mirror of https://github.com/ArduPilot/ardupilot
630 lines
17 KiB
C++
630 lines
17 KiB
C++
/*
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* vector3.cpp
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* Copyright (C) Andrew Tridgell 2012
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*
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* This file is free software: you can redistribute it and/or modify it
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* under the terms of the GNU General Public License as published by the
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* Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This file is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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* See the GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License along
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* with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#pragma GCC optimize("O2")
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#include "AP_Math.h"
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#include <AP_InternalError/AP_InternalError.h>
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// rotate a vector by a standard rotation, attempting
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// to use the minimum number of floating point operations
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template <typename T>
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void Vector3<T>::rotate(enum Rotation rotation)
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{
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T tmp;
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switch (rotation) {
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case ROTATION_NONE:
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return;
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case ROTATION_YAW_45: {
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tmp = HALF_SQRT_2*(ftype)(x - y);
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y = HALF_SQRT_2*(ftype)(x + y);
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x = tmp;
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return;
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}
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case ROTATION_YAW_90: {
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tmp = x; x = -y; y = tmp;
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return;
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}
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case ROTATION_YAW_135: {
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tmp = -HALF_SQRT_2*(ftype)(x + y);
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y = HALF_SQRT_2*(ftype)(x - y);
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x = tmp;
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return;
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}
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case ROTATION_YAW_180:
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x = -x; y = -y;
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return;
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case ROTATION_YAW_225: {
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tmp = HALF_SQRT_2*(ftype)(y - x);
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y = -HALF_SQRT_2*(ftype)(x + y);
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x = tmp;
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return;
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}
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case ROTATION_YAW_270: {
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tmp = x; x = y; y = -tmp;
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return;
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}
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case ROTATION_YAW_315: {
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tmp = HALF_SQRT_2*(ftype)(x + y);
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y = HALF_SQRT_2*(ftype)(y - x);
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x = tmp;
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return;
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}
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case ROTATION_ROLL_180: {
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y = -y; z = -z;
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return;
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}
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case ROTATION_ROLL_180_YAW_45: {
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tmp = HALF_SQRT_2*(ftype)(x + y);
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y = HALF_SQRT_2*(ftype)(x - y);
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x = tmp; z = -z;
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return;
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}
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case ROTATION_ROLL_180_YAW_90:
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case ROTATION_PITCH_180_YAW_270: {
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tmp = x; x = y; y = tmp; z = -z;
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return;
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}
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case ROTATION_ROLL_180_YAW_135: {
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tmp = HALF_SQRT_2*(ftype)(y - x);
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y = HALF_SQRT_2*(ftype)(y + x);
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x = tmp; z = -z;
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return;
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}
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case ROTATION_PITCH_180: {
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x = -x; z = -z;
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return;
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}
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case ROTATION_ROLL_180_YAW_225: {
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tmp = -HALF_SQRT_2*(ftype)(x + y);
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y = HALF_SQRT_2*(ftype)(y - x);
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x = tmp; z = -z;
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return;
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}
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case ROTATION_ROLL_180_YAW_270:
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case ROTATION_PITCH_180_YAW_90: {
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tmp = x; x = -y; y = -tmp; z = -z;
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return;
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}
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case ROTATION_ROLL_180_YAW_315: {
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tmp = HALF_SQRT_2*(ftype)(x - y);
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y = -HALF_SQRT_2*(ftype)(x + y);
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x = tmp; z = -z;
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return;
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}
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case ROTATION_ROLL_90: {
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tmp = z; z = y; y = -tmp;
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return;
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}
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case ROTATION_ROLL_90_YAW_45: {
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tmp = z; z = y; y = -tmp;
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tmp = HALF_SQRT_2*(ftype)(x - y);
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y = HALF_SQRT_2*(ftype)(x + y);
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x = tmp;
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return;
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}
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case ROTATION_ROLL_90_YAW_90: {
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tmp = z; z = y; y = -tmp;
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tmp = x; x = -y; y = tmp;
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return;
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}
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case ROTATION_ROLL_90_YAW_135: {
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tmp = z; z = y; y = -tmp;
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tmp = -HALF_SQRT_2*(ftype)(x + y);
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y = HALF_SQRT_2*(ftype)(x - y);
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x = tmp;
