Interest in human emotion recognition, regarding physiological signals, has recently risen. In this study, an efficient emotion recognition system, based on geometrical analysis of autonomic nervous system signals, is presented. The electrocardiogram recordings of 47 college students were obtained during rest condition and affective visual stimuli. Pictures with four emotional contents, including happiness, peacefulness, sadness, and fear were selected. Then, ten lags of Poincare plot were constructed for heart rate variability (HRV) segments. For each lag, five geometrical indices were extracted. Next, these features were fed into an automatic classification system for the recognition of the four affective states and rest condition. The results showed that the Poincare plots have different shapes for different lags, as well as for different affective states. Considering higher lags, the greatest increment in SD1 and decrements in SD2 occurred during the happiness stimuli. In contrast, the minimum changes in the Poincare measures were perceived during the fear inducements. Therefore, the HRV geometrical shapes and dynamics were altered by the positive and negative values of valence-based emotion dimension. Using a probabilistic neural network, a maximum recognition rate of 97.45% was attained. Applying the proposed methodology based on lagged Poincare indices, a valuable tool for discriminating the emotional states was provided.