SphericalProjectorForwardFcn.m

function uv = SphericalProjectorForwardFcn(xy,K,R,scale)
% Brief:
%    This function calculates the forward projection of world coordinates (xy)
%    to spherical camera image coordinates (uv).
%
% Details:
%    The function takes the world coordinates (xy), the camera intrinsic matrix (K),
%    and the rotation matrix (R), and computes the corresponding image coordinates (uv).
%    The scale parameter is used to normalize the image coordinates after the projection.
%
% Syntax:
%     uv = SphericalProjectorForwardFcn(xy,K,R,scale)
%
% Inputs:
%    xy - [m,2] size,[double] type, 输入点集坐标
%    K - [3,3] size,[double] type, 相机内参矩阵
%    R - [3,3] size,[double] type, 旋转矩阵R
%    scale - [1,1] size,[double] type, 用于归一化图像坐标的缩放因子
%
% Outputs:
%    uv - [m,2] size,[double] type, 输出点集坐标
%
% Example:
%    None
% 
% See also: geometricTransform2d
%
% Reference: 
%   https://github.com/opencv/opencv/blob/5c6c6af4ec1f35e1c20f366258793f711e428c1a/modules/stitching/include/opencv2/stitching/detail/warpers_inl.hpp#L253
%   

% Author:                          cuixingxing
% Email:                           cuixingxing150@gmail.com
% Created:                         03-Mar-2025 16:54:25
% Version history revision notes:
%                                  None
% Implementation In Matlab R2024b
% Copyright © 2025 TheMatrix.All Rights Reserved.
%

arguments
      xy (:,2) double
      K (3,3) double
      R (3,3) double
      scale (1,1) double = mean([K(1,1),K(2,2)]);
end

xyz_ = R/K*[xy';ones(1,size(xy,1))];
xyz_ = xyz_';

x_ = xyz_(:,1);
y_ = xyz_(:,2);
z_ = xyz_(:,3);

u = atan2(x_,z_);
w = y_./sqrt(x_.^2+y_.^2+z_.^2);

mask = isfinite(w);

v = w;
v(mask) = pi-acos(w(mask));
v(~mask) = 0;

% scale = mean([K(1,1),K(2,2)]);
uv = scale*[u,v];
end