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return;
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}
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case ROTATION_ROLL_270: {
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tmp = z; z = -y; y = tmp;
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return;
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}
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case ROTATION_ROLL_270_YAW_45: {
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tmp = z; z = -y; y = tmp;
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tmp = HALF_SQRT_2*(ftype)(x - y);
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y = HALF_SQRT_2*(ftype)(x + y);
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x = tmp;
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return;
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}
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case ROTATION_ROLL_270_YAW_90: {
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tmp = z; z = -y; y = tmp;
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tmp = x; x = -y; y = tmp;
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return;
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}
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case ROTATION_ROLL_270_YAW_135: {
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tmp = z; z = -y; y = tmp;
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tmp = -HALF_SQRT_2*(ftype)(x + y);
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y = HALF_SQRT_2*(ftype)(x - y);
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x = tmp;
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return;
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}
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case ROTATION_PITCH_90: {
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tmp = z; z = -x; x = tmp;
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return;
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}
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case ROTATION_PITCH_270: {
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tmp = z; z = x; x = -tmp;
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return;
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}
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case ROTATION_ROLL_90_PITCH_90: {
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tmp = z; z = y; y = -tmp;
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tmp = z; z = -x; x = tmp;
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return;
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}
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case ROTATION_ROLL_180_PITCH_90: {
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y = -y; z = -z;
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tmp = z; z = -x; x = tmp;
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return;
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}
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case ROTATION_ROLL_270_PITCH_90: {
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tmp = z; z = -y; y = tmp;
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tmp = z; z = -x; x = tmp;
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return;
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}
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case ROTATION_ROLL_90_PITCH_180: {
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tmp = z; z = y; y = -tmp;
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x = -x; z = -z;
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return;
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}
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case ROTATION_ROLL_270_PITCH_180: {
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tmp = z; z = -y; y = tmp;
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x = -x; z = -z;
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return;
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}
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case ROTATION_ROLL_90_PITCH_270: {
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tmp = z; z = y; y = -tmp;
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tmp = z; z = x; x = -tmp;
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return;
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}
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case ROTATION_ROLL_180_PITCH_270: {
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y = -y; z = -z;
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tmp = z; z = x; x = -tmp;
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return;
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}
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case ROTATION_ROLL_270_PITCH_270: {
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tmp = z; z = -y; y = tmp;
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tmp = z; z = x; x = -tmp;
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return;
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}
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case ROTATION_ROLL_90_PITCH_180_YAW_90: {
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tmp = z; z = y; y = -tmp;
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x = -x; z = -z;
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tmp = x; x = -y; y = tmp;
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return;
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}
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case ROTATION_ROLL_90_YAW_270: {
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tmp = z; z = y; y = -tmp;
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tmp = x; x = y; y = -tmp;
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return;
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}
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case ROTATION_ROLL_90_PITCH_68_YAW_293: {
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T tmpx = x;
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T tmpy = y;
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T tmpz = z;
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x = 0.14303897231223747232853327204793 * tmpx + 0.36877648650320382639478111741482 * tmpy + -0.91844638134308709265241077446262 * tmpz;
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y = -0.33213277779664740485543461545603 * tmpx + -0.85628942146641884303193137384369 * tmpy + -0.39554550256296522325882847326284 * tmpz;
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z = -0.93232380121551217122544130688766 * tmpx + 0.36162457008209242248497616856184 * tmpy + 0.00000000000000002214311861220361 * tmpz;
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return;
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}
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case ROTATION_PITCH_315: {
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tmp = HALF_SQRT_2*(ftype)(x - z);
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z = HALF_SQRT_2*(ftype)(x + z);
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x = tmp;
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return;
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}
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case ROTATION_ROLL_90_PITCH_315: {
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tmp = z; z = y; y = -tmp;
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tmp = HALF_SQRT_2*(ftype)(x - z);
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z = HALF_SQRT_2*(ftype)(x + z);
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x = tmp;
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return;
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}
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case ROTATION_PITCH_7: {
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const T sin_pitch = 0.1218693434051474899781908334262; // sinF(pitch);
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const T cos_pitch = 0.99254615164132198312785249072476; // cosF(pitch);
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T tmpx = x;
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T tmpz = z;
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x = cos_pitch * tmpx + sin_pitch * tmpz;
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z = -sin_pitch * tmpx + cos_pitch * tmpz;
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return;
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}
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case ROTATION_ROLL_45: {
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tmp = HALF_SQRT_2*(ftype)(y - z);
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z = HALF_SQRT_2*(ftype)(y + z);
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y = tmp;
