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The accurate orientation measurement in real time contributes significantly to the control of mobile robots, and further assists them to realize some fundamental functions, such as automatic pilot, cargo delivery, target tracking, etc. The traditional magnetic compass has been denounced for its susceptibility to ferro or electromagnetic materials, vehicular motion, and latitude variation. Hence, in this paper, we aim at proposing a novel nonmagnetic compass named floor visual compass (FVC) for mobile robots working in controlled indoor scenarios, which is mainly implemented by a downward-looking monocular camera. With previously laid auxiliary strips on the floor, which are parallel to the reference axis, the FVC is able to estimate the robot's orientation by means of image processing technologies and interval arithmetics. Considering the computational complexity of the visual orientation measurement, an event trigger for FVC is designed, to reduce the frequency of the correction operation using the visual orientation measurements. The real-world experiment verifies the effectiveness of the proposed nonmagnetic compass.