Disabled external gits
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926
cs440-acg/ext/openexr/IlmBase/Imath/ImathEuler.h
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926
cs440-acg/ext/openexr/IlmBase/Imath/ImathEuler.h
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///////////////////////////////////////////////////////////////////////////
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//
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// Copyright (c) 2002-2012, Industrial Light & Magic, a division of Lucas
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// Digital Ltd. LLC
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//
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// All rights reserved.
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following disclaimer
|
||||
// in the documentation and/or other materials provided with the
|
||||
// distribution.
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// * Neither the name of Industrial Light & Magic nor the names of
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// its contributors may be used to endorse or promote products derived
|
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
||||
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
|
||||
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
||||
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
||||
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
||||
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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///////////////////////////////////////////////////////////////////////////
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#ifndef INCLUDED_IMATHEULER_H
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#define INCLUDED_IMATHEULER_H
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//----------------------------------------------------------------------
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//
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// template class Euler<T>
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//
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// This class represents euler angle orientations. The class
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// inherits from Vec3 to it can be freely cast. The additional
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// information is the euler priorities rep. This class is
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// essentially a rip off of Ken Shoemake's GemsIV code. It has
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// been modified minimally to make it more understandable, but
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// hardly enough to make it easy to grok completely.
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//
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// There are 24 possible combonations of Euler angle
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// representations of which 12 are common in CG and you will
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// probably only use 6 of these which in this scheme are the
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// non-relative-non-repeating types.
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//
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// The representations can be partitioned according to two
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// criteria:
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//
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// 1) Are the angles measured relative to a set of fixed axis
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// or relative to each other (the latter being what happens
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// when rotation matrices are multiplied together and is
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// almost ubiquitous in the cg community)
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//
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// 2) Is one of the rotations repeated (ala XYX rotation)
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//
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// When you construct a given representation from scratch you
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// must order the angles according to their priorities. So, the
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// easiest is a softimage or aerospace (yaw/pitch/roll) ordering
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// of ZYX.
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//
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// float x_rot = 1;
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// float y_rot = 2;
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// float z_rot = 3;
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//
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// Eulerf angles(z_rot, y_rot, x_rot, Eulerf::ZYX);
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// -or-
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// Eulerf angles( V3f(z_rot,y_rot,z_rot), Eulerf::ZYX );
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//
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// If instead, the order was YXZ for instance you would have to
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// do this:
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//
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// float x_rot = 1;
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// float y_rot = 2;
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// float z_rot = 3;
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//
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// Eulerf angles(y_rot, x_rot, z_rot, Eulerf::YXZ);
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// -or-
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// Eulerf angles( V3f(y_rot,x_rot,z_rot), Eulerf::YXZ );
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//
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// Notice how the order you put the angles into the three slots
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// should correspond to the enum (YXZ) ordering. The input angle
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// vector is called the "ijk" vector -- not an "xyz" vector. The
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// ijk vector order is the same as the enum. If you treat the
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// Euler<> as a Vec<> (which it inherts from) you will find the
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// angles are ordered in the same way, i.e.:
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//
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// V3f v = angles;
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// // v.x == y_rot, v.y == x_rot, v.z == z_rot
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//
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// If you just want the x, y, and z angles stored in a vector in
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// that order, you can do this:
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//
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// V3f v = angles.toXYZVector()
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// // v.x == x_rot, v.y == y_rot, v.z == z_rot
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//
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// If you want to set the Euler with an XYZVector use the
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// optional layout argument:
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//
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// Eulerf angles(x_rot, y_rot, z_rot,
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// Eulerf::YXZ,
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// Eulerf::XYZLayout);
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//
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// This is the same as:
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//
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// Eulerf angles(y_rot, x_rot, z_rot, Eulerf::YXZ);
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//
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// Note that this won't do anything intelligent if you have a
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// repeated axis in the euler angles (e.g. XYX)
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//
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// If you need to use the "relative" versions of these, you will
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// need to use the "r" enums.
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//
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// The units of the rotation angles are assumed to be radians.
