CREATEPLANE Create a plane in parametrized form.
PLANE = createPlane(P1, P2, P3)
creates a plane containing the 3 points
PLANE = createPlane(PTS)
The 3 points are packed into a single 3x3 array.
PLANE = createPlane(P0, N);
Creates a plane from a point and from a normal to the plane. The
parameter N is given either as a 3D vector (1-by-3 row vector), or as
[THETA PHI], where THETA is the colatitute (angle with the vertical
axis) and PHI is angle with Ox axis, counted counter-clockwise (both
given in radians).
PLANE = createPlane(P0, Dip, DipDir);
Creates a plane from a point and from a dip and dip direction angles
of the plane. Parameters Dip and DipDir angles are given as numbers.
Dip : maximum inclination to the horizontal.
DipDir : direction of the horizontal trace of the line of dip,
measured clockwise from north.
The created plane data has the following format:
PLANE = [X0 Y0 Z0 DX1 DY1 DZ1 DX2 DY2 DZ2], with
- (X0, Y0, Z0) is a point belonging to the plane
- (DX1, DY1, DZ1) is a first direction vector
- (DX2, DY2, DZ2) is a second direction vector
The 2 direction vectors are normalized and orthogonal.
See also:
planes3d, medianPlane
---------
author: David Legland
INRA - TPV URPOI - BIA IMASTE
created the 18/02/2005.0001 function plane = createPlane(varargin) 0002 %CREATEPLANE Create a plane in parametrized form. 0003 % 0004 % PLANE = createPlane(P1, P2, P3) 0005 % creates a plane containing the 3 points 0006 % 0007 % PLANE = createPlane(PTS) 0008 % The 3 points are packed into a single 3x3 array. 0009 % 0010 % PLANE = createPlane(P0, N); 0011 % Creates a plane from a point and from a normal to the plane. The 0012 % parameter N is given either as a 3D vector (1-by-3 row vector), or as 0013 % [THETA PHI], where THETA is the colatitute (angle with the vertical 0014 % axis) and PHI is angle with Ox axis, counted counter-clockwise (both 0015 % given in radians). 0016 % 0017 % PLANE = createPlane(P0, Dip, DipDir); 0018 % Creates a plane from a point and from a dip and dip direction angles 0019 % of the plane. Parameters Dip and DipDir angles are given as numbers. 0020 % Dip : maximum inclination to the horizontal. 0021 % DipDir : direction of the horizontal trace of the line of dip, 0022 % measured clockwise from north. 0023 % 0024 % The created plane data has the following format: 0025 % PLANE = [X0 Y0 Z0 DX1 DY1 DZ1 DX2 DY2 DZ2], with 0026 % - (X0, Y0, Z0) is a point belonging to the plane 0027 % - (DX1, DY1, DZ1) is a first direction vector 0028 % - (DX2, DY2, DZ2) is a second direction vector 0029 % The 2 direction vectors are normalized and orthogonal. 0030 % 0031 % See also: 0032 % planes3d, medianPlane 0033 % 0034 % --------- 0035 % author: David Legland 0036 % INRA - TPV URPOI - BIA IMASTE 0037 % created the 18/02/2005. 0038 % 0039 0040 % HISTORY 0041 % 24/11/2005 add possibility to pack points for plane creation 0042 % 21/08/2006 return normalized planes 0043 % 06/11/2006 update doc for planes created from normal 0044 0045 if length(varargin) == 1 0046 var = varargin{1}; 0047 0048 if iscell(var) 0049 plane = zeros([length(var) 9]); 0050 for i=1:length(var) 0051 plane(i,:) = createPlane(var{i}); 0052 end 0053 elseif size(var, 1) >= 3 0054 % 3 points in a single array 0055 p1 = var(1,:); 0056 p2 = var(2,:); 0057 p3 = var(3,:); 0058 0059 % create direction vectors 0060 v1 = p2 - p1; 0061 v2 = p3 - p1; 0062 0063 % create plane 0064 plane = normalizePlane([p1 v1 v2]); 0065 return; 0066 end 0067 0068 elseif length(varargin) == 2 0069 % plane origin 0070 p0 = varargin{1}; 0071 0072 % second parameter is either a 3D vector or a 3D angle (2 params) 0073 var = varargin{2}; 0074 if size(var, 2) == 2 0075 % normal is given in spherical coordinates 0076 n = sph2cart2([var ones(size(var, 1))]); 0077 elseif size(var, 2)==3 0078 % normal is given by a 3D vector 0079 n = normalizeVector3d(var); 0080 else 0081 error ('wrong number of parameters in createPlane'); 0082 end 0083 0084 % ensure same dimension for parameters 0085 if size(p0, 1)==1 0086 p0 = repmat(p0, [size(n, 1) 1]); 0087 end 0088 if size(n, 1)==1 0089 n = repmat(n, [size(p0, 1) 1]); 0090 end 0091 0092 % find a vector not colinear to the normal 0093 v0 = repmat([1 0 0], [size(p0, 1) 1]); 0094 inds = vectorNorm3d(cross(n, v0, 2))<1e-14; 0095 v0(inds, :) = repmat([0 1 0], [sum(inds) 1]); 0096 % if abs(cross(n, v0, 2))<1e-14 0097 % v0 = repmat([0 1 0], [size(p0, 1) 1]); 0098 % end 0099 0100 % create direction vectors 0101 v1 = normalizeVector3d(cross(n, v0, 2)); 0102 v2 = -normalizeVector3d(cross(v1, n, 2)); 0103 0104 % concatenate result in the array representing the plane 0105 plane = [p0 v1 v2]; 0106 return; 0107 0108 elseif length(varargin)==3 0109 var1 = varargin{1}; 0110 var2 = varargin{2}; 0111 var3 = varargin{3}; 0112 0113 if size(var1, 2) == 3 && size(var2, 2) == 3 && size(var3, 2) == 3 0114 p1 = var1; 0115 p2 = var2; 0116 p3 = var3; 0117 0118 % create direction vectors 0119 v1 = p2 - p1; 0120 v2 = p3 - p1; 0121 0122 plane = normalizePlane([p1 v1 v2]); 0123 return; 0124 elseif size(var1, 2) == 3 && size(var2, 2) == 1 && size(var3, 2) == 1 0125 p0 = var1; 0126 n = [sin(var2)*sin(var3) sin(var2)*cos(var3) cos(var2)]; 0127 0128 % find a vector not colinear to the normal 0129 v0 = repmat([1 0 0], [size(p0, 1) 1]); 0130 inds = vectorNorm3d(cross(n, v0, 2))<1e-14; 0131 v0(inds, :) = repmat([0 1 0], [sum(inds) 1]); 0132 0133 % create direction vectors 0134 v1 = normalizeVector3d(cross(n, v0, 2)); 0135 v2 = -normalizeVector3d(cross(v1, n, 2)); 0136 0137 % concatenate result in the array representing the plane 0138 plane = [p0 v1 v2]; 0139 return; 0140 else 0141 error('Wrong argument in "createPlane".'); 0142 end 0143 else 0144 error('Wrong number of arguments in "createPlane".'); 0145 end 0146