In this paper, we obtain a generalized version of the well-known distance function family L p norm. We prove that the new functions satisfy distance function properties. By using these functions, convex symmetric shapes distance from a given point. We also show that these symmetric can be described as loci, the set of points which are in equal convex shapes can be easily parameterized. We also Condition. We provide a fast ray marching algorithm for rendering show these distance functions satisfy a Lipschitz type shapes described by these distance functions. These distance func-tions can be used as building blocks for some implicit mod-eling tools such as soft objects, constructive soft geometry, freps or ray-quadrics.