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//
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//----------------------------------------------------------------------
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#include "ImathMath.h"
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#include "ImathVec.h"
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#include "ImathQuat.h"
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#include "ImathMatrix.h"
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#include "ImathLimits.h"
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#include "ImathNamespace.h"
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#include <iostream>
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IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
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#if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
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// Disable MS VC++ warnings about conversion from double to float
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#pragma warning(disable:4244)
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#endif
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template <class T>
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class Euler : public Vec3<T>
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{
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public:
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using Vec3<T>::x;
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using Vec3<T>::y;
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using Vec3<T>::z;
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enum Order
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{
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//
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// All 24 possible orderings
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//
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XYZ = 0x0101, // "usual" orderings
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XZY = 0x0001,
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YZX = 0x1101,
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YXZ = 0x1001,
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ZXY = 0x2101,
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ZYX = 0x2001,
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XZX = 0x0011, // first axis repeated
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XYX = 0x0111,
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YXY = 0x1011,
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YZY = 0x1111,
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ZYZ = 0x2011,
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ZXZ = 0x2111,
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XYZr = 0x2000, // relative orderings -- not common
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XZYr = 0x2100,
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YZXr = 0x1000,
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YXZr = 0x1100,
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ZXYr = 0x0000,
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ZYXr = 0x0100,
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XZXr = 0x2110, // relative first axis repeated
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XYXr = 0x2010,
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YXYr = 0x1110,
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YZYr = 0x1010,
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ZYZr = 0x0110,
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ZXZr = 0x0010,
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// ||||
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// VVVV
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// Legend: ABCD
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// A -> Initial Axis (0==x, 1==y, 2==z)
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// B -> Parity Even (1==true)
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// C -> Initial Repeated (1==true)
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// D -> Frame Static (1==true)
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//
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Legal = XYZ | XZY | YZX | YXZ | ZXY | ZYX |
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XZX | XYX | YXY | YZY | ZYZ | ZXZ |
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XYZr| XZYr| YZXr| YXZr| ZXYr| ZYXr|
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XZXr| XYXr| YXYr| YZYr| ZYZr| ZXZr,
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Min = 0x0000,
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Max = 0x2111,
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Default = XYZ
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};
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enum Axis { X = 0, Y = 1, Z = 2 };
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enum InputLayout { XYZLayout, IJKLayout };
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//--------------------------------------------------------------------
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// Constructors -- all default to ZYX non-relative ala softimage
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// (where there is no argument to specify it)
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//
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// The Euler-from-matrix constructors assume that the matrix does
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// not include shear or non-uniform scaling, but the constructors
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// do not examine the matrix to verify this assumption. If necessary,
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// you can adjust the matrix by calling the removeScalingAndShear()
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// function, defined in ImathMatrixAlgo.h.
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//--------------------------------------------------------------------
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Euler();
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Euler(const Euler&);
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Euler(Order p);
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Euler(const Vec3<T> &v, Order o = Default, InputLayout l = IJKLayout);
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Euler(T i, T j, T k, Order o = Default, InputLayout l = IJKLayout);
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Euler(const Euler<T> &euler, Order newp);
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Euler(const Matrix33<T> &, Order o = Default);
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Euler(const Matrix44<T> &, Order o = Default);
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//---------------------------------
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// Algebraic functions/ Operators
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//---------------------------------
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const Euler<T>& operator= (const Euler<T>&);
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const Euler<T>& operator= (const Vec3<T>&);
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//--------------------------------------------------------
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// Set the euler value
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// This does NOT convert the angles, but setXYZVector()
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// does reorder the input vector.
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//--------------------------------------------------------
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static bool legal(Order);
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void setXYZVector(const Vec3<T> &);
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Order order() const;
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void setOrder(Order);
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void set(Axis initial,
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bool relative,
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bool parityEven,
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bool firstRepeats);
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//------------------------------------------------------------
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// Conversions, toXYZVector() reorders the angles so that
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// the X rotation comes first, followed by the Y and Z
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// in cases like XYX ordering, the repeated angle will be
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// in the "z" component
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//
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// The Euler-from-matrix extract() functions assume that the
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// matrix does not include shear or non-uniform scaling, but
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// the extract() functions do not examine the matrix to verify
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// this assumption. If necessary, you can adjust the matrix
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// by calling the removeScalingAndShear() function, defined
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// in ImathMatrixAlgo.h.
