| Description |
%poly_poly_proj Project a planar polyline on another polyline.
%*******************************************************************************
% function: poly_poly_proj
% Description: Compute the distances (cross-ranges) from a set of points
% P <p(1), p(2), ..., p(m)> on a plane to the planar polyline
% V <v(1), v(2), ..., v(n)>, and the distances (ranges) from the
% projections of P on V to the first point of a segment containing
% the projected point. Planar polyline V is defined as a set of n-1
% segments connecting n ordered vertices v(1), v(2), ..., v(n) on a
% plane.
% In case when the shortest distance is to the vertex of the
% polyline (see p(2) in the picture below), the cross range
% cr(2) will be the distance to the vertex and the range will be
% the length of this segment (segment # 3)
%
% p(1)
% o p(m)
% | o
% cr(1)-> | p(k) /
% | o / <- cr(m)
% v(1) v(2) | cr(k)-> | /
% x---x | | v(n)/
% \ | x-->|--------x <- r(m) = 0
% \ | v(3) / r(k)
% v(3) x->|--------x r(2)
% |->| \ <-cr(2)
% r(1) \
% o p(2)
% Input:
% xp - x coordinates of the first polyline (vector of length m)
% yp - y coordinates of the first polyline (vector of length m)
% xv - x coordinates of the second polyline (vector of length n)
% yv - y coordinates of the second polyline (vector of length n)
% Output:
% rpv - vector (of length m) of distances (ranges) from the projections on
% the second polyline to the beginnings of the segments containing
% these projections
% crpv - vector (of length m) of distances (cross-ranges) from points of the
% first polyline (P) to a second polyline (V), defined as a minimal
% distance from each point of the first polyline to any segment of a
% second polyline. Note that cr is a signed value! The sign of
% cross range is determined using a local coordinate system, where
% X axis is along the rib k, from point v(k) to v(k+1), Z axis is
% out of plane, and Y axis completes the right-hand system. The
% sign of projected point's p(j) y coordinate will determine the
% cross-range sign for this point.
% y
% ^
% | o p(j)
% | /|
% | / | <- cr > 0
% |/ |
% x---|-------x--------------> x
% v(k) v(k+1)
% spv - total projected path length. Can be negative, if P and V are in the
% opposite directions
% xppv - vector of x coordinates of the first polyline projections on the
% second polyline
% yppv - vector of y coordinates of the first polyline projections on the
% second polyline
% jppv - indices of the first points in segments containing the projections
% (vector of length m). In the abovementioned example, this vector
% should be jpv = [2, 4, 5, 6]. Note that the shortest distances
% of points p(1), p(2) and p(4) are not to the second polyline's
% ribs, but to the verices.
% Routines:
% Revision history:
% 12/05/2009 - added dimension parameter to cross function-Michael Yoshpe
% 26/11/2008 - created by Michael Yoshpe
% Remarks:
% Based on routine p_poly_dist that computed the distance from point to
% polygon
%******************************************************************************* |
