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R8218/utils/@CoordinateSystem/CoordinateSystem.m
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CoordinateSystem.m
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classdef CoordinateSystem < handle
% Useful to define, use, and test a coordinate system.
%
% Can be tested on orthogonality, right or left handedness.
%
% Can be used to express global points in local coordinates
% and vice versa.
% Can be used to project points on planes spanned by the
% CoordinateSystem axes.
properties
origin = [];
end
properties (Hidden = true)
xAxis = [];
yAxis = [];
zAxis = [];
rotationMatrix = [];
end
methods
function obj = CoordinateSystem()
end
function output = isEmpty(obj)
output = isempty(obj.origin) ||...
isempty(obj.xAxis) ||...
isempty(obj.yAxis) ||...
isempty(obj.zAxis);
end
function set.xAxis(obj,value)
obj.xAxis = value;
obj.rotationMatrix(:,1) = value'/norm(value);
end
function set.yAxis(obj,value)
obj.yAxis = value;
obj.rotationMatrix(:,2) = value'/norm(value);
end
function set.zAxis(obj,value)
obj.zAxis = value;
obj.rotationMatrix(:,3) = value'/norm(value);
end
function output = getRotationMatrix(obj)
assert(obj.isOrthogonal,"CoordinateSystem is not orthogonal. Can't get its rotation matrix");
output = obj.rotationMatrix;
end
function localPoints = express(obj,globalPoints)
% Give the coordinates of global cartesian points in present coordinate system
assert(not(obj.isEmpty),'Coordinate System has not been initialized yet.');
assert(size(globalPoints,2) == 3,'Points have to be a Nx3 double array.')
localPoints = (globalPoints-obj.origin) * obj.rotationMatrix;
end
function globalPoints = getGlobalCoordinatesOfLocalPoints(obj,localPoints)
% Give the coordinates of local points in global cartesian coordinate system
assert(not(obj.isEmpty),'Coordinate System has not been initialized yet.');
assert(size(localPoints,2) == 3,'Points have to be a Nx3 double array.')
globalPoints = (localPoints * obj.rotationMatrix') + obj.origin;
end
function projected = projectOnXYPlane(obj,points)
assert(not(obj.isEmpty),'Coordinate System has not been initialized yet.');
projectionPlane = Plane;
projectionPlane.fit([obj.origin;(obj.origin + obj.xAxis);(obj.origin + obj.yAxis)]);
projected = projectionPlane.projectOnPlane(points);
end
function projected = projectOnYZPlane(obj,points)
assert(not(obj.isEmpty),'Coordinate System has not been initialized yet.');
projectionPlane = Plane;
projectionPlane.fit([obj.origin;(obj.origin + obj.yAxis);(obj.origin + obj.zAxis)]);
projected = projectionPlane.projectOnPlane(points);
end
function projected = projectOnZXPlane(obj,points)
assert(not(obj.isEmpty),'Coordinate System has not been initialized yet.');
projectionPlane = Plane;
projectionPlane.fit([obj.origin;(obj.origin + obj.zAxis);(obj.origin + obj.xAxis)]);
projected = projectionPlane.projectOnPlane(points);
end
function output = isOrthogonal(obj)
% The axes comparison can't be done looking for strict equality due to
% rounded values. Therefore the values must be evaluated with a given
% tolerance
assert(not(obj.isEmpty),'Coordinate System has not been initialized yet.');
minAngle = (pi/2)-(10^-6); % Arbitrarily defined as a deviation of
% a millionth of a radian
if dot(obj.xAxis,obj.yAxis) > norm(obj.xAxis)*norm(obj.yAxis)*cos(minAngle)
output = false;
return
end
if dot(obj.xAxis,obj.zAxis) > norm(obj.xAxis)*norm(obj.zAxis)*cos(minAngle)
output = false;
return
end
if dot(obj.zAxis,obj.yAxis) > norm(obj.zAxis)*norm(obj.yAxis)*cos(minAngle)
output = false;
return
end
output = true;
end
function output = isRightHanded(obj)
% The comparison between a theoretical right-handed axis and the actual
% z Axis can't be done looking for strict vector equality due to rounded
% values. Therefore the norm of the sum of the two vectors is evaluated.
assert(not(obj.isEmpty),'Coordinate System has not been initialized yet.');
if not(obj.isOrthogonal)
output = false;
return
end
rightHandedAxis = cross(obj.xAxis,obj.yAxis);
if norm(rightHandedAxis+obj.zAxis) < norm(rightHandedAxis)
output = false;
return
end
output = true;
end
function output = isLeftHanded(obj)
assert(not(obj.isEmpty),'Coordinate System has not been initialized yet.');
if not(obj.isOrthogonal)
output = false;
return
end
if obj.isRightHanded
output = false;
return
end
output = true;
end
function output = plot(obj,axesColor,center)
axisLength = 50;
if (center)
origin = [0 0 0];
else
origin = obj.origin;
end
X = [origin; origin + obj.xAxis*axisLength];
Y = [origin; origin + obj.yAxis*axisLength];
Z = [origin; origin + obj.zAxis*axisLength];
plotHandle(1) = plot3(X(:,1),X(:,2),X(:,3),'Color',axesColor,'LineWidth', 3);
hold on
% set the point a bit further to plot axis name
X(2,:) = X(2,:) + obj.xAxis*2;
plotHandle(2) = text(X(2,1),X(2,2),X(2,3),'X');
plotHandle(3) = plot3(Y(:,1),Y(:,2),Y(:,3),'Color',axesColor,'LineWidth', 3);
% set the point a bit further to plot axis name
Y(2,:) = Y(2,:) + obj.yAxis*2;
plotHandle(4) = text(Y(2,1),Y(2,2),Y(2,3),'Y');
plotHandle(5) = plot3(Z(:,1),Z(:,2),Z(:,3),'Color',axesColor,'LineWidth', 3);
% set the point a bit further to plot axis name
Z(2,:) = Z(2,:) + obj.zAxis*2;
plotHandle(6) = text(Z(2,1),Z(2,2),Z(2,3),'Z');
output = plotHandle;
end
end
end
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