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// This file is part of libigl, a simple c++ geometry processing library.
//
// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla Public License
// v. 2.0. If a copy of the MPL was not distributed with this file, You can
// obtain one at http://mozilla.org/MPL/2.0/.
#ifndef IGL_CANONICAL_QUATERNIONS_H
#define IGL_CANONICAL_QUATERNIONS_H
#include "igl_inline.h"
// Define some canonical quaternions for floats and doubles
// A Quaternion, q, is defined here as an arrays of four scalars (x,y,z,w),
// such that q = x*i + y*j + z*k + w
namespace igl
{
// Float versions
#define SQRT_2_OVER_2 0.707106781f
// Identity
const float IDENTITY_QUAT_F[4] = {0,0,0,1};
// The following match the Matlab canonical views
// X point right, Y pointing up and Z point out
const float XY_PLANE_QUAT_F[4] = {0,0,0,1};
// X points right, Y points *in* and Z points up
const float XZ_PLANE_QUAT_F[4] = {-SQRT_2_OVER_2,0,0,SQRT_2_OVER_2};
// X points out, Y points right, and Z points up
const float YZ_PLANE_QUAT_F[4] = {-0.5,-0.5,-0.5,0.5};
const float CANONICAL_VIEW_QUAT_F[][4] =
{
{ 0, 0, 0, 1}, // 0
{ 0, 0, SQRT_2_OVER_2, SQRT_2_OVER_2}, // 1
{ 0, 0, 1, 0}, // 2
{ 0, 0, SQRT_2_OVER_2,-SQRT_2_OVER_2}, // 3
{ 0, -1, 0, 0}, // 4
{-SQRT_2_OVER_2, SQRT_2_OVER_2, 0, 0}, // 5
{ -1, 0, 0, 0}, // 6
{-SQRT_2_OVER_2,-SQRT_2_OVER_2, 0, 0}, // 7
{ -0.5, -0.5, -0.5, 0.5}, // 8
{ 0,-SQRT_2_OVER_2, 0, SQRT_2_OVER_2}, // 9
{ 0.5, -0.5, 0.5, 0.5}, // 10
{ SQRT_2_OVER_2, 0, SQRT_2_OVER_2, 0}, // 11
{ SQRT_2_OVER_2, 0,-SQRT_2_OVER_2, 0}, // 12
{ 0.5, 0.5, -0.5, 0.5}, // 13
{ 0, SQRT_2_OVER_2, 0, SQRT_2_OVER_2}, // 14
{ -0.5, 0.5, 0.5, 0.5}, // 15
{ 0, SQRT_2_OVER_2, SQRT_2_OVER_2, 0}, // 16
{ -0.5, 0.5, 0.5, -0.5}, // 17
{-SQRT_2_OVER_2, 0, 0,-SQRT_2_OVER_2}, // 18
{ -0.5, -0.5, -0.5, -0.5}, // 19
{-SQRT_2_OVER_2, 0, 0, SQRT_2_OVER_2}, // 20
{ -0.5, -0.5, 0.5, 0.5}, // 21
{ 0,-SQRT_2_OVER_2, SQRT_2_OVER_2, 0}, // 22
{ 0.5, -0.5, 0.5, -0.5} // 23
};
#undef SQRT_2_OVER_2
// Double versions
#define SQRT_2_OVER_2 0.70710678118654757
// Identity
const double IDENTITY_QUAT_D[4] = {0,0,0,1};
// The following match the Matlab canonical views
// X point right, Y pointing up and Z point out
const double XY_PLANE_QUAT_D[4] = {0,0,0,1};
// X points right, Y points *in* and Z points up
const double XZ_PLANE_QUAT_D[4] = {-SQRT_2_OVER_2,0,0,SQRT_2_OVER_2};
// X points out, Y points right, and Z points up
const double YZ_PLANE_QUAT_D[4] = {-0.5,-0.5,-0.5,0.5};
const double CANONICAL_VIEW_QUAT_D[][4] =
{
{ 0, 0, 0, 1},
{ 0, 0, SQRT_2_OVER_2, SQRT_2_OVER_2},
{ 0, 0, 1, 0},
{ 0, 0, SQRT_2_OVER_2,-SQRT_2_OVER_2},
{ 0, -1, 0, 0},
{-SQRT_2_OVER_2, SQRT_2_OVER_2, 0, 0},
{ -1, 0, 0, 0},
{-SQRT_2_OVER_2,-SQRT_2_OVER_2, 0, 0},
{ -0.5, -0.5, -0.5, 0.5},
{ 0,-SQRT_2_OVER_2, 0, SQRT_2_OVER_2},
{ 0.5, -0.5, 0.5, 0.5},
{ SQRT_2_OVER_2, 0, SQRT_2_OVER_2, 0},
{ SQRT_2_OVER_2, 0,-SQRT_2_OVER_2, 0},
{ 0.5, 0.5, -0.5, 0.5},
{ 0, SQRT_2_OVER_2, 0, SQRT_2_OVER_2},
{ -0.5, 0.5, 0.5, 0.5},
{ 0, SQRT_2_OVER_2, SQRT_2_OVER_2, 0},
{ -0.5, 0.5, 0.5, -0.5},
{-SQRT_2_OVER_2, 0, 0,-SQRT_2_OVER_2},
{ -0.5, -0.5, -0.5, -0.5},
{-SQRT_2_OVER_2, 0, 0, SQRT_2_OVER_2},
{ -0.5, -0.5, 0.5, 0.5},
{ 0,-SQRT_2_OVER_2, SQRT_2_OVER_2, 0},
{ 0.5, -0.5, 0.5, -0.5}
};
#undef SQRT_2_OVER_2
#define NUM_CANONICAL_VIEW_QUAT 24
// NOTE: I want to rather be able to return a Q_type[][] but C++ is not
// making it easy. So instead I've written a per-element accessor
// Return element [i][j] of the corresponding CANONICAL_VIEW_QUAT_* of the
// given templated type
// Inputs:
// i index of quaternion
// j index of coordinate in quaternion i
// Returns values of CANONICAL_VIEW_QUAT_*[i][j]
template <typename Q_type>
IGL_INLINE Q_type CANONICAL_VIEW_QUAT(int i, int j);
// Template specializations for float and double
template <>
IGL_INLINE float CANONICAL_VIEW_QUAT<float>(int i, int j);
template <>
IGL_INLINE double CANONICAL_VIEW_QUAT<double>(int i, int j);
}
#ifndef IGL_STATIC_LIBRARY
# include "canonical_quaternions.cpp"
#endif
#endif
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