Analyzing the anatomy of the aorta and left ventricular outflow tract (LVOT) is crucial for risk assessment and planning of transcatheter aortic valve implantation (TAVI). We propose 2D cross-sectional annotation and point cloud-based surface reconstruction to train a fully automatic 3D segmentation network for the aortic root and the LVOT. Our sparse annotation scheme enables easy and fast training data generation for tubular structures like the aortic root. Based on this annotation concept, we trained a 3D segmentation model that achieves a Dice similarity coefficient (DSC) of 0.9 and an average surface distance (ASD) of 0.96 mm. In addition, we show that our fully automatic segmentation approach facilitates reproducible and quantifiable measurements for TAVI planning. Our approach achieves an aortic annulus maximum diameter difference between prediction and annotation of 0.45 mm (inter-observer variance: 0.25 mm).