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//------------------------------------------------------------
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void extract(const Matrix33<T>&);
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void extract(const Matrix44<T>&);
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void extract(const Quat<T>&);
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Matrix33<T> toMatrix33() const;
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Matrix44<T> toMatrix44() const;
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Quat<T> toQuat() const;
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Vec3<T> toXYZVector() const;
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//---------------------------------------------------
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// Use this function to unpack angles from ijk form
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//---------------------------------------------------
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void angleOrder(int &i, int &j, int &k) const;
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//---------------------------------------------------
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// Use this function to determine mapping from xyz to ijk
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// - reshuffles the xyz to match the order
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//---------------------------------------------------
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void angleMapping(int &i, int &j, int &k) const;
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//----------------------------------------------------------------------
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//
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// Utility methods for getting continuous rotations. None of these
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// methods change the orientation given by its inputs (or at least
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// that is the intent).
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//
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// angleMod() converts an angle to its equivalent in [-PI, PI]
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//
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// simpleXYZRotation() adjusts xyzRot so that its components differ
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// from targetXyzRot by no more than +-PI
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//
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// nearestRotation() adjusts xyzRot so that its components differ
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// from targetXyzRot by as little as possible.
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// Note that xyz here really means ijk, because
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// the order must be provided.
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//
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// makeNear() adjusts "this" Euler so that its components differ
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// from target by as little as possible. This method
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// might not make sense for Eulers with different order
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// and it probably doesn't work for repeated axis and
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// relative orderings (TODO).
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//
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//-----------------------------------------------------------------------
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static float angleMod (T angle);
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static void simpleXYZRotation (Vec3<T> &xyzRot,
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const Vec3<T> &targetXyzRot);
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static void nearestRotation (Vec3<T> &xyzRot,
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const Vec3<T> &targetXyzRot,
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Order order = XYZ);
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void makeNear (const Euler<T> &target);
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bool frameStatic() const { return _frameStatic; }
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bool initialRepeated() const { return _initialRepeated; }
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bool parityEven() const { return _parityEven; }
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Axis initialAxis() const { return _initialAxis; }
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protected:
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bool _frameStatic : 1; // relative or static rotations
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bool _initialRepeated : 1; // init axis repeated as last
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bool _parityEven : 1; // "parity of axis permutation"
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#if defined _WIN32 || defined _WIN64
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Axis _initialAxis ; // First axis of rotation
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#else
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Axis _initialAxis : 2; // First axis of rotation
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#endif
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};
