Accurate 3D representations of cardiac structures allow quantitative analysis of anatomy and function. In this work, we propose a method for reconstructing complete 3D cardiac shapes from segmentations of sparse planes in CT angiography (CTA) for application in 2D transthoracic echocardiography (TTE). Our method uses a neural implicit function to reconstruct the 3D shape of the cardiac chambers and left-ventricle myocardium from sparse CTA planes. To investigate the feasibility of achieving 3D reconstruction from 2D TTE, we select planes that mimic the standard apical 2D TTE views. During training, a multi-layer perceptron learns shape priors from 3D segmentations of the target structures in CTA. At test time, the network reconstructs 3D cardiac shapes from segmentations of TTE-mimicking CTA planes by jointly optimizing the latent code and the rigid transforms that map the observed planes into 3D space. For each heart, we simulate four realistic apical views, and we compare reconstructed multi-class volumes with the reference CTA volumes. On a held-out set of CTA segmentations, our approach achieves an average Dice coefficient of 0.86 $\pm$ 0.04 across all structures. Our method also achieves markedly lower volume errors than the clinical standard, Simpson's biplane rule: 4.88 $\pm$ 4.26 mL vs. 8.14 $\pm$ 6.04 mL, respectively, for the left ventricle; and 6.40 $\pm$ 7.37 mL vs. 37.76 $\pm$ 22.96 mL, respectively, for the left atrium. This suggests that our approach offers a viable route to more accurate 3D chamber quantification in 2D transthoracic echocardiography.