Here is a sample of the relevant texts:
QuoteDisplay MorePD26. Of desires, all that do not lead to a sense of pain, if they are not satisfied, are not necessary, but involve a craving which is easily dispelled when the object is hard to procure, or they seem likely to produce harm.
PD29. Among desires, some are natural (and necessary, some natural) but not necessary, and others neither natural nor necessary, but due to idle imagination.
PD30. Wherever, in the case of desires which are physical, but do not lead to a sense of pain if they are not fulfilled, the effort is intense, such pleasures are due to idle imagination; and it is not owing to their own nature that they fail to be dispelled, but owing to the empty imaginings of the man.
Men. 127. We must consider that of desires some are natural, others vain, and of the natural some are necessary and others merely natural; and of the necessary some are necessary for happiness, others for the repose of the body, and others for very life.
Diog. Oen Fr. 32. Each (virtue?) therefore ............... means of (?) ... just as if a mother for whatever reasons sees that the possessing nature has been summoned there, it then being necessary to allow the court to asked what each (virtue?) is doing and for whom .................................... [We must show] both which of the desires are natural and which are not; and in general all things that [are included] in the [former category are easily attained] .....
Diog. Oen Fr. 34. Let us first discuss states, keeping an eye on the point that, when the emotions which disturb the soul are removed, those which produce pleasure enter into it to take their place.
Well, what are the disturbing emotions? [They are] fears —of the gods, of death, and of [pains]— and, besides [these], desires that [outrun] the limits fixed by nature. These are the roots of all evils, and, [unless] we cut them off, [a multitude] of evils will grow [upon] us.
Diog. Oen NF 131 = YF 189. Vain desires, like those for fame and such things, are not only vain, but, as well as being vain, also difficult to fulfil. It is not unlike drinking much, yet always being thirsty. To be master of Pella, but [to have troubles for company, is vain].
Diog. Oen Fr. 153. Of the desires some are vain, others natural. Now those that are natural seek after such things as [are necessary] for our nature’s enjoyment, [while those that are vain] ................................................................................... What [need to mention the] fabulous treasures of Croesus and his gold ingots or the rivers running with gold for him? What [benefit], father Zeus, [did he derive] from these [richness]?
DRN Book IV, ~1084. For therein there is hope that from the same body, whence comes the source of their flame, the fire may in turn be quenched. Yet nature protests that all this happens just the other way; and this is the one thing, whereof the more and more we have, the more does our heart burn with the cursed desire. For meat and drink are taken within the limbs; and since they are able to take up their abode in certain parts, thereby the desire for water and bread is easily sated. But from the face and beauteous bloom of man nothing passes into the body to be enjoyed save delicate images; and often this love-sick hope is scattered to the winds.
And here is how I would synthesize all of this information;
The test of whether a desire is necessary is in determining whether a feeling of pain results if that desire is not satisfied. If pain results, the desire is necessary. If pain does not result, the desire is unnecessary.
The test of whether a desire is natural is in determining whether there is a fixed limit in nature to which the object of desire is subjected. If there is a fixed limit in nature, the desire is natural. If there is not a fixed limit in nature, the desire is unnatural. Cassius is fond of quoting the dictum that hard cases make bad law, and we should probably be cautious when we approach the boundary between natural and unnatural desires. Remember, the purpose of this exercise is not to achieve a perfect score, or to make the grade, or to get on Santa's (or St. Peter's) nice list; the purpose is to secure a life of pleasure and to minimize, so far as it's reasonable to do so, the presence of pain.
Epicurus typically defines these terms in the negative, as in Principal Doctrine 26, and his advice to students on ethical questions is also offered in negative terms, as it is in Vatican Saying 51;
QuoteVS51. You tell me that the stimulus of the flesh makes you too prone to the pleasures of love. Provided that you do not break the laws, or good customs, and do not distress any of your neighbors, or do harm to your body, or squander your pittance, you may indulge your inclination as you please. Yet it is impossible not to come up against one or other of these barriers, for the pleasures of love never profited a man and he is lucky if they do him no harm.
You have to do the math yourself, for yourself!