Underlying many structured light systems, especially those based on laser scanning, is a simple vision task: tracking a light spot. To accomplish this, scanners use conventional CMOS sensors to capture, transmit, and process millions of pixel measurements. This approach, while capable of achieving high-fidelity 3D scans, is wasteful in terms of (often scarce) sensing and computational resources. We present a structured light system based on position sensing diodes (PSDs), an unconventional sensing modality that directly measures the centroid of the spatial distribution of incident light, thus enabling high-resolution 3D laser scanning with a minimal amount of sensor data. We develop theory and computational algorithms for PSD-based structured light under a variety of light transport effects. We demonstrate the benefits of the proposed techniques using a hardware prototype on several real-world scenes, including optically-challenging objects with long-range inter-reflections and scattering.