matlab 三维重建 曲面转实体

function [x_out, y_out, z_out] = surf2solid(x,y,z, S, delta) % % file: surf2solid.m, (c) Matthew Roughan, Mon Feb 14 2011 % directory: /home/mroughan/src/matlab/STL/ % created: Mon Feb 14 2011 % author: Matthew Roughan % email: matthew.roughan@adelaide.edu.au % % Convert a surface into a solid object for printing on a 3D printer % % This routine only works for surfaces defined on a rectangular % grid. The matrices X and Y define the axis limits only. % % The assumption is that % -- the surface is a function z(x,y) % -- the input are given in triples (x,y, z(x,y)) similar to the matrix input option % of surf, mesh or other similar commands % i.e., x, and y specify regular, rectangular lattice points % but note that this doesn't support the 1, or 2 argument versions of these commands % and assumes that x and y are matrices, not vectors % -- x values increase along rows % y values along columns, e.g., as if they are the outputs of % [x,y] = meshgrid( 1:3, 1:4 ) % % The output will be a solid with height given by z at each point (x,y), and % -- the surface z will be shifted by z_0, such that z+z_0 >= delta % where delta is the minimum z height % -- the (x,y) co-ordinates will be shifted so that (x+x_0, y_y_o) is "centered" % -- the x, y, and z values will be scaled so that the largest value of % (max(x) - min(x), (max(y)-min(y)), and 2*(max(z)-min(z)) % is such that the largest of these dimensions is size S where S in measured in mm % (NB: matlab co-ordinates come out roughly as mm in the makerbot) % -- the surface z(x,y)+z_0 will have vertical walls going down to the (x,y) plane, % and the bottom surface of the object will be the part of the (x,y) plane including % the (x,y) points of the input (suitable rescaled) % (e.g. see what meshz does) % % NB: fair bit of code is inspired by meshz % err_id = 'surf2solid:InvalidInput'; % check inputs if (nargin < 3) error(err_id,'Need to input at least 3 arguments.') end if ischar(x) || ischar(y) || ischar(z) error(err_id,'Input should not be characters.') end [m,n] = size(z); [mx,nx] = size(x); [my,ny] = size(y); if (m == 1 || n == 1) error(err_id,'Arrays must have size >1 in each direction.') end if (~isequal(size(z),size(x)) || ~isequal(size(z),size(y))) error(err_id,'Input arrays (x,y,z) should all be the same size.') end if (~all(isfinite(z))) error(err_id,'z must have finite values.') end if (~all(isfinite(y))) error(err_id,'y must have finite values.') end if (~all(isfinite(x))) error(err_id,'x must have finite values.') end if (nargin < 4) S = 40; % make the default max length along an axis 40mm end if (S>100) error(err_id,'S must be <= 100 due to size of build platform') end if (nargin < 5) delta = 3; % make the default minimum height 3 mm end if (delta < 0) error(err_id,'delta must be >=0 to build') end % scale co-ordinates x_diff = max(max(x)) - min(min(x)); y_diff = max(max(y)) - min(min(y)); z_diff = 2*(max(max(z)) - min(min(z))); max_diff = max([x_diff; y_diff; z_diff]); scale_factor = S/max_diff x_s = scale_factor * x; y_s = scale_factor * y; z_s = scale_factor * z; mx_x = max(max(x_s)); mn_x = min(min(x_s)); mx_y = max(max(y_s)); mn_y = min(min(y_s)); mx_z = max(max(z_s)); mn_z = min(min(z_s)); % shift the min z co-ordinate z = z_s + delta - mn_z; % center the (x,y) co-ordinates x = x_s - (mx_x + mn_x)/2; y = y_s - (mx_y + mn_y)/2; xmin = min(min(x)); ymin = min(min(y)); xmax = max(max(x)); ymax = max(max(y)); % create an extended Z matrix % z_out = [[ 0 0 zeros(1,n) 0 0 ]; % [ 0 0 z(1,:) 0 0 ]; % [zeros(m,1) z(:,1) z z(:,n) zeros(m,1)]; % [ 0 0 z(m,:) 0 0 ]; % [ 0 0 zeros(1,n) 0 0 ]; % ]; z_out = [[z(1,1) z(1,:) z(1,n)]; [z(:,1) z z(:,n)]; [z(m,1) z(m,:) z(m,n)]; ]; z_out = zero_pad(z_out, 2); % extend the x and y arrays d = [1 1]; mm = [m m]; nn = [n n]; x_out = [[ x(d,d) x(d,:) x(d,nn) ]; [ x(:,d) x x(:,nn) ]; [ x(mm,d) x(mm,:) x(mm,nn) ]; ]; x_out = zero_pad(x_out, 1); y_out = [[ y(d,d) y(d,:) y(d,nn) ]; [ y(:,d) y y(:,nn) ]; [ y(mm,d) y(mm,:) y(mm,nn) ]; ]; y_out = zero_pad(y_out, 1); mesh(x_out, y_out, z_out); function B = zero_pad(A, k) % % pad zeros around entire outside of array to width k % %%% B = padarray( padarray(A, k)', k)'; [mA,nA] = size(A); B = [[zeros(k,k) zeros(k,nA) zeros(k,k)]; [zeros(mA,k) A zeros(mA,k)]; [zeros(k,k) zeros(k,nA) zeros(k,k)]; ];