In this work, we formulate a fully-graphical axiomatization for CVQC representing both continuous functions in position and momentum space, and discrete functions in the Fock number basis. In addition to the Fourier transform between position and momentum space, and the Hermite transform between position and Fock space, we identify exciting new graph-theoretic structure capturing heftier CVQC interactions. We ensure this calculus is complete for all of Gaussian CVQC interpreted in infinite-dimensional Hilbert space, by translating the completeness in affine Lagrangian relations by Booth, Carette, and Comfort. Applying our calculus for quantum error correction, we derive graphical representations of the Gottesman-Kitaev-Preskill (GKP) code encoder, syndrome measurement, and magic state distillation of Hadamard eigenstates. Finally, we present a fully-graphical proof of correctness of Gaussian boson sampling.