Your picture shows voltage-regulated supply. If you look at LM317's datasheet you will find a generic 3 pin regulator schematic which shows current source function. While I could draw over your schematic, it would be ugly and it wouldn't bring the point across as well as if you read about it yourself.
Basic idea is that linear regulator will try to set its output voltage based on voltage at its reference ("adj") pin. For LM317 this reference voltage is 1.25V, for LM7805 it is 5V, for LM7812 it is 12V et cetera. Regulator will do everything it can to maintain its reference voltage - if voltage is too low, it will increase its output, if it is too high, it will decrease it.
Ohm's law dictates that if there is a fixed voltage potential (= reference voltage) across known resistance, you also know the current though this resistance. From there on Kirchhoff's law applies, if current enters one point it must exit somewhere and the only point to exit (towards ground where the loop closes) is through your load. So all you need to do is to put the current-setting resistor and your load (filament/heater) in series, from the output of the regulator. Resistor is connected between OUT and ADJ pins and its value is calculated with formula R = 1.25V / I, where I is current your desire. The load is connected between far end of the resistor (the point where ADJ pin connects) and ground. Since regulator will try to maintain voltage across the resistor at fixed value, this inevitably means that current though it (and regulator and load, which are all connected in series) must be according to the above equation. Your load (heater/filament) is nice ohmic load so once it achieves stable temperature it will function as a fixed resistor and draw fixed current. Before it heats up, regulator will eat extra voltage and momentarily heat up instead of filament/heater, thereby prolonging its life.
You should definitely look at the datasheet mentioned above, it will all make sense immediately when you see the picture and read this text.
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