openXsensor/helper_3dmath.h

   1 // I2C device class (I2Cdev) demonstration Arduino sketch for MPU6050 class, 3D math helper
   2 // 6/5/2012 by Jeff Rowberg <jeff@rowberg.net>
   3 // Updates should (hopefully) always be available at https://github.com/jrowberg/i2cdevlib
   4 //
   5 // Changelog:
   6 //     2012-06-05 - add 3D math helper file to DMP6 example sketch
   7
   8 /* ============================================
   9 I2Cdev device library code is placed under the MIT license
  10 Copyright (c) 2012 Jeff Rowberg
  11
  12 Permission is hereby granted, free of charge, to any person obtaining a copy
  13 of this software and associated documentation files (the "Software"), to deal
  14 in the Software without restriction, including without limitation the rights
  15 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  16 copies of the Software, and to permit persons to whom the Software is
  17 furnished to do so, subject to the following conditions:
  18
  19 The above copyright notice and this permission notice shall be included in
  20 all copies or substantial portions of the Software.
  21
  22 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  23 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  24 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  25 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  26 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  27 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
  28 THE SOFTWARE.
  29 ===============================================
  30 */
  31
  32 #ifndef _HELPER_3DMATH_H_
  33 #define _HELPER_3DMATH_H_
  34
  35 #include <Arduino.h>
  36
  37 class Quaternion {
  38     public:
  39         float w;
  40         float x;
  41         float y;
  42         float z;
  43
  44         Quaternion() {
  45             w = 1.0f;
  46             x = 0.0f;
  47             y = 0.0f;
  48             z = 0.0f;
  49         }
  50
  51         Quaternion(float nw, float nx, float ny, float nz) {
  52             w = nw;
  53             x = nx;
  54             y = ny;
  55             z = nz;
  56         }
  57
  58         Quaternion getProduct(Quaternion q) {
  59             // Quaternion multiplication is defined by:
  60             //     (Q1 * Q2).w = (w1w2 - x1x2 - y1y2 - z1z2)
  61             //     (Q1 * Q2).x = (w1x2 + x1w2 + y1z2 - z1y2)
  62             //     (Q1 * Q2).y = (w1y2 - x1z2 + y1w2 + z1x2)
  63             //     (Q1 * Q2).z = (w1z2 + x1y2 - y1x2 + z1w2
  64             return Quaternion(
  65                 w*q.w - x*q.x - y*q.y - z*q.z,  // new w
  66                 w*q.x + x*q.w + y*q.z - z*q.y,  // new x
  67                 w*q.y - x*q.z + y*q.w + z*q.x,  // new y
  68                 w*q.z + x*q.y - y*q.x + z*q.w); // new z
  69         }
  70
  71         Quaternion getConjugate() {
  72             return Quaternion(w, -x, -y, -z);
  73         }
  74
  75         float getMagnitude() {
  76             return sqrt(w*w + x*x + y*y + z*z);
  77         }
  78
  79         void normalize() {
  80             float m = getMagnitude();
  81             w /= m;
  82             x /= m;
  83             y /= m;
  84             z /= m;
  85         }
  86
  87         Quaternion getNormalized() {
  88             Quaternion r(w, x, y, z);
  89             r.normalize();
  90             return r;
  91         }
  92 };
  93
  94 class VectorInt16 {
  95     public:
  96         int16_t x;
  97         int16_t y;
  98         int16_t z;
  99
 100         VectorInt16() {
 101             x = 0;
 102             y = 0;
 103             z = 0;
 104         }
 105
 106         VectorInt16(int16_t nx, int16_t ny, int16_t nz) {
 107             x = nx;
 108             y = ny;
 109             z = nz;
 110         }
 111
 112         float getMagnitude() {
 113             return sqrt(x*x + y*y + z*z);
 114         }
 115
 116         void normalize() {
 117             float m = getMagnitude();
 118             x /= m;
 119             y /= m;
 120             z /= m;
 121         }
 122
 123         VectorInt16 getNormalized() {
 124             VectorInt16 r(x, y, z);
 125             r.normalize();
 126             return r;
 127         }
 128
 129         void rotate(Quaternion *q) {
 130             // http://www.cprogramming.com/tutorial/3d/quaternions.html
 131             // http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/transforms/index.htm
 132             // http://content.gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation
 133             // ^ or: http://webcache.googleusercontent.com/search?q=cache:xgJAp3bDNhQJ:content.gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation&hl=en&gl=us&strip=1
 134
 135             // P_out = q * P_in * conj(q)
 136             // - P_out is the output vector
 137             // - q is the orientation quaternion
 138             // - P_in is the input vector (a*aReal)
 139             // - conj(q) is the conjugate of the orientation quaternion (q=[w,x,y,z], q*=[w,-x,-y,-z])
 140             Quaternion p(0, x, y, z);
 141
 142             // quaternion multiplication: q * p, stored back in p
 143             p = q -> getProduct(p);
 144
 145             // quaternion multiplication: p * conj(q), stored back in p
 146             p = p.getProduct(q -> getConjugate());
 147
 148             // p quaternion is now [0, x', y', z']
 149             x = p.x;
 150             y = p.y;
 151             z = p.z;
 152         }
 153
 154         VectorInt16 getRotated(Quaternion *q) {
 155             VectorInt16 r(x, y, z);
 156             r.rotate(q);
 157             return r;
 158         }
 159 };
 160
 161 class VectorFloat {
 162     public:
 163         float x;
 164         float y;
 165         float z;
 166
 167         VectorFloat() {
 168             x = 0;
 169             y = 0;
 170             z = 0;
 171         }
 172
 173         VectorFloat(float nx, float ny, float nz) {
 174             x = nx;
 175             y = ny;
 176             z = nz;
 177         }
 178
 179         float getMagnitude() {
 180             return sqrt(x*x + y*y + z*z);
 181         }
 182
 183         void normalize() {
 184             float m = getMagnitude();
 185             x /= m;
 186             y /= m;
 187             z /= m;
 188         }
 189
 190         VectorFloat getNormalized() {
 191             VectorFloat r(x, y, z);
 192             r.normalize();
 193             return r;
 194         }
 195
 196         void rotate(Quaternion *q) {
 197             Quaternion p(0, x, y, z);
 198
 199             // quaternion multiplication: q * p, stored back in p
 200             p = q -> getProduct(p);
 201
 202             // quaternion multiplication: p * conj(q), stored back in p
 203             p = p.getProduct(q -> getConjugate());
 204
 205             // p quaternion is now [0, x', y', z']
 206             x = p.x;
 207             y = p.y;
 208             z = p.z;
 209         }
 210
 211         VectorFloat getRotated(Quaternion *q) {
 212             VectorFloat r(x, y, z);
 213             r.rotate(q);
 214             return r;
 215         }
 216 };
 217
 218 #endif /* _HELPER_3DMATH_H_ */