TRANSFORMPOINT3D Transform a point with a 3D affine transform.
PT2 = transformPoint3d(PT1, TRANS);
PT2 = transformPoint3d(X1, Y1, Z1, TRANS);
where PT1 has the form [xp yp zp], and TRANS is a 3-by-3, 3-by-4, or
4-by-4 matrix, returns the point transformed according to the affine
transform specified by TRANS.
The function accepts transforms given using the following formats:
[a b c] , [a b c j] , or [a b c j]
[d e f] [d e f k] [d e f k]
[g h i] [g h i l] [g h i l]
[0 0 0 1]
PT2 = transformPoint3d(PT1, TRANS)
also work when PT1 is a N-by-3-by-M-by-P-by-ETC array of double. In
this case, PT2 has the same size as PT1.
PT2 = transformPoint3d(X1, Y1, Z1, TRANS);
also work when X1, Y1 and Z1 are 3 arrays with the same size. In this
case, PT2 will be a 1-by-3 cell containing {X Y Z} outputs of size(X1).
[X2, Y2, Z2] = transformPoint3d(...);
returns the result in 3 different arrays the same size as the input.
This form can be useful when used with functions like meshgrid or warp.
MESH2 = transformPoint3d(MESH, TRANS)
transforms the field 'vertices' of the struct MESH and returns the same
struct with the transformed vertices.
(It is recommended to use the function 'transformMesh', within the
"meshes3d" module).
See also
points3d, transforms3d, transformMesh, createTranslation3d
createRotationOx, createRotationOy, createRotationOz, createScaling0001 function varargout = transformPoint3d(pts, transfo, varargin) 0002 %TRANSFORMPOINT3D Transform a point with a 3D affine transform. 0003 % 0004 % PT2 = transformPoint3d(PT1, TRANS); 0005 % PT2 = transformPoint3d(X1, Y1, Z1, TRANS); 0006 % where PT1 has the form [xp yp zp], and TRANS is a 3-by-3, 3-by-4, or 0007 % 4-by-4 matrix, returns the point transformed according to the affine 0008 % transform specified by TRANS. 0009 % 0010 % The function accepts transforms given using the following formats: 0011 % [a b c] , [a b c j] , or [a b c j] 0012 % [d e f] [d e f k] [d e f k] 0013 % [g h i] [g h i l] [g h i l] 0014 % [0 0 0 1] 0015 % 0016 % PT2 = transformPoint3d(PT1, TRANS) 0017 % also work when PT1 is a N-by-3-by-M-by-P-by-ETC array of double. In 0018 % this case, PT2 has the same size as PT1. 0019 % 0020 % PT2 = transformPoint3d(X1, Y1, Z1, TRANS); 0021 % also work when X1, Y1 and Z1 are 3 arrays with the same size. In this 0022 % case, PT2 will be a 1-by-3 cell containing {X Y Z} outputs of size(X1). 0023 % 0024 % [X2, Y2, Z2] = transformPoint3d(...); 0025 % returns the result in 3 different arrays the same size as the input. 0026 % This form can be useful when used with functions like meshgrid or warp. 0027 % 0028 % MESH2 = transformPoint3d(MESH, TRANS) 0029 % transforms the field 'vertices' of the struct MESH and returns the same 0030 % struct with the transformed vertices. 0031 % (It is recommended to use the function 'transformMesh', within the 0032 % "meshes3d" module). 0033 % 0034 % See also 0035 % points3d, transforms3d, transformMesh, createTranslation3d 0036 % createRotationOx, createRotationOy, createRotationOz, createScaling 0037 % 0038 0039 % ------ 0040 % Author: David Legland 0041 % E-mail: david.legland@inrae.fr 0042 % Created: 2005-02-10 0043 % Copyright 2005-2024 INRA - TPV URPOI - BIA IMASTE 0044 0045 %% Parse input arguments 0046 0047 % Check special case: if first argument is a struct with a field named 0048 % 'vertices', then the output will be the same struct, but with the 0049 % transformed vertices. 0050 if nargin == 2 && isstruct(pts) && isfield(pts, 'vertices') 0051 mesh = pts; 0052 mesh.vertices = transformPoint3d(mesh.vertices, transfo); 0053 varargout = {mesh}; 0054 return; 0055 end 0056 0057 % Parse x, y, and z coordinates of input points from input arguments 0058 if nargin == 2 0059 % Point coordinates are given in a single N-by-3-by-M-by-etc argument. 0060 % Preallocate x, y, and z to size N-by-1-by-M-by-etc, then fill them in 0061 dim = size(pts); 0062 dim(2) = 1; 0063 [x, y, z] = deal(zeros(dim, class(pts))); 0064 x(:) = pts(:,1,:); 0065 y(:) = pts(:,2,:); 0066 z(:) = pts(:,3,:); 0067 0068 elseif nargin == 4 0069 % Point coordinates are given in 3 different arrays 0070 x = pts; 0071 y = transfo; 0072 z = varargin{1}; 0073 transfo = varargin{2}; 0074 dim = size(x); 0075 0076 else 0077 error('MatGeom:geom3d:WrongInputArgumentNumber', ... 0078 'Requires number of input arguments to be either 2 or 4'); 0079 end 0080 0081 0082 %% Process transformation matrix 0083 0084 % extract the linear and the translation parts of the matrix 0085 linear = transfo(1:3, 1:3)'; 0086 trans = [0 0 0]; 0087 if size(transfo, 2) > 3 0088 trans = transfo(1:3, 4)'; 0089 end 0090 0091 0092 %% Main processing 0093 0094 % convert coordinates 0095 try 0096 % vectorial processing, if there is enough memory. 0097 % same as: 0098 % res = (transfo * [x(:) y(:) z(:) ones(NP, 1)]')'; 0099 res = bsxfun(@plus, [x(:) y(:) z(:)] * linear, trans); 0100 0101 % Back-fill x,y,z with new result (saves calling costly reshape()) 0102 x(:) = res(:,1); 0103 y(:) = res(:,2); 0104 z(:) = res(:,3); 0105 0106 catch ME 0107 disp(ME.message) 0108 % process each point one by one, writing in existing array 0109 NP = numel(x); 0110 for i = 1:NP 0111 res = [x(i) y(i) z(i)] * linear + trans; 0112 x(i) = res(1); 0113 y(i) = res(2); 0114 z(i) = res(3); 0115 end 0116 end 0117 0118 % process output arguments 0119 if nargout <= 1 0120 % results are stored in a unique array 0121 if length(dim) > 2 && dim(2) > 1 0122 warning('geom3d:shapeMismatch',... 0123 'Shape mismatch: Non-vector xyz input should have multiple x,y,z output arguments. Cell {x,y,z} returned instead.') 0124 varargout{1} = {x,y,z}; 0125 else 0126 varargout{1} = [x y z]; 0127 end 0128 0129 elseif nargout == 3 0130 % results are returned in three array with same size. 0131 varargout = {x, y, z}; 0132 end