Evolution of additive manufacturing, particularly in 3D printing, has facilitated the production of complex architected materials, combining strength and lightness. Traditional inspection methods are unsuitable for them, necessitating a tomography-based inspection method to examine their internal structure. This work presents a fast and accurate 3D Virtual Image Correlation (3D-VIC) algorithm, leveraging the existence of a Computer-Aided Design (CAD) model, essential for the material's printing. The approach involves comparing virtual projections of the CAD model with those obtained from a printed material via tomography. The CAD model is adjusted using radial basis function interpolation to align the virtual and real projections. In this paper, the algorithm's performance is evaluated based on binning and noise. Subsequently, a shape measurement is performed using actual projections on a tetrahedral architected material. Compared to existing shape measurement methods using computed tomography, the proposed approach requires less projections and does not induce the biases linked to the 3D image reconstruction process. Thus, it constitutes a robust and efficient VIC method for shape measurements from tomographic images.