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In this paper we present a general methodology for designing mirrors of catadioptric onmidirectional sensors encompassing linear projection properties, the so called constant resolution cameras. The linearity is stated between 3D distances (or angles) and pixel coordinates. We include three practical cases of interest of linear constraints for both standard (cartesian pixel distribution) and log-polar cameras: constant vertical, horizontal and angular resolution. Finally, the formulation is applied in designing a camera combining some of the presented practical cases. Resulting images show that the design was successful as the desired linear properties were obtained.