The human placenta nourishes the growing fetus during pregnancy. The newly developing field of placenta analysis seeks to understand relationships between the health of a placenta and the health of the baby. Previous studies have shown that the median and mean placental chorionic shapes are round, and deviation from such prototypical shape is related to a decreased placental functional efficiency. In this study, we propose the use of a nearly-continuous shape descriptor, called the signed deviation vector, to systematically study the relationship between various maternal and fetal characteristics and the shape of the placental surface. The proposed shape descriptor measures the amount and the direction of deviation a placental shape is away from normal. Using techniques including Principal Component Analysis (PCA) and Fisher's Linear Discriminant Analysis (LDA), we can independently examine how much of the placental shape is affected by maternal, newborn and placental characteristics. The results allow us to understand how significantly various maternal and fetal conditions affect the overall shape of the placenta growth.