A geometrically-motivated method for primary-ambient decomposition is proposed and evaluated in an up-mixing application. The method consists of two steps, accommodating a particularly intuitive explanation. The first step consists of signal-adaptive rotations applied on the input stereo scene, which translate the primary sound sources into the center of the rotated scene. The second step applies a center-channel extraction method, based on a simple signal model and optimal in the mean-squared-error sense. The performance is evaluated by using the estimated ambient component to enable surround sound starting from real-world stereo signals. The participants in the reported listening test are asked to adjust the audio scene envelopment and find the audio settings that pleases them the most. The possibility for up-mixing enabled by the proposed method is used extensively, and the user satisfaction is significantly increased compared to the original stereo mix.