A novel guidance algorithm is proposed for the attitude reorientation of a rigid body spacecraft in the presence of multiple types of attitude-constrained zones. In this direction, two types of attitude-constrained zones are first developed using unit quaternions, namely, the attitude-forbidden and -mandatory zones. The paper then utilizes a convex parameterization of forbidden and mandatory zones for constructing a strictly convex logarithmic barrier potential that is subsequently used for the synthesis of feedback attitude control laws while the inevitable unwinding phenomenon is given a simple and effective remedy. Model-independent and model-dependent control laws are then implemented by using the Lyapunov direct method and the modified integrator backstepping method. The paper concludes with a set of simulation results to evaluate the effectiveness and demonstrate the viability of the proposed methodology.