In the modern urban society, human brain is not being sufficiently trained to deal with problems which require strong 3D spatial visualization. As a result, when teaching subjects richly infused with geometry and mathematics it is usually a challenge for the learners to follow the instructor and visualize how mathematical concepts reflect in 3D geometry and colors. We have proposed an approach that allows for defining geometry, visual appearance and tangible physical properties of virtual objects by using mathematical formulas. It allows the learners to get immersed within the 3D scene and explore the shapes which are being modeled visually and haptically. We illustrate this concept with our function-based extension of X3D and VRML. Besides definition of objects with mathematical functions straight in the scene file, standard X3D and VRML objects can be converted into tangible ones as well as augmented with function-defined visual appearances. Since the function-defined models are small in size, it is possible to perform their collaborative interactive modifications with concurrent synchronous visualization at each client computer with any required level of detail which we illustrate with an interactive modeling tool used in education in our university.