In this work, the problem of construct ing mathemat icalmodels of a 3-D surfaces of arbitrary shapes is considered. Asurvey is presented for previous work and a comparison betweenexisting models imply that the field is dominated by modelsbased on parametric funct ion. However, the parametr icfunctions used is a subclass of the implicit algebraicfunctions, the parametric functions are not closed under manygeometric operations under which the implicit algebraicfunctions are closed, the algebraic degree of a degreen-parametric surface is n2 and a bidegree n-parametric surfacecan be of algebraic degree up to 2n2, whereas for a surfacedefined by an implicit algebraic equation its algebraic degreeis the same as the degree of the defining equation, more~verthe point classification problem is greatly simplified whenusing implicit algebraic representation. For these reasons andothers, attention is focused on modeling with implicitfunction, especially that of low degree.A mathemat ical model is developed to controlsingularities of quadrics and cubics, also a mathematicalmodel for detrmining the equations of the projections of theintersection of two algebraic surfaces is established.The above entities are utilized in constructing threemodels for 3-D surfaces of arbi trary shapes based on lowdegree implicit functions. In the first model the buildingunit is a quadratic patch with natural intersection boundariesand a near et overall continuity. In the second model thebuilding unit is a cubic implicit patch with quadraticparametric boundary curves. A CO overall continuity isgauranteed wi th at least two degrees of freedom used tocontrol singularities and to enhance the overall continuity tobe eO+. In the third model a side vertex interpolation schemeis used to construct three cubic patches for every inputwater. The presence of fiber increases the work required to fracture the GFRMspecimens and altered their failure mode from a brittle to more ductile failure. Theaddition of 10% silica fume of cement weight enhances the mechanical properties ofthe specimens stored in water media at all ages. For specimens stored in sulfate themechanical properties enhances with the addition of 10% SF up to 180 days and afterthat they decreases. Sulfate resistant cement shows high strength in sulfate mediacompared to those specimens stored in water media especially in compressive andtensile strengths without fib er volume fraction but it has a negative effect on theflexural strength. Specimens made with OPC + 10% SF had the highest compressivestrength compared to those made with sulfate resistant cement or OPC, for specimensstored in water media with or without fiber. In sulfate media, SRC gives the highestcompressive strength. GFRM Specimens made by OPC + 10% SF had the highestvalues of the tensile strength at early ages up to 180 days.