Image composition aims to seamlessly integrate a foreground object into a background, where generating realistic and geometrically accurate shadows remains a persistent challenge. While recent diffusion-based methods have outperformed GAN-based approaches, existing techniques, such as the diffusion-based relighting framework IC-Light, still fall short in producing shadows with both high appearance realism and geometric precision, especially in composite images. To address these limitations, we propose a novel shadow generation framework based on a Keypoints Linear Model (KPLM) and a Shadow Triangle Algorithm (STA). KPLM models articulated human bodies using nine keypoints and one bounding block, enabling physically plausible shadow projection and dynamic shading across joints, thereby enhancing visual realism. STA further improves geometric accuracy by computing shadow angles, lengths, and spatial positions through explicit geometric formulations. Extensive experiments demonstrate that our method achieves state-of-the-art performance on shadow realism benchmarks, particularly under complex human poses, and generalizes effectively to multi-directional relighting scenarios such as those supported by IC-Light.