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During the earliest production stages of an animated movie, it is common to begin the process with a series of exploratory paintings.

“They are abstract and loose and just delicious paintings,” says Chris Sanders, the director of films such as Lilo & Stitch, How to Train Your Dragon, and The Croods. But something special happened during the production of Sanders’ latest film, The Wild Robot, while he was sitting in a meeting and being shown some of these conceptual paintings.

“Someone pushed a button,” Sanders recalls, “and one of them started to move. And the camera started pushing through it.” What Sanders had taken for a painting was actually a finished scene of the movie. “And I cannot put too fine a point on it; I really didn’t think...