Differentiable surface rendering has significantly advanced 3D reconstruction. Existing surface rendering methods assume that the local surface is planar, and thus employ linear approximation based on the Singed Distance Field (SDF) values to predict the point on the surface. However, this assumption overlooks the inherently irregular and non-planar nature of object surfaces in the real world. Consequently, the approximate points tend to deviate from the zero-level set, affecting the fidelity of the reconstructed shape. In this paper, we propose a novel surface rendering method termed CPT-VR, which leverages the Closet Point Transform (CPT) and View and Reflection direction vectors to enhance the quality of reconstruction. Specifically, leveraging the physical property of CPT that accurately projects points near the surface onto the zero-level set, we correct the deviated points, thus achieving an accurate geometry representation. Based on our accurate geometry representation, incorporating the reflection vector into our method can facilitate the appearance modeling of specular regions. Moreover, to enable our method to no longer be dependent on any prior knowledge of the background, we present a background model to learn the background appearance. Compared to previous state-of-the-art methods, CPT-VR achieves better surface reconstruction quality, even for cases with complex structures and specular highlights.