findOnWhichSperePolygon.m

%{
 * Copyright (C) 2013-2025, 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 
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 * 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
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 *    this list of conditions and the following disclaimer in the documentation
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 * AUTHOR: Bruce JK Huang (bjhuang[at]umich.edu)
 * WEBSITE: https://www.brucerobot.com/
%}

function [which_polygon, plane, uinit_point_xy] = findOnWhichSperePolygon(point, size, division, r)
    if ~exist('r', 'var')
        r = 2;
    end
    if ~exist('division', 'var')
        division = 4;
    end
    point_unit = point ./ size;
    [x, y, z] = sphere(division); 
    x = x(division:end,:);
    y = y(division:end,:);
    z = z(division:end,:); 
    z = z - z(1,1); % move to (x, y, 0)

    a = gradient(z);
    fig_handle = createFigHandle(1, "sphere");
    hs = surf(fig_handle, r.*x,r.*y,r.*z, 'AlphaData',a, 'FaceAlpha','flat',...
        'FaceColor','blue');
    direction = [0 0 1]; 
    rotate(hs, direction, 180/division) 
    XData = hs.XData;
    YData = hs.YData;
    ZData = hs.ZData;
    uinit_point_xy = [point_unit(3), point_unit(2), point_unit(1)];
    for i = 1:division
    %     j = mod(j, 4);
        plane(i).object_vertices.x = [0 XData(1, i), XData(1, i+1)];
        plane(i).object_vertices.y = [0 YData(1, i), YData(1, i+1)];
        plane(i).object_vertices.z = [ZData(2,i) ZData(1, i), ZData(1, i+1)];

        plane(i).triangle.x = [0 XData(1, i), XData(1, i+1)];
        plane(i).triangle.y = [0 YData(1, i), YData(1, i+1)];
        plane(i).triangle.z = [0 ZData(1, i), ZData(1, i+1)];
        [plane(i).normal, plane(i).centroid, plane(i).R] = computePlaneReturnR(plane(i));
    %     scatter3(plane(i).triangle.x, plane(i).triangle.y, plane(i).triangle.z, 'y', 'fill')
        plane(i).angle_sum = computeAngleSum(plane(i).triangle, uinit_point_xy); 
        plane(i).status = 0;
        if abs(plane(i).angle_sum - 2*pi) < 1e-5
            plane(i).status = 1;
            interior = point;
        end
    end
    [~, which_polygon] = min(abs([plane(:).angle_sum]- 2*pi));
end