Near-horizontal shore platforms display highly irregular plan shapes, but little is known about the way in which these irregularities influence the significant wave height (Hs) on the platforms and the frequency components of the nearshore wave field. We use a nonlinear Boussinesq wave model to conduct harmonic and bispectral mode decomposition analyses, studying the control of concave and convex platform edges over wind (WW: 0.125 - 0.33 Hz), swell (SW: 0.05 - 0.125 Hz) and infragravity (IG: 0.008 - 0.05 Hz) frequencies. For breaking and non-breaking waves, increasing the platform edge concavity intensified wave divergence and subsequent attenuation of SW and IG across the outer platforms, reducing by up to 25%. Increasing the platform edge convexity intensified focusing and amplification of SW and WW over the outer platforms, increasing by up to 18% and 55% for breaking and non-breaking waves. In the presence of breaking, IG amplification depended on the generation of wave divergence across the inner platform, a condition determined by a critical convex curvature threshold (Κ=1.8) balancing wave focusing from refraction and defocusing from breaking. We find that convex curvature can determine the relative dominance of WW, SW and IG across platforms. Alongshore, coherent wave interactions governed IG stationary patterns defined by a node near the platform centreline and two antinodes on either side of concave edges. A node was generated at the platform centreline, and two antinodes were observed on either side of the convex edges for Κ>1.8, with the opposite pattern observed for Κ<1.8.