1/************************************************************** 2 * 3 * Licensed to the Apache Software Foundation (ASF) under one 4 * or more contributor license agreements. See the NOTICE file 5 * distributed with this work for additional information 6 * regarding copyright ownership. The ASF licenses this file 7 * to you under the Apache License, Version 2.0 (the 8 * "License"); you may not use this file except in compliance 9 * with the License. You may obtain a copy of the License at 10 * 11 * http://www.apache.org/licenses/LICENSE-2.0 12 * 13 * Unless required by applicable law or agreed to in writing, 14 * software distributed under the License is distributed on an 15 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY 16 * KIND, either express or implied. See the License for the 17 * specific language governing permissions and limitations 18 * under the License. 19 * 20 *************************************************************/ 21 22 23#ifndef __com_sun_star_geometry_AffineMatrix2D_idl__ 24#define __com_sun_star_geometry_AffineMatrix2D_idl__ 25 26module com { module sun { module star { module geometry { 27 28/** This structure defines a 2 by 3 affine matrix.<p> 29 30 The matrix defined by this structure constitutes an affine mapping 31 of a point in 2D to another point in 2D. The last line of a 32 complete 3 by 3 matrix is omitted, since it is implicitly assumed 33 to be [0,0,1].<p> 34 35 An affine mapping, as performed by this matrix, can be written out 36 as follows, where <code>xs</code> and <code>ys</code> are the source, and 37 <code>xd</code> and <code>yd</code> the corresponding result coordinates: 38 39 <code> 40 xd = m00*xs + m01*ys + m02; 41 yd = m10*xs + m11*ys + m12; 42 </code><p> 43 44 Thus, in common matrix language, with M being the 45 <type>AffineMatrix2D</type> and vs=[xs,ys]^T, vd=[xd,yd]^T two 2D 46 vectors, the affine transformation is written as 47 vd=M*vs. Concatenation of transformations amounts to 48 multiplication of matrices, i.e. a translation, given by T, 49 followed by a rotation, given by R, is expressed as vd=R*(T*vs) in 50 the above notation. Since matrix multiplication is associative, 51 this can be shortened to vd=(R*T)*vs=M'*vs. Therefore, a set of 52 consecutive transformations can be accumulated into a single 53 AffineMatrix2D, by multiplying the current transformation with the 54 additional transformation from the left.<p> 55 56 Due to this transformational approach, all geometry data types are 57 points in abstract integer or real coordinate spaces, without any 58 physical dimensions attached to them. This physical measurement 59 units are typically only added when using these data types to 60 render something onto a physical output device, like a screen or a 61 printer, Then, the total transformation matrix and the device 62 resolution determine the actual measurement unit.<p> 63 64 @since OpenOffice 2.0 65 */ 66published struct AffineMatrix2D 67{ 68 /// The top, left matrix entry. 69 double m00; 70 71 /// The top, middle matrix entry. 72 double m01; 73 74 /// The top, right matrix entry. 75 double m02; 76 77 /// The bottom, left matrix entry. 78 double m10; 79 80 /// The bottom, middle matrix entry. 81 double m11; 82 83 /// The bottom, right matrix entry. 84 double m12; 85}; 86 87}; }; }; }; 88 89#endif 90