Step 1Have a large bowl of ice water ready.
Step 2Combine the gelatin and water until blended. Let sit until the gelatin has softened, about 5 minutes.
Step 3Pour the yogurt in the top of a double boiler set over, but not touching, simmering water. Using a whisk, add the sugar to the yogurt and stir until well mixed. The mixture should be hot but not boiling. Add the softened gelatin and continue stirring with the whisk to blend well, about 3 minutes. Remove from heat.
Step 4Set the saucepan in the bowl of ice water and stir until cool.
Step 5Beat the cream only until it holds soft peaks, about 4 minutes. If it is too stiff, it will turn into butter, so don't overbeat. Gently fold the whipped cream into the yogurt mixture. Spoon into a mold or bowl and refrigerate long enough to set up and thicken, about 2 hours.
Step 6An hour before serving, cut the flesh of the melon into 1-inch slices, or, if you have a melon baller, make melon balls.
Step 7Serve the yogurt cream on a flat plate. Decorate the edges with melon balls and berries. Garnish the middle with a sprig of mint and you will have a dessert that looks like a jewel.