1 /* ----------------------------------------------------------------------
2 * Project: CMSIS DSP Library
3 * Title: arm_quaternion2rotation_f32.c
4 * Description: Floating-point quaternion 2 rotation conversion
5 *
6 * $Date: 23 April 2021
7 * $Revision: V1.9.0
8 *
9 * Target Processor: Cortex-M and Cortex-A cores
10 * -------------------------------------------------------------------- */
11 /*
12 * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved.
13 *
14 * SPDX-License-Identifier: Apache-2.0
15 *
16 * Licensed under the Apache License, Version 2.0 (the License); you may
17 * not use this file except in compliance with the License.
18 * You may obtain a copy of the License at
19 *
20 * www.apache.org/licenses/LICENSE-2.0
21 *
22 * Unless required by applicable law or agreed to in writing, software
23 * distributed under the License is distributed on an AS IS BASIS, WITHOUT
24 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
25 * See the License for the specific language governing permissions and
26 * limitations under the License.
27 */
28
29 #include "dsp/quaternion_math_functions.h"
30 #include <math.h>
31
32 /**
33 @ingroup groupQuaternionMath
34 */
35
36 /**
37 @defgroup QuatConv Quaternion conversions
38
39 Conversions between quaternion and rotation representations.
40 */
41
42 /**
43 @ingroup QuatConv
44 */
45
46 /**
47 @defgroup QuatRot Quaternion to Rotation
48
49 Conversions from quaternion to rotation.
50 */
51
52 /**
53 @addtogroup QuatRot
54 @{
55 */
56
57 /**
58 @brief Conversion of quaternion to equivalent rotation matrix.
59 @param[in] pInputQuaternions points to an array of normalized quaternions
60 @param[out] pOutputRotations points to an array of 3x3 rotations (in row order)
61 @param[in] nbQuaternions number of quaternions in the array
62 @return none.
63
64 @par
65 Format of rotation matrix
66
67
68 The quaternion a + ib + jc + kd is converted into rotation matrix:
69 <pre>
70 a^2 + b^2 - c^2 - d^2 2bc - 2ad 2bd + 2ac
71 2bc + 2ad a^2 - b^2 + c^2 - d^2 2cd - 2ab
72 2bd - 2ac 2cd + 2ab a^2 - b^2 - c^2 + d^2
73 </pre>
74 Rotation matrix is saved in row order : R00 R01 R02 R10 R11 R12 R20 R21 R22
75 */
76
77 #if defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE)
78
79 #include "arm_helium_utils.h"
80
arm_quaternion2rotation_f32(const float32_t * pInputQuaternions,float32_t * pOutputRotations,uint32_t nbQuaternions)81 void arm_quaternion2rotation_f32(const float32_t *pInputQuaternions,
82 float32_t *pOutputRotations,
83 uint32_t nbQuaternions)
84 {
85 f32x4_t vec0,vec1, vec2 ,vec3;
86 float32_t q2q3, tmp1, tmp2 ;
87
88 for(uint32_t nb=0; nb < nbQuaternions; nb++)
89 {
90
91 // q0 q1 q2 q3
92 vec0 = vld1q(pInputQuaternions);
93
94 // q0^2 q1^2 q2^2 q3^2
95 vec1 = vmulq(vec0,vec0);
96
97 // q0^2 q1q0 q2q0 q3q0
98 vec2 = vmulq_n_f32(vec0, vgetq_lane(vec0,0));
99
100 // 2 (q0^2 q1q0 q2q0 q3q0)
101 vec2 = vmulq_n_f32(vec2, 2.0f);
102
103
104 // 2 q2q3
105 q2q3 = vgetq_lane(vec0,2) * vgetq_lane(vec0,3);
