If you have any expertise in Spanish, French, German, or Japanese, I’d appreciate any feedback you can give me about the words I chose in those languages. Would they be the word one would think of when shown the picture? Thanks, in advance.

• Corrected spelling of siete (Spanish for seven)
• Corrected spelling of colores (Spanish for colors)

Today, I am working on adding animal drawings.

The first five respondents to this article will receive a Promotional Code to download the app for free! (Edit: all promo codes dished out… if you really want one and will publicly review my app in your blog, I’ll dig up another promo code for you.)

Features

• Kid-friendly interface! Just pick the letters you want!
• Guides your child to the proper spelling of each word.
• Adapts to your child! Cards that consistently give your child trouble show up more often.
• Support for English, Spanish, and French! (German and Japanese Kana coming soon)
• Lots of words to learn (with more coming soon).
• Three different skill levels to challenge your kid!
• Exercise some or all of the categories: Numbers, Colors, Foods (with more coming soon).

At this point, I am far more comfortable with Objective-C and the Cocoa class hierarchy than I was even a month ago. I still think Objective-C is awful. You take a nice functional Smalltalk-ish language, you throw away most of the functional, you pretend like you have garbage collection when you don’t, you strip out any form of execution control, you add some funky compiler pragma-looking things (including one called synthesize that only fabricates about half of what you’d want it to build), you change the semantics of ->, and then you interleave it with C! Wahoo! Instant headache!

But, after I found the for-each sort of construction, my code got quite a bit simpler. A whole bunch of loops like this:

NSEnumerator* ee = [myArray enumerator];
MyItem* item;
while ( ( item = (MyItem*)[ee nextObject] ) != nil ) {
   ...
}

went to this:

for ( MyItem* item in myArrayOrEnumerator ) {
   ...
}

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….

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 and where is some multiple of . Then, I could walk along the spiral getting to the origin when going around the origin 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 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.

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 normalized to range between zero and one):

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 value before interpolating to get a speed up in the beginning and then slow down in the end.

I might like to decelerate faster than I accelerate though so I might employ a fancier (higher-order) polynomial like:

But, in this case, I wanted the tile to overshoot the target a bit and then nestle/wiggle into place. So, I experimented with a bunch of different polynomials. I was having real trouble getting them to behave in a way that felt right. So, I went back to the physics of it.

What I wanted was pretty similar to damped spring motion. Imagine you’ve tied a heavy weight to a spring and suspended it all in a jar of oil. If you perturb the weight, it will bounce up and down but
each bounce is closer to the equilibrium point than the previous bounce. (Actually, it’s more complicated than that. If the spring is too weak or the oil too viscous, the weight will just slowly return to the equilibrium point without ever going past it. That’s called overdamped harmonic oscillation. What I want is called underdamped harmonic oscillation and that’s all I will concern myself with here.) The equation for this motion is:

To get it to wiggle an appropriate amount, I was using and effectively making the cosine into a sine.

This is all well and good, but to really scale my t, I need this to start at zero and approach one. So, I was really using:

Well, now it starts zig-zagging on the way to its destination. It already starts cutting back long before it makes it to where it’s going. I needed to get close to the destination much sooner. So, I jiggered the term:

This looks terrible though. I hit the destination is less than a tenth of a second and then not again until about half a second. The reason for this is that the oscillations happen at a fixed rate. never changes and moves steadily along so that keeps the same frequency throughout my interval. So, I jiggered the going into the sine function to make my oscillations start out slowly and really speed up toward the end.

This is much better, but it still didn’t give the feeling of settling in because the second oscillation was almost as high as the first. I could up the value of and get somewhere. But, I wanted it to be even more dramatic. So, I changed the in the exponent to (and used a slightly higher : was 3 and is now 4):

This was pretty decent, but I felt the initial attack was a bit strong. So, I dropped down the exponent on my base curve from 4 to 2:

This is pretty nice. It looks pretty natural (despite making an entire mess out of damped harmonic motion). It doesn’t ease in at all though so I might still need to replace the with something of a higher order. But, I might not mind the tile achieving instant velocity. It gives it that I’m really supposed to be over there sort of urgency.