Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Stir in the linguine, and return to a boil. Cook until the pasta has cooked through, but is still firm to the bite, about 11 minutes.
While pasta is cooking, combine the olive oil, pineapple juice, orange juice, orange zest, lemon zest, salt, pepper, and garlic in a blender. Blend on high speed until smooth.
Pour sauce into a large skillet over medium-high heat. Bring to a simmer and cook for 2 minutes. Add the shrimp and parsley; cook until shrimp are pink and cooked through, 3 to 5 minutes.
Drain the linguini, and place on a serving platter. Spoon the shrimp and sauce over the pasta, and top with a sprinkle of Parmesan cheese.