Showing papers on "Centroid published in 1971"

System for resolving the sizes and centroid locations of buried objects

Abstract: A broadband, radar-type system for resolving the sizes and centroid locations of objects buried at a maximum depth in the order of 6 to 10 feet is disclosed. The system uses a carrier frequency which is high enough so that an instantaneous bandwidth of about 25 percent provides resolution in the order of 1 foot. The system antenna includes impedance matching and focusing means. Polarization diversity of the transmitted beam may be accomplished to distinguish between elongated and generally round objects.

Quadrics associated with a simplex in n-space

Abstract: It is well known that the projections of a pair of points from the vertices of a triangle onto the opposite sides lie on a conic and that when the points are the centroid and orthocentre of the triangle, this conic is a circle. Analogously the projections of the centroid and orthocentre of a simplex from its vertices onto the opposite ( n —1)-dimensional faces, if the simplex is orthocentric, lie on a hypersphere [2, 5]. Further the projections of two points onto the edges of a general simplex from the opposite faces lie on quadric [1]; and when the points are the centroid and orthocentre respectively and the simplex is orthocentric, this quadric is a hypersphere [2]. The results as regards projections onto ( n —l)-dimensional and 1-dimensional faces being thus known, it remains to see what results hold in the case of intermediary faces. And in this note we prove that a similar result holds for projections onto intermediary faces as well.