Many models exist for predicting toxicities based on dose-volume histograms (DVHs) or dose-surface histograms (DSHs). This approach has several drawbacks as firstly the reduction of the dose distribution to a histogram results in the loss of spatial information and secondly the bins of the histograms are highly correlated with each other. Furthermore, some of the complex nonlinear models proposed in the past lack a direct physical interpretation and the ability to predict probabilities rather than binary outcomes. We propose a parameterized representation of the 3D distribution of the dose to the rectal wall which explicitly includes geometrical information in the form of the eccentricity of the dose distribution as well as its lateral and longitudinal extent. We use a nonlinear kernel-based probabilistic model to predict late rectal toxicity based on the parameterized dose distribution and assessed its predictive power using data from the MRC RT01 trial (ISCTRN 47772397). The endpoints under consideration were rectal bleeding, loose stools, and a global toxicity score. We extract simple rules identifying 3D dose patterns related to a specifically low risk of complication. Normal tissue complication probability (NTCP) models based on parameterized representations of geometrical and volumetric measures resulted in areas under the curve (AUCs) of 0.66, 0.63 and 0.67 for predicting rectal bleeding, loose stools and global toxicity, respectively. In comparison, NTCP models based on standard DVHs performed worse and resulted in AUCs of 0.59 for all three endpoints. In conclusion, we have presented low-dimensional, interpretable and nonlinear NTCP models based on the parameterized representation of the dose to the rectal wall. These models had a higher predictive power than models based on standard DVHs and their low dimensionality allowed for the identification of 3D dose patterns related to a low risk of complication.