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return;
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}
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case ROTATION_ROLL_315: {
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tmp = HALF_SQRT_2*(ftype)(y + z);
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z = HALF_SQRT_2*(ftype)(z - y);
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y = tmp;
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return;
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}
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case ROTATION_CUSTOM:
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// Error: caller must perform custom rotations via matrix multiplication
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INTERNAL_ERROR(AP_InternalError::error_t::flow_of_control);
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return;
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case ROTATION_MAX:
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break;
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}
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// rotation invalid
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INTERNAL_ERROR(AP_InternalError::error_t::bad_rotation);
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}
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template <typename T>
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void Vector3<T>::rotate_inverse(enum Rotation rotation)
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{
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Vector3<T> x_vec(1.0f,0.0f,0.0f);
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Vector3<T> y_vec(0.0f,1.0f,0.0f);
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Vector3<T> z_vec(0.0f,0.0f,1.0f);
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x_vec.rotate(rotation);
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y_vec.rotate(rotation);
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z_vec.rotate(rotation);
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Matrix3<T> M(
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x_vec.x, y_vec.x, z_vec.x,
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x_vec.y, y_vec.y, z_vec.y,
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x_vec.z, y_vec.z, z_vec.z
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);
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(*this) = M.mul_transpose(*this);
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}
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// rotate vector by angle in radians in xy plane leaving z untouched
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template <typename T>
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void Vector3<T>::rotate_xy(T angle_rad)
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{
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const T cs = cosF(angle_rad);
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const T sn = sinF(angle_rad);
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T rx = x * cs - y * sn;
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T ry = x * sn + y * cs;
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x = rx;
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y = ry;
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}
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// vector cross product
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template <typename T>
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Vector3<T> Vector3<T>::operator %(const Vector3<T> &v) const
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{
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Vector3<T> temp(y*v.z - z*v.y, z*v.x - x*v.z, x*v.y - y*v.x);
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return temp;
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}
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// dot product
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template <typename T>
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T Vector3<T>::operator *(const Vector3<T> &v) const
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{
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return x*v.x + y*v.y + z*v.z;
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}
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template <typename T>
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T Vector3<T>::length(void) const
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{
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return norm(x, y, z);
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}
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// limit xy component vector to a given length. returns true if vector was limited
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template <typename T>
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bool Vector3<T>::limit_length_xy(T max_length)
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{
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const T length_xy = norm(x, y);
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if ((length_xy > max_length) && is_positive(length_xy)) {
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x *= (max_length / length_xy);
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y *= (max_length / length_xy);
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return true;
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}
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return false;
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}
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template <typename T>
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Vector3<T> &Vector3<T>::operator *=(const T num)
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{
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x*=num; y*=num; z*=num;
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return *this;
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}
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template <typename T>
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Vector3<T> &Vector3<T>::operator /=(const T num)
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{
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x /= num; y /= num; z /= num;
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return *this;
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}
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template <typename T>
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Vector3<T> &Vector3<T>::operator -=(const Vector3<T> &v)
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{
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x -= v.x; y -= v.y; z -= v.z;
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return *this;
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}
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template <typename T>
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bool Vector3<T>::is_nan(void) const
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{
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return isnan(x) || isnan(y) || isnan(z);
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}
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template <typename T>
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bool Vector3<T>::is_inf(void) const
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{
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return isinf(x) || isinf(y) || isinf(z);
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}
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template <typename T>
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Vector3<T> &Vector3<T>::operator +=(const Vector3<T> &v)
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{
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x+=v.x; y+=v.y; z+=v.z;
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return *this;
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}
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template <typename T>
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Vector3<T> Vector3<T>::operator /(const T num) const
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{
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return Vector3<T>(x/num, y/num, z/num);
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}
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template <typename T>
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Vector3<T> Vector3<T>::operator *(const T num) const
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{
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return Vector3<T>(x*num, y*num, z*num);
