Geometric design and space planning using the marching squares and marching cube algorithms

In the paper we present a method for area and volume approximation using modifications to the marching cubes algorithm of Lorensen and Cline (1987). Approximations to two and three-dimensional objects using marching squares and marching cubes have been covered extensively. Given an approximation to an object, an algorithm is presented which allows a simple method that can approximate the area or volume of the object. More interestingly the method can be used to estimate the area encapsulated between two points on the surface and a line or the volume encapsulated between three points on the surface and a plane. This is of use in room and space planning operations or the design of rooms and manufactured products.