Put the watermelon chunks in a blender. Using an apple corer, remove the seeds from the cucumber; the seeds will come out in tube-like lengths; reserve the seeds. Add half of the cucumber and half of the pepper to the blender. Blend until smooth. Add the olive oil and blend until a smooth emulsion is formed. Season with salt and vinegar. Strain the gazpacho and refrigerate until chilled.
Using a sharp knife, slice off the tops and bottoms of each of the tomatoes. Locate the fleshy dividing wall of one segment inside the tomato. Slice into the wall and open up the flesh to expose the seeds. Remove the seeds and their pulp by slicing through the tomato core. Set aside the seeds. Your aim is to keep the pulp of the seeds together to create tomato seed "fillets" that are separate from the firmer tomato flesh. Repeat with each segment of the tomato.
Cut the remaining cucumber and red pepper into 1/2-inch dice. Cut the cucumber seed tubes into 1/2-inch pieces.
In the bottom of each soup plate, arrange the diced cucumber, red pepper, cucumber seeds, tomato seeds and croutons. Pour the gazpacho at the table.