We propose efficient methods for implementing 3-D reconstruction algorithms for Compton camera. Since reconstructing Compton scattered data involves the surface integral over the cone associated with the measurement bin, it is crucial to develop a computationally efficient surface integration method. In this work we assume that a cone is made up of a series of ellipses (or circles) stacked up one o top of the other. In order to reduce computational burden for tracing ellipses formed by the intersection of a cone and an image plane, we construct a series of imaginary planes perpendicular to the cone axis so that each plane contains a circle, not an ellipse. In this case the surface integral can be performed by adding uniform samples along each circle. The experimental results demonstrate that our method using imaginary planes significantly improves computational efficiency while keeping reconstruction accuracy.