This work considers the problem of generating computationally efficient quadrotor motion primitives between a given pose (position, velocity, and acceleration) and a goal plane in the presence of obstacles. A new motion primitive tool based on the logistic curve is proposed and a closed-form analytic approach is developed to satisfy constraints on starting pose, goal plane, velocity, acceleration, and jerk. The geometric obstacle avoidance problem is represented as a combinatorial set problem and a heuristic approach is proposed to accelerate the solution search. Numerical examples are presented to highlight the fast motion primitive generation in multi-obstacle pose-to-plane scenarios.