Converts curves in BezStruct to svg format.

bez2svg.m

% Converts curves in BezStruct to svg format.                                  
%                                   
%                                   
% Input(s)                          
%   BezStruct: 
%    BezCurves: Structure of Bezier curves for each of the 6 fundamental curves
%               Sheer, Freeboard, Profile, A (homotopy), eta1 and eta2
%    sections:  Section curves derived from the Bezier functions at nSections 
%               intervals along the hull
%    functions: Symbolically defined functions for each section (eta), and a 
%               final set for the transom, (trans_x, trans_y, trans_z)
%    Boat parameters:
%          LOA: Length overall
%         Beam: Maximum beam
%        Draft: Maximum draft
%      Midship: Distance from bow of maximum beam
%
%   svgDir: Directory containing output svg files for each curve
%                                   
%                                   
% Output(s)                         
%   Bow/stern and section curves saved to separate files in svgDir                                
%                                   
% Example:                          
% BezStruct = BezierHull(<curves.xlsx>);
% bez2svg(BezStruct,svgDir);                                  
%                                   
% See also: BezierHull, idNestObjects                        
%                                   
%                                   
% Dependencies: func2Coords, pts2svg, funcSolve, disperse                    
                                    
%                                   
%                                   
% Written by: John Peach 06-Sep-2021
% Wild Peaches                      
%                                   
% Revisions:                        
                                    
                                    
function bez2svg(BezStruct,svgDir)    

    % Distance between sections, number of sections
    dSect  = 0.5;
    LOA    = BezStruct.LOA;
    xt     = dSect:dSect:LOA-dSect;
    nSects = numel(xt); 
    ft2in  = 12;
    
    % Sheer, freeboard and profile at each section
    t       = linspace(0,1,50);
    BZ.s    = BezStruct.symFuncs.s;
    BZ.f    = BezStruct.symFuncs.f;
    BZ.p    = BezStruct.symFuncs.p;
    BZ.A    = BezStruct.symFuncs.A;
    BZ.eta1 = BezStruct.symFuncs.eta1;
    BZ.eta2 = BezStruct.symFuncs.eta2;
    BZ.LOA  = LOA;
    
    %% Bow sheer 
    Pts = func2Coords(BZ.s,[LOA-dSect,LOA],LOA,50);
    bowPts = ft2in * [Pts; [Pts(1,1) Pts(end,2)]; Pts(1,:)];
    % Write points to svg format
    pts2svg(bowPts,'bowSheer',svgDir);  

    %% Stern sheer 
    Pts = func2Coords(BZ.s,[0,dSect],LOA,100);
    sternPts = ft2in * [Pts; [Pts(end,1),0]; Pts(1,:)];
    pts2svg(sternPts,'sternSheer',svgDir);
         
    %% Combined freeboard/profile at bow and stern
    fPts = func2Coords(BZ.f,[LOA-dSect,LOA],LOA,50);
    pPts = func2Coords(BZ.p,[LOA-dSect,LOA],LOA,50);
    bowPts = ft2in * [fPts; flipud(pPts); fPts(1,:)];  
    pts2svg(bowPts,'bowFbdProf',svgDir);   

    fPts = func2Coords(BZ.f,[0,dSect],LOA,50);
    pPts = func2Coords(BZ.p,[0,dSect],LOA,50);
    sternPts = ft2in * [fPts;flipud(pPts);fPts(1,:)];            
    pts2svg(sternPts,'sternFbdProf',svgDir);   
    
    %% Sections
    for k = 1:nSects
        rtPts = section_at_x(xt(k),BZ,50);
        ltPts = flipud([-rtPts(:,1) rtPts(:,2)]);
        section = ft2in * [rtPts; ltPts; rtPts(1,:)];
        secFName = ['Section_',num2str(xt(k))];
        pts2svg(section,secFName,svgDir);        
    endfor
                                           
endfunction  

function Pts = func2Coords(func,Rng,LOA,nPts)
    % Locations on x-axis in Rng 
    x = linspace(min(Rng),max(Rng),nPts);
    
    % Values of parameter t generating x
    t = funcSolve(func.x,x)';
    