106 q2q3 = q2q3 * 2.0f;
107
108 // 2 (q0q1 q1^2 q2q1 q3q1)
109 vec3 = vmulq_n_f32(vec0, vgetq_lane(vec0,1));
110 vec3 = vmulq_n_f32(vec3, 2.0f);
111
112
113
114 vec0 = vsetq_lane(vgetq_lane(vec1,0) + vgetq_lane(vec1,1),vec0,0);
115 vec0 = vsetq_lane(vgetq_lane(vec0,0) - vgetq_lane(vec1,2),vec0,0);
116 vec0 = vsetq_lane(vgetq_lane(vec0,0) - vgetq_lane(vec1,3),vec0,0);
117 vec0 = vsetq_lane(vgetq_lane(vec3,2) - vgetq_lane(vec2,3),vec0,1);
118 vec0 = vsetq_lane(vgetq_lane(vec3,3) + vgetq_lane(vec2,2),vec0,2);
119 vec0 = vsetq_lane(vgetq_lane(vec3,2) + vgetq_lane(vec2,3),vec0,3);
120
121 vst1q(pOutputRotations, vec0);
122 pOutputRotations += 4;
123
124 tmp1 = vgetq_lane(vec1,0) - vgetq_lane(vec1,1);
125 tmp2 = vgetq_lane(vec1,2) - vgetq_lane(vec1,3);
126
127
128 vec0 = vsetq_lane(tmp1 + tmp2,vec0,0);
129 vec0 = vsetq_lane(q2q3 - vgetq_lane(vec2,1) ,vec0,1);
130 vec0 = vsetq_lane(vgetq_lane(vec3,3) - vgetq_lane(vec2,2),vec0,2);
131 vec0 = vsetq_lane(q2q3 + vgetq_lane(vec2,1) ,vec0,3);
132
133 vst1q(pOutputRotations, vec0);
134 pOutputRotations += 4;
135
136 *pOutputRotations = tmp1 - tmp2;
137 pOutputRotations ++;
138
139 pInputQuaternions += 4;
140 }
141 }
142
143 #else
arm_quaternion2rotation_f32(const float32_t * pInputQuaternions,float32_t * pOutputRotations,uint32_t nbQuaternions)144 void arm_quaternion2rotation_f32(const float32_t *pInputQuaternions,
145 float32_t *pOutputRotations,
146 uint32_t nbQuaternions)
147 {
148 for(uint32_t nb=0; nb < nbQuaternions; nb++)
149 {
150 float32_t q00 = SQ(pInputQuaternions[0 + nb * 4]);
151 float32_t q11 = SQ(pInputQuaternions[1 + nb * 4]);
152 float32_t q22 = SQ(pInputQuaternions[2 + nb * 4]);
153 float32_t q33 = SQ(pInputQuaternions[3 + nb * 4]);
154 float32_t q01 = pInputQuaternions[0 + nb * 4]*pInputQuaternions[1 + nb * 4];
155 float32_t q02 = pInputQuaternions[0 + nb * 4]*pInputQuaternions[2 + nb * 4];
156 float32_t q03 = pInputQuaternions[0 + nb * 4]*pInputQuaternions[3 + nb * 4];
157 float32_t q12 = pInputQuaternions[1 + nb * 4]*pInputQuaternions[2 + nb * 4];
158 float32_t q13 = pInputQuaternions[1 + nb * 4]*pInputQuaternions[3 + nb * 4];
159 float32_t q23 = pInputQuaternions[2 + nb * 4]*pInputQuaternions[3 + nb * 4];
160
161 float32_t xx = q00 + q11 - q22 - q33;
162 float32_t yy = q00 - q11 + q22 - q33;
163 float32_t zz = q00 - q11 - q22 + q33;
164 float32_t xy = 2*(q12 - q03);
165 float32_t xz = 2*(q13 + q02);
166 float32_t yx = 2*(q12 + q03);
167 float32_t yz = 2*(q23 - q01);
168 float32_t zx = 2*(q13 - q02);
169 float32_t zy = 2*(q23 + q01);
170
171 pOutputRotations[0 + nb * 9] = xx; pOutputRotations[1 + nb * 9] = xy; pOutputRotations[2 + nb * 9] = xz;
172 pOutputRotations[3 + nb * 9] = yx; pOutputRotations[4 + nb * 9] = yy; pOutputRotations[5 + nb * 9] = yz;
173 pOutputRotations[6 + nb * 9] = zx; pOutputRotations[7 + nb * 9] = zy; pOutputRotations[8 + nb * 9] = zz;
174 }
175 }
176 #endif /* defined(ARM_MATH_MVEF) && !defined(ARM_MATH_AUTOVECTORIZE) */
177
178 /**
179 @} end of QuatRot group
180 */
181