The visualization of a voltage stability region can conveniently monitor the voltage security margin of power systems and provide a decision-making basis to the dispatcher. An ideal model（independent normal distribution） random optimization algorithm and a general model（non-independent normal distribution） data fitting algorithm of Monte Carlo are presented to realize visualization of the static voltage stability region in cut-set space to overcome the incapability of providing credibility in the probabilistic sense of the current algorithm. The ideal model random optimization algorithm is simple and effective for solving the hyperplane equation of the voltage stability region boundary in cut-set space. The objective function of random optimization and the accuracy probabilistic index are presented to assess the accuracy of using the solution to estimate voltage stability in cut-set space. The algorithm proposed can be used to select cut-set line power and improve the accuracy probabilistic index. The concept of cut-set space is extended to quasi cut-set space to improve the accuracy probabilistic index and realize static voltage stability region visualization. The algorithm has been validated by an IEEE 39-bus system.