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A computational method for quantitative analysis of temporomandibular joint (TMJ) configuration using occlusal positioning splints is proposed and demonstrated. The method models a positioning splint as a physical realization of a predefined rigid transformation of the mandible, derived from multimodal data, including CBCT, facial motion acquisition, and dental scans integrated within a common coordinate system. Splints corresponding to selected mandibular positions are designed and fabricated, and their positioning accuracy is evaluated using repeated scans of plaster models. Discrepancies are represented as error transformations and analyzed statistically in the space of rigid motions. The estimated transformations are propagated to segmented TMJ structures, enabling simulation-based evaluation of joint space changes. Transformation-based error analysis and surface distance metrics are used to quantify differences between planned and achieved configurations. The method enables indirect assessment of TMJ configuration using a single anatomical model and transformation data, reducing the need for repeated imaging across multiple mandibular positions. This study is intended as a methodological demonstration, supported by a clear step-by-step graphical presentation, and does not aim to provide clinical validation.