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//--------------------
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// Convenient typedefs
|
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//--------------------
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typedef Euler<float> Eulerf;
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typedef Euler<double> Eulerd;
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|
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|
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//---------------
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// Implementation
|
||||
//---------------
|
||||
|
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template<class T>
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inline void
|
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Euler<T>::angleOrder(int &i, int &j, int &k) const
|
||||
{
|
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i = _initialAxis;
|
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j = _parityEven ? (i+1)%3 : (i > 0 ? i-1 : 2);
|
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k = _parityEven ? (i > 0 ? i-1 : 2) : (i+1)%3;
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}
|
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|
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template<class T>
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inline void
|
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Euler<T>::angleMapping(int &i, int &j, int &k) const
|
||||
{
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||||
int m[3];
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|
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m[_initialAxis] = 0;
|
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m[(_initialAxis+1) % 3] = _parityEven ? 1 : 2;
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m[(_initialAxis+2) % 3] = _parityEven ? 2 : 1;
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i = m[0];
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j = m[1];
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k = m[2];
|
||||
}
|
||||
|
||||
template<class T>
|
||||
inline void
|
||||
Euler<T>::setXYZVector(const Vec3<T> &v)
|
||||
{
|
||||
int i,j,k;
|
||||
angleMapping(i,j,k);
|
||||
(*this)[i] = v.x;
|
||||
(*this)[j] = v.y;
|
||||
(*this)[k] = v.z;
|
||||
}
|
||||
|
||||
template<class T>
|
||||
inline Vec3<T>
|
||||
Euler<T>::toXYZVector() const
|
||||
{
|
||||
int i,j,k;
|
||||
angleMapping(i,j,k);
|
||||
return Vec3<T>((*this)[i],(*this)[j],(*this)[k]);
|
||||
}
|
||||
|
||||
|
||||
template<class T>
|
||||
Euler<T>::Euler() :
|
||||
Vec3<T>(0,0,0),
|
||||
_frameStatic(true),
|
||||
_initialRepeated(false),
|
||||
_parityEven(true),
|
||||
_initialAxis(X)
|
||||
{}
|
||||
|
||||
template<class T>
|
||||
Euler<T>::Euler(typename Euler<T>::Order p) :
|
||||
Vec3<T>(0,0,0),
|
||||
_frameStatic(true),
|
||||
_initialRepeated(false),
|
||||
_parityEven(true),
|
||||
_initialAxis(X)
|
||||
{
|
||||
setOrder(p);
|
||||
}
|
||||
|
||||
template<class T>
|
||||
inline Euler<T>::Euler( const Vec3<T> &v,
|
||||
typename Euler<T>::Order p,
|
||||
typename Euler<T>::InputLayout l )
|
||||
{
|
||||
setOrder(p);
|
||||
if ( l == XYZLayout ) setXYZVector(v);
|
||||
else { x = v.x; y = v.y; z = v.z; }
|
||||
}
|
||||
|
||||
template<class T>
|
||||
inline Euler<T>::Euler(const Euler<T> &euler)
|
||||
{
|
||||
operator=(euler);
|
||||
}
|
||||
|
||||
template<class T>
|
||||
inline Euler<T>::Euler(const Euler<T> &euler,Order p)
|
||||
{
|
||||
setOrder(p);
|
||||
Matrix33<T> M = euler.toMatrix33();
|
||||
extract(M);
|
||||
}
|
||||
|
||||
template<class T>
|
||||
inline Euler<T>::Euler( T xi, T yi, T zi,
|
||||
typename Euler<T>::Order p,
|
||||
typename Euler<T>::InputLayout l)
|
||||
{
|
||||
setOrder(p);
|
||||
if ( l == XYZLayout ) setXYZVector(Vec3<T>(xi,yi,zi));
|
||||
else { x = xi; y = yi; z = zi; }
|
||||
}
|
||||
|
||||
template<class T>
|
||||
inline Euler<T>::Euler( const Matrix33<T> &M, typename Euler::Order p )
|
||||
{
|
||||
setOrder(p);
|
||||
extract(M);
|
||||
}
|
||||
|
||||
template<class T>
|
||||
inline Euler<T>::Euler( const Matrix44<T> &M, typename Euler::Order p )
|
||||
{
|
||||
setOrder(p);
|
||||
extract(M);
|
||||
}
|
||||
|
||||
template<class T>
|
||||
inline void Euler<T>::extract(const Quat<T> &q)
|
||||
{
|
||||
extract(q.toMatrix33());
|
||||
}
|
||||
|
||||
template<class T>
|
||||
void Euler<T>::extract(const Matrix33<T> &M)
|
||||
{
|
||||
int i,j,k;
|
||||
angleOrder(i,j,k);
|
||||
|
||||
if (_initialRepeated)
|
||||
{
|
||||
//
|
||||
// Extract the first angle, x.
|
||||
//
|
||||
|
||||
x = Math<T>::atan2 (M[j][i], M[k][i]);
|
||||
|
||||
//
|
||||
// Remove the x rotation from M, so that the remaining
|
||||
// rotation, N, is only around two axes, and gimbal lock
|
||||
// cannot occur.
|
||||
//
|
||||
|
||||
Vec3<T> r (0, 0, 0);
|
||||
r[i] = (_parityEven? -x: x);
|
||||
|
||||
Matrix44<T> N;
|
||||
N.rotate (r);
|
||||
|
||||
N = N * Matrix44<T> (M[0][0], M[0][1], M[0][2], 0,
|
||||
M[1][0], M[1][1], M[1][2], 0,
|
||||
M[2][0], M[2][1], M[2][2], 0,
|
||||
0, 0, 0, 1);
|
||||
//
|
||||
// Extract the other two angles, y and z, from N.
|
||||
//
|
||||
|
||||
T sy = Math<T>::sqrt (N[j][i]*N[j][i] + N[k][i]*N[k][i]);
|
||||
y = Math<T>::atan2 (sy, N[i][i]);
|
||||
z = Math<T>::atan2 (N[j][k], N[j][j]);
|
||||
}
|
||||
else
|
||||
{
|
||||
//
|
||||
// Extract the first angle, x.
|
||||
//
|
||||
|
||||
x = Math<T>::atan2 (M[j][k], M[k][k]);
|
||||
|
||||
//
|
||||
// Remove the x rotation from M, so that the remaining
|
||||
// rotation, N, is only around two axes, and gimbal lock
|
||||
// cannot occur.
