1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
|
## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function res = transformEllipse(elli, transfo)
%TRANSFORMELLIPSE Apply an affine transformation to an ellipse.
%
% ELLI2 = transformEllipse(ELLI, TRANSFO)
%
% Example
% % apply an arbitrary transform to a simple ellipse
% elli = [5 4 3 2 0];
% rot = createRotation(pi/6);
% sca = createScaling([2.5 1.5]);
% tra = createTranslation([4 3]);
% transfo = sca * rot * tra;
% elli2 = transformEllipse(elli, transfo);
% % display original and transformed ellipses
% figure; hold on; axis equal; axis([0 20 0 20]);
% drawEllipse(elli, 'k');
% drawEllipse(elli2, 'b');
% % Compare with transform on polygonal approximation
% poly = ellipseToPolygon(elli, 100);
% drawPolygon(transformPoint(poly, transfo), 'm');
%
% Reference
% https://math.stackexchange.com/questions/3076317/what-is-the-equation-for-an-ellipse-in-standard-form-after-an-arbitrary-matrix-t
%
% See also
% ellipses2d, transforms2d, transformPoint
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2022-09-05, using Matlab 9.12.0.1884302 (R2022a)
% Copyright 2022-2023 INRAE - BIA Research Unit - BIBS Platform (Nantes)
% first extract coefficients of cartesian representation
coeffs = ellipseCartesianCoefficients(elli);
% writing the matrix of the general conic equation x^t * Q * x = 0
Q = [...
coeffs(1) coeffs(2)/2 coeffs(4)/2; ...
coeffs(2)/2 coeffs(3) coeffs(5)/2; ...
coeffs(4)/2 coeffs(5)/2 coeffs(6)];
% compute the matrix form of the transformed ellipse
Minv = inv(transfo);
Q2 = Minv' * Q * Minv;
coeffs2 = [Q2(1,1) 2*Q2(1,2) Q2(2,2) 2*Q2(1,3) 2*Q2(2,3) Q2(3,3)];
res = createEllipse('CartesianCoefficients', coeffs2);
|