## Sneak Peek: Screenshot for Spelling iPhone AppMay 6th, 2009 Patrick Stein

Earlier, I gave a sneak peek at some artwork for the children’s spelling game I am making for the iPhone. Here is a screenshot of the application (click for full size):

I need to touch up the jaunty logo tiles in the upper left. Some of them are worse for the wear after the perspective transformations and rotations. More to follow….

## A Eureka MomentMay 1st, 2009 Patrick Stein

I was pondering the Phony Physics again as I set to work on my iPhone app.

In the previous post, I twiddled the equations for damped spring motion until I found something visually pleasing. Last night, I went back to the drawing (a.k.a. white) board.

What if I used an exponential spiral (parameterized by arc length). Then, I could easily adjust the number of times it bounces back and forth. I could use a spiral like $r(t) = \alpha K (1-t)^n$ and $\theta(t) = K(1-t)$ where $K$ is some multiple of $2\pi$. Then, I could walk along the spiral getting to the origin when $t = 1$ going around the origin $\frac{K}{2\pi}$ times in the process. If I follow the curve at a fixed rate, then I guarantee that my oscillations will pick up speed as I approach the origin.

Rather than have it spiral into the center, I am just using the x-coordinate of the spiral as my new $t$ value to interpolate with. I like the effect for the most part. It overshoots a little bit far on the first oscillation. I may tweak it some more before it’s all over. For now though, I am sticking with it.

I will post some graphs soon.

## Sneak Peak: Artwork for Spelling iPhone AppMay 1st, 2009 Patrick Stein

My first iPhone app is a children’s spelling game. Development is coming along well now that I’ve discovered cocos2d-iphone. I should have screenshots to show early next week. For now, here is a sneak peak at one of the cards in the game.

## Phony Physics (a.k.a. Fun with Interpolation)April 3rd, 2009 Patrick Stein

In a previous post, I mentioned looking for a polynomial for an application. I am working on an application that involves clicking or dragging tiles around. Once you release the tile, I want it to snap to where it’s supposed to be.

The easiest way to do this is to just warp it to where it’s supposed to go. This isn’t very visually pleasing. The next best thing is to set up a time-interval on which it moves into place. Then, linearly interpolate from where it is to where it’s going (here with $t$ normalized to range between zero and one):

$(1-t)x_0 + tx_1$

That’s much better than just warping, but it doesn’t have any sort of fade-in or fade-out. It instantaneously has its maximum velocity and then instantaneously stops at the end.

Typically, then one uses a cubic spline to scale the $t$ value before interpolating to get a speed up in the beginning and then slow down in the end.
Read the rest of this entry ⇒