For what you're doing, you're gonna have to rethink a bit. From the data sheet, it appears that each 2" segment looks like
simulate this circuit – Schematic created using CircuitLab
Since each LED should have a current-limiting resistor, you'll need 450 of them, about 500 ohms, 1/4 watt each. The resistors will need to be mounted somewhere where they have good airflow, since they will dissipate about 100 watts total. (10 amps times 12 volts is 120 watts, and it's got to go somewhere.) Just bundling them together and putting them in a hidden box is almost certain to cause Bad Problems.
Your final assembly should look something like
simulate this circuit
except extended to 150 units.
Each of the 3 drive lines needs to provide 12 volts at about 3 amps, or you can drive all 3 simultaneously with a total of 9 amps, so a 10-amp supply will probably do. There is a small chance, though, that driving all the LEDs on may draw slightly more than 10 amps, and the power supply will get unhappy. I don't have enough information to be sure. If you want to play it safe, cut back on the current a bit and use something like 560 or 620 ohm resistors. You may even want to mix values a bit to produce different drive currents, in order to get just the color you want. Experiment on a single segment before you commit to a final design. Be aware, though, that if you drive all of them the result will be (approximately) white. If you only want to produce amber light, don't turn on the blues. As a matter of fact, if you only want amber, forget about hooking up the blue leads entirely and cut your workload by 30%.
Your logic schematic is not ideal in this case, since your master drive could easily be folded into the 3 color drive signals, but I'll keep it anyways.
The master drive is relatively easy, and can be done with an NPN transistor, or actually with an NPN Darlington (you won't get 10 amps with a single stage driven by LSTTL logic). What you really want is an n-type MOSFET. Your drive circuit would look like
simulate this circuit
The MOSFET should have a current rating of 20 volts or better, and 10 amps or better. However, that is very modest as MOSFETs go.
The 3 color channel drives are a little trickier, and for these you need p-type MOSFETs. The circuit is complicated by the fact that LSTTL will not handle 12 volts on the output without Letting The Magic Smoke Out, so you need to make slightly more complicated switches.
simulate this circuit
I've shown the NPN buffer transistor as a 2N3904, but almost any small-signal NPN will do. 2N3904s are cheap and readily available. Try someplace like Jameco.
I hope this helps.
The BuckPuck is a step-down ("buck") converter. You must provide it with a voltage at least 2.5V above the forward voltage of the LEDs. The LED has a typical Vf of 3.2V, so you want your input voltage to be at least 5.7V. Call it 6V or higher. The BuckPuck will take an input voltage all the way up to 32VDC, although the efficiency drops a bit.
It is regulated to provide constant current. In other words, the BuckPuck will vary its output voltage so that the current remains the same. The buckpuck doesn't care if you have one or three LEDs in series, it will simply create whatever voltage necessary to push 700mA through the circuit. Of course, this output voltage cannot be greater than 2.5V less than the input voltage.
Because of this, you don't need any limiting resistors in the LED paths. This also means that you want to select your FETs (or transistors) to have small resistances when switched on ( \$R_{ds-on}\$ in the datasheets)
However, this presents a problem in your multiple-path design. If you turn off one of the LEDs before turning on another, then there is nowhere for the current to go. The output voltage will shoot up to the maximum possible, as the BuckPuck tries to keep pushing 700mA.
A solution is to turn on one of the LEDs just before turning off another one. MOSFETs take time to turn on and turn off, so you may need to add a delay in your code to ensure that there is always a current path available.
As for as PWM dimming, basically you just switch the CTRL pin on and off fairly rapidly. The datasheet says that you need to keep the PWM frequency under 10kHz. I would keep it down to around 1kHz, or even slower. What you're doing is turning the LED on and off faster than the eye can detect. What you end up seeing is the average brightness.
However, you can only do this directly if you have 5V logic outputs. The RPi has 3.3V outputs. The datasheet gives the following examples, which won't work for you because you don't have 5V logic:
Read Page 4 of the datasheet very carefully. Also note that the microcontroller ground (the RPi ground) is tied to LED-.
Conveniently, the REF pin provides 5V for your use. You need to switch this 5V into the CTRL pin. One option is to use a small optoisolator (optocoupler), such as the Sharp PC713V0YSZXF.
If you don't know how to use an optoisolator, I would look for answers here :)
Good luck.
Best Answer
A & B are electronically the same. Position does not matter.
C is not always recommended. The diode with the lowest Vf will set the voltage across the parallel leds. If you badly mismatch them, you will get one diode that conducts more current than the others and can lead to one burning out then the rest following. This is really overblown (pun totally intended) fud. Parallel leds with a single resistor is common. Just match the leds for brightness by eyeballing them, then confirm that the voltage across them are fairly identical. For one off projects this is enough. All it requires is careful selection of parts.
A/B is ""safer"" but C requires less parts. You are fine as is.