|
||||
//
|
||||
|
||||
Vec3<T> r (0, 0, 0);
|
||||
r[i] = (_parityEven? -x: x);
|
||||
|
||||
Matrix44<T> N;
|
||||
N.rotate (r);
|
||||
|
||||
N = N * Matrix44<T> (M[0][0], M[0][1], M[0][2], 0,
|
||||
M[1][0], M[1][1], M[1][2], 0,
|
||||
M[2][0], M[2][1], M[2][2], 0,
|
||||
0, 0, 0, 1);
|
||||
//
|
||||
// Extract the other two angles, y and z, from N.
|
||||
//
|
||||
|
||||
T cy = Math<T>::sqrt (N[i][i]*N[i][i] + N[i][j]*N[i][j]);
|
||||
y = Math<T>::atan2 (-N[i][k], cy);
|
||||
z = Math<T>::atan2 (-N[j][i], N[j][j]);
|
||||
}
|
||||
|
||||
if (!_parityEven)
|
||||
*this *= -1;
|
||||
|
||||
if (!_frameStatic)
|
||||
{
|
||||
T t = x;
|
||||
x = z;
|
||||
z = t;
|
||||
}
|
||||
}
|
||||
|
||||
template<class T>
|
||||
void Euler<T>::extract(const Matrix44<T> &M)
|
||||
{
|
||||
int i,j,k;
|
||||
angleOrder(i,j,k);
|
||||
|
||||
if (_initialRepeated)
|
||||
{
|
||||
//
|
||||
// Extract the first angle, x.
|
||||
//
|
||||
|
||||
x = Math<T>::atan2 (M[j][i], M[k][i]);
|
||||
|
||||
//
|
||||
// Remove the x rotation from M, so that the remaining
|
||||
// rotation, N, is only around two axes, and gimbal lock
|
||||
// cannot occur.
|
||||
//
|
||||
|
||||
Vec3<T> r (0, 0, 0);
|
||||
r[i] = (_parityEven? -x: x);
|
||||
|
||||
Matrix44<T> N;
|
||||
N.rotate (r);
|
||||
N = N * M;
|
||||
|
||||
//
|
||||
// Extract the other two angles, y and z, from N.
|
||||
//
|
||||
|
||||
T sy = Math<T>::sqrt (N[j][i]*N[j][i] + N[k][i]*N[k][i]);
|
||||
y = Math<T>::atan2 (sy, N[i][i]);
|
||||
z = Math<T>::atan2 (N[j][k], N[j][j]);
|
||||
}
|
||||
else
|
||||
{
|
||||
//
|
||||
// Extract the first angle, x.
|
||||
//
|
||||
|
||||
x = Math<T>::atan2 (M[j][k], M[k][k]);
|
||||
|
||||
//
|
||||
// Remove the x rotation from M, so that the remaining
|
||||
// rotation, N, is only around two axes, and gimbal lock
|
||||
// cannot occur.
|
||||
//
|
||||
|
||||
Vec3<T> r (0, 0, 0);
|
||||
r[i] = (_parityEven? -x: x);
|
||||
|
||||
Matrix44<T> N;
|
||||
N.rotate (r);
|
||||
N = N * M;
|
||||
|
||||
//
|
||||
// Extract the other two angles, y and z, from N.
|
||||
//
|
||||
|
||||
T cy = Math<T>::sqrt (N[i][i]*N[i][i] + N[i][j]*N[i][j]);
|
||||
y = Math<T>::atan2 (-N[i][k], cy);
|
||||
z = Math<T>::atan2 (-N[j][i], N[j][j]);
|
||||
}
|
||||
|
||||
if (!_parityEven)
|
||||
*this *= -1;
|
||||
|
||||
if (!_frameStatic)
|
||||
{
|
||||
T t = x;
|
||||
x = z;
|
||||
z = t;
|
||||
}
|
||||
}
|
||||
|
||||
template<class T>
|
||||
Matrix33<T> Euler<T>::toMatrix33() const
|
||||
{
|
||||
int i,j,k;
|
||||
angleOrder(i,j,k);
|
||||
|
||||
Vec3<T> angles;
|
||||
|
||||
if ( _frameStatic ) angles = (*this);
|
||||
else angles = Vec3<T>(z,y,x);
|
||||
|
||||
if ( !_parityEven ) angles *= -1.0;
|
||||
|
||||
T ci = Math<T>::cos(angles.x);
|
||||
