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In recent years, the demand for dental implants has surged, driven by their high success rates and esthetic advantages. However, accurate prediction of missing teeth for precise digital implant planning remains a challenge due to the intricate nature of dental structures and the variability in tooth loss patterns. This study presents a novel framework for accurate prediction of missing teeth in different patterns, facilitating digital implant planning. The proposed framework begins by estimating point-to-point correspondence among a dataset of dental mesh models reconstructed from CBCT images of healthy subjects. Subsequently, tooth dictionaries are constructed for each tooth type, encoding their position and shape information based on the established point-to-point correspondence. To predict missing teeth in a given dental mesh model, sparse coefficients are learned by sparsely representing adjacent teeth of the missing teeth using the corresponding tooth dictionaries. These coefficients are then applied to the dictionaries of the missing teeth to generate accurate predictions of their positions and shapes. The evaluation results on real subjects shows that our proposed framework achieves an average prediction error of 1.04mm for predictions of single missing tooth and an average prediction error of 1.33mm for the prediction of 14 missing teeth, which demonstrates its capability of accurately predicting missing teeth in various patterns. By accurately predicting missing teeth, dental professionals can improve the planning and placement of dental implants, leading to better esthetic and functional outcomes for patients undergoing dental implant procedures.