This paper describes how the web-based visualization can be greatly improved using the function-based shape modeling technique. The improvement is possible because the proposed function-defined VRML shape node allows the content creators to describe any complex models with relatively small functions compared to the large-size polygonal mesh based VRML nodes. These function-defined shapes can be used together with the common VRML shapes. The proposed node has a few implementations capable of visualizing geometric shapes defined with HyperFun language as well as in any proprietary function-defined data format. For fast visualization of the function-defined shapes, we have developed an improved continuation polygonization algorithm specifically designed for VRML visualization. The design, the implementation details, and the application examples of the proposed node are discussed.