Geometric (proxy-based) haptic rendering algorithms are widely used in impedance-type haptic rendering. Such methods are useful for developing complex virtual environment because they reduce mechanistic problems of determining reaction forces into geometric problems of updating proxy positions. This paper aims to apply geometric algorithms to wider variations of haptic rendering systems. First, we present a method to include viscous damping in impedance-type haptic rendering. Second, we propose a method to utilize geometric algorithms in admittance-type haptic rendering. The results of implementation experiments are presented.