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_AffineMatrix3D_idl__ 24#define __com_sun_star_geometry_AffineMatrix3D_idl__ 25 26module com { module sun { module star { module geometry { 27 28/** This structure defines a 3 by 4 affine matrix.<p> 29 30 The matrix defined by this structure constitutes an affine mapping 31 of a point in 3D to another point in 3D. The last line of a 32 complete 4 by 4 matrix is omitted, since it is implicitly assumed 33 to be [0,0,0,1].<p> 34 35 An affine mapping, as performed by this matrix, can be written out 36 as follows, where <code>xs, ys</code> and <code>zs</code> are the source, and 37 <code>xd, yd</code> and <code>zd</code> the corresponding result coordinates: 38 39 <code> 40 xd = m00*xs + m01*ys + m02*zs + m03; 41 yd = m10*xs + m11*ys + m12*zs + m13; 42 zd = m20*xs + m21*ys + m22*zs + m23; 43 </code><p> 44 45 Thus, in common matrix language, with M being the 46 <type>AffineMatrix3D</type> and vs=[xs,ys,zs]^T, vd=[xd,yd,zd]^T two 3D 47 vectors, the affine transformation is written as 48 vd=M*vs. Concatenation of transformations amounts to 49 multiplication of matrices, i.e. a translation, given by T, 50 followed by a rotation, given by R, is expressed as vd=R*(T*vs) in 51 the above notation. Since matrix multiplication is associative, 52 this can be shortened to vd=(R*T)*vs=M'*vs. Therefore, a set of 53 consecutive transformations can be accumulated into a single 54 AffineMatrix3D, by multiplying the current transformation with the 55 additional transformation from the left.<p> 56 57 Due to this transformational approach, all geometry data types are 58 points in abstract integer or real coordinate spaces, without any 59 physical dimensions attached to them. This physical measurement 60 units are typically only added when using these data types to 61 render something onto a physical output device. For 3D coordinates 62 there is also a projection from 3D to 2D device coordiantes needed. 63 Only then the total transformation matrix (oncluding projection to 2D) 64 and the device resolution determine the actual measurement unit in 3D.<p> 65 66 @since OpenOffice 2.0 67 */ 68struct AffineMatrix3D 69{ 70 /// The top, left matrix entry. 71 double m00; 72 73 /// The top, left middle matrix entry. 74 double m01; 75 76 /// The top, right middle matrix entry. 77 double m02; 78 79 /// The top, right matrix entry. 80 double m03; 81 82 /// The middle, left matrix entry. 83 double m10; 84 85 /// The middle, middle left matrix entry. 86 double m11; 87 88 /// The middle, middle right matrix entry. 89 double m12; 90 91 /// The middle, right matrix entry. 92 double m13; 93 94 /// The bottom, left matrix entry. 95 double m20; 96 97 /// The bottom, middle left matrix entry. 98 double m21; 99 100 /// The bottom, middle right matrix entry. 101 double m22; 102 103 /// The bottom, right matrix entry. 104 double m23; 105}; 106 107}; }; }; }; 108 109#endif 110