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 % INRA - TPV URPOI - BIA IMASTE 0042 % created the 10/02/2005. 0043 % 0044 0045 % 23/03/2006 add support for non vector point data 0046 % 26/10/2006 better support for large data handling: iterate on points 0047 % in the case of a memory lack. 0048 % 20/04/2007 add link to rotationXX functions 0049 % 29/09/2010 fix bug in catch case 0050 % 12/03/2011 slightly reduce memory usage 0051 0052 0053 %% Parse input arguments 0054 0055 % Check special case: if first argument is a struct with a field named 0056 % 'vertices', then the output will be the same struct, but with the 0057 % transformed vertices. 0058 if nargin == 2 && isstruct(pts) && isfield(pts, 'vertices') 0059 mesh = pts; 0060 mesh.vertices = transformPoint3d(mesh.vertices, transfo); 0061 varargout = {mesh}; 0062 return; 0063 end 0064 0065 % Parse x, y, and z coordinates of input points from input arguments 0066 if nargin == 2 0067 % Point coordinates are given in a single N-by-3-by-M-by-etc argument. 0068 % Preallocate x, y, and z to size N-by-1-by-M-by-etc, then fill them in 0069 dim = size(pts); 0070 dim(2) = 1; 0071 [x, y, z] = deal(zeros(dim, class(pts))); 0072 x(:) = pts(:,1,:); 0073 y(:) = pts(:,2,:); 0074 z(:) = pts(:,3,:); 0075 0076 elseif nargin == 4 0077 % Point coordinates are given in 3 different arrays 0078 x = pts; 0079 y = transfo; 0080 z = varargin{1}; 0081 transfo = varargin{2}; 0082 dim = size(x); 0083 0084 else 0085 error('MatGeom:geom3d:WrongInputArgumentNumber', ... 0086 'Requires number of input arguments to be either 2 or 4'); 0087 end 0088 0089 0090 %% Process transformation matrix 0091 0092 % extract the linear and the translation parts of the matrix 0093 linear = transfo(1:3, 1:3)'; 0094 trans = [0 0 0]; 0095 if size(transfo, 2) > 3 0096 trans = transfo(1:3, 4)'; 0097 end 0098 0099 0100 %% Main processing 0101 0102 % convert coordinates 0103 try 0104 % vectorial processing, if there is enough memory. 0105 % same as: 0106 % res = (transfo * [x(:) y(:) z(:) ones(NP, 1)]')'; 0107 res = bsxfun(@plus, [x(:) y(:) z(:)] * linear, trans); 0108 0109 % Back-fill x,y,z with new result (saves calling costly reshape()) 0110 x(:) = res(:,1); 0111 y(:) = res(:,2); 0112 z(:) = res(:,3); 0113 0114 catch ME 0115 disp(ME.message) 0116 % process each point one by one, writing in existing array 0117 NP = numel(x); 0118 for i = 1:NP 0119 res = [x(i) y(i) z(i)] * linear + trans; 0120 x(i) = res(1); 0121 y(i) = res(2); 0122 z(i) = res(3); 0123 end 0124 end 0125 0126 % process output arguments 0127 if nargout <= 1 0128 % results are stored in a unique array 0129 if length(dim) > 2 && dim(2) > 1 0130 warning('geom3d:shapeMismatch',... 0131 'Shape mismatch: Non-vector xyz input should have multiple x,y,z output arguments. Cell {x,y,z} returned instead.') 0132 varargout{1} = {x,y,z}; 0133 else 0134 varargout{1} = [x y z]; 0135 end 0136 0137 elseif nargout == 3 0138 % results are returned in three array with same size. 0139 varargout = {x, y, z}; 0140 end