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Coronary artery disease (CAD) remains the leading cause of death worldwide. Patients with suspected CAD undergo coronary CT angiography (CCTA) to evaluate the risk of cardiovascular events and determine the treatment. Clinical analysis of coronary arteries in CCTA comprises the identification of atherosclerotic plaque, as well as the grading of any coronary artery stenosis typically obtained through the CAD-Reporting and Data System (CAD-RADS). This requires analysis of the coronary lumen and plaque. While voxel-wise segmentation is a commonly used approach in various segmentation tasks, it does not guarantee topologically plausible shapes. To address this, in this work, we propose to directly infer surface meshes for coronary artery lumen and plaque based on a centerline prior and use it in the downstream task of CAD-RADS scoring. The method is developed and evaluated using a total of 2407 CCTA scans. Our method achieved lesion-wise volume intraclass correlation coefficients of 0.98, 0.79, and 0.85 for calcified, non-calcified, and total plaque volume respectively. Patient-level CAD-RADS categorization was evaluated on a representative hold-out test set of 300 scans, for which the achieved linearly weighted kappa ($\kappa$) was 0.75. CAD-RADS categorization on the set of 658 scans from another hospital and scanner led to a $\kappa$ of 0.71. The results demonstrate that direct inference of coronary artery meshes for lumen and plaque is feasible, and allows for the automated prediction of routinely performed CAD-RADS categorization., Comment: 12 pages, 6 figures, accepted in IEEE Transactions on Medical Imaging