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