Computer aided modeling technique for 3d free-form objects and apparatus

Abstract

A set of points (x,y,z) satisfying relation F(x,y,z)=a, where F(x,y,z) represents density distribution in a 3D space x-y-z, is defined as a surface of object, a set of points (x,y,z) satisfying relation F(x,y,z)>a as an outside of object and a set of points (x,y,z) satisfying relation F(x,y,z)<a as an outside of object. Density distribution c(x,y,z) generated by the designer and density distribution Fq(x,y,z) already existing in the space are blended according to equation Gq(x,y,z)=.PSI.(Fq(x,y,z), c(x,y,z)) using a smooth function .PSI.(.xi., .zeta.) having two variables .xi., .zeta., thereby generating density distribution Gq(x,y,z). Sampling data .LAMBDA..sub.q up to the mth-order partial derivative of the density distribution Gq(x,y,z) is determined on a finite number of points in the 3D space. A smooth function Fq(x,y,z) for interpolating this sampling data .LAMBDA..sub.q is generated, and new density distribution Fq(x,y,z) is expressed by the generated function, thereby updating the density distribution Fq(x,y,z). The density distribution F(x,y,z) obtained by convex combination of a number n of smooth functions Fq(x,y,z) (q=1, 2, . . . , n) at each coordinate point is assumed to be density distribution F(x,y,z) for expressing an object.