This modeling study investigates whether an orderly convergence of neuronal selectivities from cortical areas V1 and V2 can produce curvature selective receptive fields found in area V4. A model of the ventral visual pathway from V1 to V4 is composed of approximately 500,000 individual integrate and fire units. The V1 and V2 models are based on recent findings about the composition of V2 receptive fields. A novel proposal is made for how V4 neurons may create selectivity for varying degrees of local curvature through the orderly convergence of afferent inputs from V2. The study employs a novel method for simulating individual spikes in large numbers of model neurons using tensor programming and GPU hardware: Assuming that convergent functional micro-architectural patterns repeat in topographically organized visual space, the details of individual unit depolarization and spike time is modeled using convolution operations combined with a model for the time course of post-synaptic potentials. The few parameters in the model are set manually, and this is sufficient to qualitatively reproduce the V4 recordings. This demonstrates that convolution is a useful model for understanding fast feed forward processing in the ventral visual path and that convolution technologies can be used for the realistic simulation of large numbers of neurons at an intermediate level of biological detail.