Trajectory data collection is a common task with many applications in our daily lives. Analyzing trajectory data enables service providers to enhance their services, which ultimately benefits users. However, directly collecting trajectory data may give rise to privacy-related issues that cannot be ignored. Local differential privacy (LDP), as the de facto privacy protection standard in a decentralized setting, enables users to perturb their trajectories locally and provides a provable privacy guarantee. Existing approaches to private trajectory data collection in a local setting typically use relaxed versions of LDP, which cannot provide a strict privacy guarantee, or require some external knowledge that is impractical to obtain and update in a timely manner. To tackle these problems, we propose a novel trajectory perturbation mechanism that relies solely on an underlying location set and satisfies pure $ε$-LDP to provide a stringent privacy guarantee. In the proposed mechanism, each point's adjacent direction information in the trajectory is used in its perturbation process. Such information serves as an effective clue to connect neighboring points and can be used to restrict the possible region of a perturbed point in order to enhance utility. To the best of our knowledge, our study is the first to use direction information for trajectory perturbation under LDP. Furthermore, based on this mechanism, we present an anchor-based method that adaptively restricts the region of each perturbed trajectory, thereby significantly boosting performance without violating the privacy constraint. Extensive experiments on both real-world and synthetic datasets demonstrate the effectiveness of the proposed mechanisms.