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}
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template <typename T>
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Vector3<T> Vector3<T>::operator -(const Vector3<T> &v) const
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{
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return Vector3<T>(x-v.x, y-v.y, z-v.z);
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}
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template <typename T>
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Vector3<T> Vector3<T>::operator +(const Vector3<T> &v) const
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{
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return Vector3<T>(x+v.x, y+v.y, z+v.z);
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}
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template <typename T>
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Vector3<T> Vector3<T>::operator -(void) const
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{
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return Vector3<T>(-x,-y,-z);
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}
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template <typename T>
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bool Vector3<T>::operator ==(const Vector3<T> &v) const
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{
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return (is_equal(x,v.x) && is_equal(y,v.y) && is_equal(z,v.z));
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}
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template <typename T>
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bool Vector3<T>::operator !=(const Vector3<T> &v) const
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{
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return (!is_equal(x,v.x) || !is_equal(y,v.y) || !is_equal(z,v.z));
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}
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template <typename T>
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T Vector3<T>::angle(const Vector3<T> &v2) const
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{
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const T len = this->length() * v2.length();
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if (len <= 0) {
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return 0.0f;
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}
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const T cosv = ((*this)*v2) / len;
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if (fabsF(cosv) >= 1) {
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return 0.0f;
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}
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return acosF(cosv);
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}
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// multiplication of transpose by a vector
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template <typename T>
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Vector3<T> Vector3<T>::operator *(const Matrix3<T> &m) const
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{
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return Vector3<T>(*this * m.colx(),
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*this * m.coly(),
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*this * m.colz());
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}
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// multiply a column vector by a row vector, returning a 3x3 matrix
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template <typename T>
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Matrix3<T> Vector3<T>::mul_rowcol(const Vector3<T> &v2) const
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{
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const Vector3<T> v1 = *this;
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return Matrix3<T>(v1.x * v2.x, v1.x * v2.y, v1.x * v2.z,
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v1.y * v2.x, v1.y * v2.y, v1.y * v2.z,
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v1.z * v2.x, v1.z * v2.y, v1.z * v2.z);
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}
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// extrapolate position given bearing and pitch (in degrees) and distance
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template <typename T>
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void Vector3<T>::offset_bearing(T bearing, T pitch, T distance)
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{
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y += cosF(radians(pitch)) * sinF(radians(bearing)) * distance;
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x += cosF(radians(pitch)) * cosF(radians(bearing)) * distance;
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z += sinF(radians(pitch)) * distance;
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}
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// distance from the tip of this vector to a line segment specified by two vectors
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template <typename T>
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T Vector3<T>::distance_to_segment(const Vector3<T> &seg_start, const Vector3<T> &seg_end) const
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{
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// triangle side lengths
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const T a = (*this-seg_start).length();
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const T b = (seg_start-seg_end).length();
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const T c = (seg_end-*this).length();
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// protect against divide by zero later
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if (::is_zero(b)) {
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return 0.0f;
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}
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// semiperimeter of triangle
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const T s = (a+b+c) * 0.5f;
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T area_squared = s*(s-a)*(s-b)*(s-c);
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// area must be constrained above 0 because a triangle could have 3 points could be on a line and float rounding could push this under 0
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if (area_squared < 0.0f) {
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area_squared = 0.0f;
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}
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const T area = safe_sqrt(area_squared);
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return 2.0f*area/b;
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}
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// Shortest distance between point(p) to a point contained in the line segment defined by w1,w2
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template <typename T>
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T Vector3<T>::closest_distance_between_line_and_point(const Vector3<T> &w1, const Vector3<T> &w2, const Vector3<T> &p)
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{
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const Vector3<T> nearest = point_on_line_closest_to_other_point(w1, w2, p);
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const T dist = (nearest - p).length();
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return dist;
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}
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// Point in the line segment defined by w1,w2 which is closest to point(p)
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// this is based on the explanation given here: www.fundza.com/vectors/point2line/index.html
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template <typename T>
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Vector3<T> Vector3<T>::point_on_line_closest_to_other_point(const Vector3<T> &w1, const Vector3<T> &w2, const Vector3<T> &p)
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{
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const Vector3<T> line_vec = w2-w1;
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const Vector3<T> p_vec = p - w1;
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const T line_vec_len = line_vec.length();
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// protection against divide by zero
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if(::is_zero(line_vec_len)) {
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return {0.0f, 0.0f, 0.0f};