    % Coordinates
    Pts = [func.x(t) func.y(t)];
                                        
endfunction 

function Pts = section_at_x(x,BZ,nPts)
    % Parameter t for each function
    st = funcSolve(BZ.s.x,x);
    ft = funcSolve(BZ.f.x,x);
    pt = funcSolve(BZ.p.x,x);
    At = funcSolve(BZ.A.x,x);
    
    % Evaluate s,f,t,A at x
    sx = BZ.s.y(st);
    fx = BZ.f.y(ft);
    px = BZ.p.y(pt);
    Ax = BZ.A.y(At);
    
    % Section curves in y,z coordinates
    y = @(t) sx * ((1-Ax) * BZ.eta1.x(t) + Ax * BZ.eta2.x(t));
    z = @(t) (fx-px) * ((1-Ax) * BZ.eta1.y(t) + Ax * BZ.eta2.y(t)) + px;
    t = linspace(0,1,nPts)';
    Pts = [y(t) z(t)];
    
endfunction

function t = funcSolve(f,y)    
    % Returns t such that f(t) = y for input values of y                                    
    %                                     
    %                                     
    % Input(s)                            
    %   f: Function handle
    %   y: Values where f(t) are required                                  
    %                                     
    % Output(s)                           
    %   t: Values such that f(t) = y 
    
    % Number of data points
    n = numel(y);
    
    % Initialize output vector
    t = nan(1,n);
    
    % Loop over each y_k to find t_k
    for k = 1:n
        try
            s = fminbnd(@(x) (f(x) - y(k)).^2,0,1);
            t(k) = s;            
        catch
        end_try_catch
    endfor
    
    % Remove values of t outside [0,1]
    t(t < 0) = nan;
    t(t > 1) = nan;

endfunction 

function pts2svg(pts,curveName,svgDir)
        
    % Open file
    svgFile = fullfile(svgDir,[curveName '.svg']);
    fid = fopen(svgFile,'w');
    
    % Dimensions of the curve
    pts = pts - min(pts) + [0.1 0.1]; % Shift to align with x,y axes + 0.1 units
    [x,y] = disperse(roundi(max(pts),5,'up'));
    
    % Write header lines
    fprintf(fid,'<?xml version="1.0" standalone="no"?>\n');
    fprintf(fid,'<svg width="%5.2fin" height="%5.2in" viewBox="0 0 %d %d" xmlns="http://www.w3.org/2000/svg" version="1.1">\n',x,y,x,y);
    fprintf(fid,'<title> End curve or section: %s </title>\n',curveName);
    fprintf(fid,'<desc>A path that draws a curve</desc>\n');
    
    % Write points to svg files
    fprintf(fid,'<path d="M %5.2f %5.2f\n',pts(1,1),pts(1,2));
    for k = 2:size(pts,1)
        fprintf(fid,'         L %5.2f %5.2f\n',pts(k,1),pts(k,2));
    endfor
    fprintf(fid,'         z"\n');
    fprintf(fid,'        fill="none" stroke="blue" stroke-width="1" />\n');
    fprintf(fid,'</svg>\n');
    
    % Close file
    fclose(fid);
    
endfunction    

% DISPERSE was created so that you can stop doing things like this:
%
%   x1 = array(1); % ...repetitive assignments from an array
%   x2 = array(2);
%   x3 = array(3);
%   x4 = array(4);
%
% and start doing things like this:
%
%   [x1 x2 x3 x4] = disperse(array);
%
% DISPERSE generalizes to arbitrary dimensions, and is extended to follow
% analogous behavior on cell arrays and structure arrays. See the html
% documentation for more details and examples.
%
% Example:
%   Grab the color channels from an RGB image:
%   [r g b] = disperse(im);

% Sam Hallman
% shallman@uci.edu
% May 26, 2010

function varargout = disperse(x)

    % num2cell on column vectors is problematic
    if ndims(x)==2 && size(x,2)==1
        x = x';
    end

    if isnumeric(x) || ischar(x) || islogical(x) || isstruct(x)
        dims = 1:ndims(x)-1;
        varargout = num2cell(x,dims);
    elseif iscell(x)
        if size(x,1) == 1
            varargout = x;
        else
            dims = 1:ndims(x)-1;
            varargout = num2cell(x,dims);
        end
    else
        error('unknown data type');
    end    

endfunction