Determining the Three-Dimensional Convex Hull of a Polyhedron

A method is presented for determining the three-dimensional convex hull of a real object that is approximated in computer storage by a polyhedron. Essentially, this technique tests all point pairs of the polyhedron for convex edges of the convex hull and then assembles the edges into the polygonal boundaries of each of the faces of the convex hull. Various techniques for optimizing this process are discussed. A computer program has been written, and typical output shapes are illustrated. Finding the three-dimensional convex hull is approximately the same computer burden as eliminating hidden lines.

[1]  Frank Rubin,et al.  A Search Procedure for Hamilton Paths and Circuits , 1974, JACM.

[2]  George Nagy.  Normalization techniques for handprinted numerals , 1970, CACM.

[3]  Azriel Rosenfeld,et al.  Picture Processing by Computer , 1969, CSUR.

[4]  V. N. Malozemov,et al.  Finding the Point of a Polyhedron Closest to the Origin , 1974 .

[5]  I. C. Braid,et al.  Designing with volumes , 1973 .

[6]  José L. Encarnação,et al.  PRADIS: an advanced programming system for 3-D-display , 1971, AFIPS '72 (Spring).

[7]  Arthur Appel.  Modeling in Three-Dimensions , 1968, IBM Syst. J..

[8]  Arthur Appel,et al.  The notion of quantitative invisibility and the machine rendering of solids , 1967, ACM National Conference.

[9]  Herbert Freeman,et al.  Computer Processing of Line-Drawing Images , 1974, CSUR.

[10]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[11]  Robert E. Tarjan,et al.  Efficient Planarity Testing , 1974, JACM.

[12]  C. Burdet.  Generating All the Faces of a Polyhedron , 1974 .

[13]  T. Kamae,et al.  A Systematic Method of Finding All Directed Circuits and Enumerating All DIrected Paths , 1967, IEEE Transactions on Circuit Theory.

[14]  M. Balinski.  An algorithm for finding all vertices of convex polyhedral sets , 1959 .

[15]  Ronald L. Graham,et al.  An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..

[16]  P. Loutrel.  Determination of Hidden Edges in Polyhedral Figures. Convex Case , 1966 .