Diff: MPU6050/helper_3dmath.h

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+// I2C device class (I2Cdev) demonstration Arduino sketch for MPU6050 class, 3D math helper
+// 6/5/2012 by Jeff Rowberg <jeff@rowberg.net>
+// Updates should (hopefully) always be available at https://github.com/jrowberg/i2cdevlib
+//
+// Changelog:
+//     2012-06-05 - add 3D math helper file to DMP6 example sketch
+
+/* ============================================
+I2Cdev device library code is placed under the MIT license
+Copyright (c) 2012 Jeff Rowberg
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
+===============================================
+*/
+
+#ifndef _HELPER_3DMATH_H_
+#define _HELPER_3DMATH_H_
+
+class Quaternion {
+    public:
+        float w;
+        float x;
+        float y;
+        float z;
+        
+        Quaternion() {
+            w = 1.0f;
+            x = 0.0f;
+            y = 0.0f;
+            z = 0.0f;
+        }
+        
+        Quaternion(float nw, float nx, float ny, float nz) {
+            w = nw;
+            x = nx;
+            y = ny;
+            z = nz;
+        }
+
+        Quaternion getProduct(Quaternion q) {
+            // Quaternion multiplication is defined by:
+            //     (Q1 * Q2).w = (w1w2 - x1x2 - y1y2 - z1z2)
+            //     (Q1 * Q2).x = (w1x2 + x1w2 + y1z2 - z1y2)
+            //     (Q1 * Q2).y = (w1y2 - x1z2 + y1w2 + z1x2)
+            //     (Q1 * Q2).z = (w1z2 + x1y2 - y1x2 + z1w2
+            return Quaternion(
+                w*q.w - x*q.x - y*q.y - z*q.z,  // new w
+                w*q.x + x*q.w + y*q.z - z*q.y,  // new x
+                w*q.y - x*q.z + y*q.w + z*q.x,  // new y
+                w*q.z + x*q.y - y*q.x + z*q.w); // new z
+        }
+
+        Quaternion getConjugate() {
+            return Quaternion(w, -x, -y, -z);
+        }
+        
+        float getMagnitude() {
+            return sqrt(w*w + x*x + y*y + z*z);
+        }
+        
+        void normalize() {
+            float m = getMagnitude();
+            w /= m;
+            x /= m;
+            y /= m;
+            z /= m;
+        }
+        
+        Quaternion getNormalized() {
+            Quaternion r(w, x, y, z);
+            r.normalize();
+            return r;
+        }
+};
+
+class VectorInt16 {
+    public:
+        int16_t x;
+        int16_t y;
+        int16_t z;
+
+        VectorInt16() {
+            x = 0;
+            y = 0;
+            z = 0;
+        }
+        
+        VectorInt16(int16_t nx, int16_t ny, int16_t nz) {
+            x = nx;
+            y = ny;
+            z = nz;
+        }
+
+        float getMagnitude() {
+            return sqrt((float)(x*x + y*y + z*z));
+        }
+
+        void normalize() {
+            float m = getMagnitude();
+            x /= m;
+            y /= m;
+            z /= m;
+        }
+        
+        VectorInt16 getNormalized() {
+            VectorInt16 r(x, y, z);
+            r.normalize();
+            return r;
+        }
+        
+        void rotate(Quaternion *q) {
+            // http://www.cprogramming.com/tutorial/3d/quaternions.html
+            // http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/transforms/index.htm
+            // http://content.gpwiki.org/index.php/OpenGL:Tutorials:Using_Quaternions_to_represent_rotation
+            // ^ 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
+        
+            // P_out = q * P_in * conj(q)
+            // - P_out is the output vector
+            // - q is the orientation quaternion
+            // - P_in is the input vector (a*aReal)
+            // - conj(q) is the conjugate of the orientation quaternion (q=[w,x,y,z], q*=[w,-x,-y,-z])
+            Quaternion p(0, x, y, z);
+
+            // quaternion multiplication: q * p, stored back in p
+            p = q -> getProduct(p);
+
+            // quaternion multiplication: p * conj(q), stored back in p
+            p = p.getProduct(q -> getConjugate());
+
+            // p quaternion is now [0, x', y', z']
+            x = p.x;
+            y = p.y;
+            z = p.z;
+        }
+
+        VectorInt16 getRotated(Quaternion *q) {
+            VectorInt16 r(x, y, z);
+            r.rotate(q);
+            return r;
+        }
+};
+
+class VectorFloat {
+    public:
+        float x;
+        float y;
+        float z;
+
+        VectorFloat() {
+            x = 0;
+            y = 0;
+            z = 0;
+        }
+        
+        VectorFloat(float nx, float ny, float nz) {
+            x = nx;
+            y = ny;
+            z = nz;
+        }
+
+        float getMagnitude() {
+            return sqrt(x*x + y*y + z*z);
+        }
+
+        void normalize() {
+            float m = getMagnitude();
+            x /= m;
+            y /= m;
+            z /= m;
+        }
+        
+        VectorFloat getNormalized() {
+            VectorFloat r(x, y, z);
+            r.normalize();
+            return r;
+        }
+        
+        void rotate(Quaternion *q) {
+            Quaternion p(0, x, y, z);
+
+            // quaternion multiplication: q * p, stored back in p
+            p = q -> getProduct(p);
+
+            // quaternion multiplication: p * conj(q), stored back in p
+            p = p.getProduct(q -> getConjugate());
+
+            // p quaternion is now [0, x', y', z']
+            x = p.x;
+            y = p.y;
+            z = p.z;
+        }
+
+        VectorFloat getRotated(Quaternion *q) {
+            VectorFloat r(x, y, z);
+            r.rotate(q);
+            return r;
+        }
+};
+
+#endif /* _HELPER_3DMATH_H_ */
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