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In lima\c{c}on-shaped gradient index dielectric cavities designed byconformal transformation optics, the variation of Q-factors and emissiondirectionality of resonant modes was traced in their system parameter space.For these cavities, their boundary shapes and refractive index profiles aredetermined in each case by a chosen conformal mapping which is taken as acoordinate transformation. Through the numerical exploration, we found thatbidirectionality factors of generic high-Q resonant modes are not directlyproportional to their Q-factors. The optimal system parameters for thecoexistence of strong bidirectionality and a high Q-factor was obtained foranisotropic whispering gallery modes supported by total internal reflection.

Optimization of conformal whispering gallery modes in lima\c{c}on-shaped transformation cavities