Forterra Systems Inc., a California startup focused on virtual reality, was in need of money and its products didn’t have much commercial appeal. Then funds came in from a source based far from Silicon Valley: In-Q-Tel Inc., a venture-capital firm in Virginia funded by the Central Intelligence Agency.

One catalyst for the 2007 infusion, according to a former Forterra executive and others familiar with it, was a recommendation by a man who sat on the board of the venture-capital firm—and also on the board of Forterra.

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