pointToLineDistance.m

%{
 * Copyright (C) 2013-2020, The Regents of The University of Michigan.
 * All rights reserved.
 * This software was developed in the Biped Lab (https://www.biped.solutions/) 
 * under the direction of Jessy Grizzle, grizzle@umich.edu. This software may 
 * be available under alternative licensing terms; contact the address above.
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 * 1. Redistributions of source code must retain the above copyright notice, this
 *    list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright notice,
 *    this list of conditions and the following disclaimer in the documentation
 *    and/or other materials provided with the distribution.
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 * The views and conclusions contained in the software and documentation are those
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 * 
 * AUTHOR: Bruce JK Huang (bjhuang[at]umich.edu)
 * WEBSITE: https://www.brucerobot.com/
%}
% v1 = [0,0];
% v2 = [3,0];
% pt = [-10,5; 0,10; 0,15];
% distance_2D = pointToLineDistance(pt, v1, v2)
function distance = pointToLineDistance(pt, v1, v2)
    % v1, v2 is 1x3
    % pt is n x 3
    % check inputs
    if nargin~=3
        error('HJW:point_to_line_distance:nargin',...
            'Incorrect number of inputs, expected 3.');
    end
    if ~isnumeric(pt) || ~any(size(pt,2)==[2 3]) || any(size(pt)==0)
        error('HJW:point_to_line_distance:pt_type_size',...
            'First input (pt) is not numeric or has an incorrect shape.')
    end
    if ~isnumeric(v1) || numel(v1)~=size(pt,2)
        error('HJW:point_to_line_distance:v_type_size',...
            ['Second input (v1) is not numeric or has an incorrect ',...
            'size.' char(10) 'Expected 1x3 or 1x2, which should match ',...
            'the first input.']) %#ok<CHARTEN>
    end
    if ~isnumeric(v2) || numel(v2)~=size(pt,2)
        error('HJW:point_to_line_distance:v_type_size',['Third input (v2) ',...
            'is not numeric or has an incorrect size.' char(10) 'Expected ',...
            '1x3 or 1x2, which should match the first input.']) %#ok<CHARTEN>
    end
    %prepare inputs
    v1=v1(:)';%force 1x3 or 1x2
    if length(v1)==2,v1(3)=0;end%extend 1x2 to 1x3 if needed
    v2=v2(:)';%force 1x3 or 1x2
    if length(v2)==2,v2(3)=0;end%extend 1x2 to 1x3 if needed
    if size(pt,2)==2,pt(1,3)=0;end%extend nx2 to nx3 if needed
    v1_ = repmat(v1,size(pt,1),1);
    v2_ = repmat(v2,size(pt,1),1);
    %actual calculation
    a = v1_ - v2_;
    b = pt - v2_;
    distance = sqrt(sum(cross(a,b,2).^2,2)) ./ sqrt(sum(a.^2,2));
    %this is equivalent to the following line for a single point
    %distance=norm(cross(v1-v2,pt-v2))/norm(v1-v2)
end