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Large-scale Vehicular Ad Hoc Network (VANET) simulators by and large employ simple statistical channel models. By design, such models do not account for specific objects in the region of interest when estimating the channel. While computationally efficient, these models were shown to be unable to provide satisfactory accuracy on a link level for typical VANET scenarios. Specifically, experimental studies have shown that both large static objects (e.g., buildings and foliage) as well as mobile objects (surrounding vehicles) have a profound impact on the quality of vehicle-to-vehicle (V2V) channels. While several recently proposed large-scale V2V channel models account for static objects (e.g., buildings) in the simulated area, there is a need for a comprehensive model that takes into account both the static and the mobile objects. To fill this gap, we designed a geometry-based, computationally manageable V2V channel model that uses the real-world locations and the actual dimensions of vehicles, buildings, and foliage to simulate the V2V channel more realistically. We use the outlines of the modeled objects to form spatial tree structures for efficient manipulation of geographic data. We distinguish and model separately the following three link types: line of sight (LOS), non-LOS due to vehicles, and non-LOS due to static objects. Apart from the model for large-scale signal variations, we also propose a simple model for small-scale signal variation using the number and size of the objects around the communicating vehicles. We validate the models against extensive measurements performed in urban, suburban, highway, and open space environment. We provide the complete simulation recipe for the implementation of the model in simulators. Finally, we implement the model in Matlab and show that it scales well by simulating networks with tens of thousands of objects and hundred thousand communicating vehicle pairs using commodity hardware.