With a food processor or blender, pulse the fresh pineapple chunks until chopped. A few pluses, you want it a bit chunky.
Put roughly blended pineapple chucks through a fine sieve or strainer with a bowl under it to catch the fresh pineapple juice.
Use the back of a spoon or rubber spatula to lightly press down to remove the juice as much as possible. Set aside the sieve with the chopped pineapple pieces.
In a saucepan place the pineapple juice, cornstarch, and sugar. Mix well with a whisk and bring to a boil.
Reduce the heat to medium and whisk until thickened, about 3 minutes.
Remove from the heat and add reserved chopped pineapple from the sieve. Lightly fold it in with a rubber spatula or spoon.
Completely cool the topping and place it an airtight container.
Chill the topping and it's ready for your cheesecake. Enjoy.