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}
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const T scale = 1/line_vec_len;
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const Vector3<T> unit_vec = line_vec * scale;
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const Vector3<T> scaled_p_vec = p_vec * scale;
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T dot_product = unit_vec * scaled_p_vec;
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dot_product = constrain_ftype(dot_product,0.0f,1.0f);
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const Vector3<T> closest_point = line_vec * dot_product;
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return (closest_point + w1);
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}
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// Closest point between two line segments
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// This implementation is borrowed from: http://geomalgorithms.com/a07-_distance.html
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// INPUT: 4 points corresponding to start and end of two line segments
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// OUTPUT: closest point on segment 2, from segment 1, gets passed on reference as "closest_point"
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template <typename T>
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void Vector3<T>::segment_to_segment_closest_point(const Vector3<T>& seg1_start, const Vector3<T>& seg1_end, const Vector3<T>& seg2_start, const Vector3<T>& seg2_end, Vector3<T>& closest_point)
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{
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// direction vectors
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const Vector3<T> line1 = seg1_end - seg1_start;
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const Vector3<T> line2 = seg2_end - seg2_start;
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const Vector3<T> diff = seg1_start - seg2_start;
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const T a = line1*line1;
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const T b = line1*line2;
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const T c = line2*line2;
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const T d = line1*diff;
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const T e = line2*diff;
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const T discriminant = (a*c) - (b*b);
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T sN, sD = discriminant; // default sD = D >= 0
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T tc, tN, tD = discriminant; // tc = tN / tD, default tD = D >= 0
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if (discriminant < FLT_EPSILON) {
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sN = 0.0; // force using point seg1_start on line 1
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sD = 1.0; // to prevent possible division by 0.0 later
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tN = e;
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tD = c;
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} else {
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// get the closest points on the infinite lines
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sN = (b*e - c*d);
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tN = (a*e - b*d);
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if (sN < 0.0) {
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// sc < 0 => the s=0 edge is visible
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sN = 0.0;
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tN = e;
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tD = c;
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} else if (sN > sD) {
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// sc > 1 => the s=1 edge is visible
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sN = sD;
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tN = e + b;
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tD = c;
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}
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}
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if (tN < 0.0) {
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// tc < 0 => the t=0 edge is visible
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tN = 0.0;
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// recompute sc for this edge
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if (-d < 0.0) {
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sN = 0.0;
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} else if (-d > a) {
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sN = sD;
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} else {
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sN = -d;
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sD = a;
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}
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} else if (tN > tD) {
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// tc > 1 => the t=1 edge is visible
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tN = tD;
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// recompute sc for this edge
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if ((-d + b) < 0.0) {
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sN = 0;
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} else if ((-d + b) > a) {
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sN = sD;
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} else {
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sN = (-d + b);
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sD = a;
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}
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}
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// finally do the division to get tc
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tc = (::is_zero(tN) ? 0.0 : tN / tD);
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// closest point on seg2
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closest_point = seg2_start + line2*tc;
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}
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// Returns true if the passed 3D segment passes through a plane defined by plane normal, and a point on the plane
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template <typename T>
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bool Vector3<T>::segment_plane_intersect(const Vector3<T>& seg_start, const Vector3<T>& seg_end, const Vector3<T>& plane_normal, const Vector3<T>& plane_point)
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{
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Vector3<T> u = seg_end - seg_start;
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Vector3<T> w = seg_start - plane_point;
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T D = plane_normal * u;
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T N = -(plane_normal * w);
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if (::is_zero(D)) {
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if (::is_zero(N)) {
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// segment lies in this plane
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return true;
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} else {
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// does not intersect
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return false;
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}
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}
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const T sI = N / D;
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if (sI < 0 || sI > 1) {
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// does not intersect
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return false;
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}
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// intersects at unique point
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return true;
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}
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// define for float and double
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template class Vector3<float>;
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template class Vector3<double>;
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// define needed ops for Vector3l
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template Vector3<int32_t> &Vector3<int32_t>::operator +=(const Vector3<int32_t> &v);
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