T cj = Math<T>::cos(angles.y);
|
||||
T ch = Math<T>::cos(angles.z);
|
||||
T si = Math<T>::sin(angles.x);
|
||||
T sj = Math<T>::sin(angles.y);
|
||||
T sh = Math<T>::sin(angles.z);
|
||||
|
||||
T cc = ci*ch;
|
||||
T cs = ci*sh;
|
||||
T sc = si*ch;
|
||||
T ss = si*sh;
|
||||
|
||||
Matrix33<T> M;
|
||||
|
||||
if ( _initialRepeated )
|
||||
{
|
||||
M[i][i] = cj; M[j][i] = sj*si; M[k][i] = sj*ci;
|
||||
M[i][j] = sj*sh; M[j][j] = -cj*ss+cc; M[k][j] = -cj*cs-sc;
|
||||
M[i][k] = -sj*ch; M[j][k] = cj*sc+cs; M[k][k] = cj*cc-ss;
|
||||
}
|
||||
else
|
||||
{
|
||||
M[i][i] = cj*ch; M[j][i] = sj*sc-cs; M[k][i] = sj*cc+ss;
|
||||
M[i][j] = cj*sh; M[j][j] = sj*ss+cc; M[k][j] = sj*cs-sc;
|
||||
M[i][k] = -sj; M[j][k] = cj*si; M[k][k] = cj*ci;
|
||||
}
|
||||
|
||||
return M;
|
||||
}
|
||||
|
||||
template<class T>
|
||||
Matrix44<T> Euler<T>::toMatrix44() const
|
||||
{
|
||||
int i,j,k;
|
||||
angleOrder(i,j,k);
|
||||
|
||||
Vec3<T> angles;
|
||||
|
||||
if ( _frameStatic ) angles = (*this);
|
||||
else angles = Vec3<T>(z,y,x);
|
||||
|
||||
if ( !_parityEven ) angles *= -1.0;
|
||||
|
||||
T ci = Math<T>::cos(angles.x);
|
||||
T cj = Math<T>::cos(angles.y);
|
||||
T ch = Math<T>::cos(angles.z);
|
||||
T si = Math<T>::sin(angles.x);
|
||||
T sj = Math<T>::sin(angles.y);
|
||||
T sh = Math<T>::sin(angles.z);
|
||||
|
||||
T cc = ci*ch;
|
||||
T cs = ci*sh;
|
||||
T sc = si*ch;
|
||||
T ss = si*sh;
|
||||
|
||||
Matrix44<T> M;
|
||||
|
||||
if ( _initialRepeated )
|
||||
{
|
||||
M[i][i] = cj; M[j][i] = sj*si; M[k][i] = sj*ci;
|
||||
M[i][j] = sj*sh; M[j][j] = -cj*ss+cc; M[k][j] = -cj*cs-sc;
|
||||
M[i][k] = -sj*ch; M[j][k] = cj*sc+cs; M[k][k] = cj*cc-ss;
|
||||
}
|
||||
else
|
||||
{
|
||||
M[i][i] = cj*ch; M[j][i] = sj*sc-cs; M[k][i] = sj*cc+ss;
|
||||
M[i][j] = cj*sh; M[j][j] = sj*ss+cc; M[k][j] = sj*cs-sc;
|
||||
M[i][k] = -sj; M[j][k] = cj*si; M[k][k] = cj*ci;
|
||||
}
|
||||
|
||||
return M;
|
||||
}
|
||||
|
||||
template<class T>
|
||||
Quat<T> Euler<T>::toQuat() const
|
||||
{
|
||||
Vec3<T> angles;
|
||||
int i,j,k;
|
||||
angleOrder(i,j,k);
|
||||
|
||||
if ( _frameStatic ) angles = (*this);
|
||||
else angles = Vec3<T>(z,y,x);
|
||||
|
||||
if ( !_parityEven ) angles.y = -angles.y;
|
||||
|
||||
T ti = angles.x*0.5;
|
||||
T tj = angles.y*0.5;
|
||||
T th = angles.z*0.5;
|
||||
T ci = Math<T>::cos(ti);
|
||||
T cj = Math<T>::cos(tj);
|
||||
T ch = Math<T>::cos(th);
|
||||
T si = Math<T>::sin(ti);
|
||||
T sj = Math<T>::sin(tj);
|
||||
T sh = Math<T>::sin(th);
|
||||
T cc = ci*ch;
|
||||
T cs = ci*sh;
|
||||
T sc = si*ch;
|
||||
T ss = si*sh;
|
||||
|
||||
T parity = _parityEven ? 1.0 : -1.0;
|
||||
|
||||
Quat<T> q;
|
||||
Vec3<T> a;
|
||||
|
||||
if ( _initialRepeated )
|
||||
{
|
||||
a[i] = cj*(cs + sc);
|
||||
a[j] = sj*(cc + ss) * parity,
|
||||
a[k] = sj*(cs - sc);
|
||||
q.r = cj*(cc - ss);
|
||||
}
|
||||
else
|
||||
{
|
||||
a[i] = cj*sc - sj*cs,
|
||||
a[j] = (cj*ss + sj*cc) * parity,
|
||||
a[k] = cj*cs - sj*sc;
|
||||
q.r = cj*cc + sj*ss;
|
||||
}
|
||||
|
||||
q.v = a;
|
||||
|
||||
return q;
|
||||
}
|
||||
|
||||
template<class T>
|
||||
inline bool
|
||||
Euler<T>::legal(typename Euler<T>::Order order)
|
||||
{
|
||||
return (order & ~Legal) ? false : true;
|
||||
}
|
||||
|
||||
template<class T>
|
||||
typename Euler<T>::Order
|
||||
Euler<T>::order() const
|
||||
{
|
||||
int foo = (_initialAxis == Z ? 0x2000 : (_initialAxis == Y ? 0x1000 : 0));
|
||||
|
||||
if (_parityEven) foo |= 0x0100;
|
||||
if (_initialRepeated) foo |= 0x0010;
|
||||
if (_frameStatic) foo++;
|
||||
|
||||
return (Order)foo;
|
||||
}
|
||||
|
||||
template<class T>
|
||||
inline void Euler<T>::setOrder(typename Euler<T>::Order p)
|
||||
{
|
||||
set( p & 0x2000 ? Z : (p & 0x1000 ? Y : X), // initial axis
|
||||
!(p & 0x1), // static?
|
||||
!!(p & 0x100), // permutation even?
|
||||
!!(p & 0x10)); // initial repeats?
|
||||
}
|
||||
|
||||
template<class T>
|
||||
void Euler<T>::set(typename Euler<T>::Axis axis,
|
||||
bool relative,
|
||||
bool parityEven,
|
||||
bool firstRepeats)
|
||||
{
|
||||
_initialAxis = axis;
|
||||
_frameStatic = !relative;
|
||||
_parityEven = parityEven;
|
||||
_initialRepeated = firstRepeats;
|
||||
}
|
||||
|
||||
template<class T>
|
||||
const Euler<T>& Euler<T>::operator= (const Euler<T> &euler)
|
||||
{
|
||||
x = euler.x;
|
||||
y = euler.y;
|
||||
z = euler.z;
|
||||
_initialAxis = euler._initialAxis;
|
||||
_frameStatic = euler._frameStatic;
|
||||
_parityEven = euler._parityEven;
|
||||
_initialRepeated = euler._initialRepeated;
|
||||
return *this;
|
||||
}
|
||||
|
||||
template<class T>
|
||||
const Euler<T>& Euler<T>::operator= (const Vec3<T> &v)
|
||||
{
|
||||
x = v.x;
|
||||
y = v.y;
|
||||
z = v.z;
|
||||
return *this;
|
||||
}
|
||||
|
||||
template<class T>
|
||||
std::ostream& operator << (std::ostream &o, const Euler<T> &euler)
|
||||
{
|
||||
char a[3] = { 'X', 'Y', 'Z' };
|
||||
|
||||
const char* r = euler.frameStatic() ? "" : "r";
|
||||
int i,j,k;
|
||||
euler.angleOrder(i,j,k);
|
||||
|
||||
if ( euler.initialRepeated() ) k = i;
|
||||
|
||||
return o << "("
|
||||
<< euler.x << " "
|
||||
<< euler.y << " "
|
||||
<< euler.z << " "
|
||||
<< a[i] << a[j] << a[k] << r << ")";
|
||||
}
|
||||
|
||||
template <class T>
|
||||
float
|
||||
Euler<T>::angleMod (T angle)
|
||||
{
|
||||
angle = fmod(T (angle), T (2 * M_PI));
|
||||
|
||||
if (angle < -M_PI) angle += 2 * M_PI;
|
||||
if (angle > +M_PI) angle -= 2 * M_PI;
|
||||
|
||||
return angle;
|
||||
}
|
||||
|
||||
template <class T>
|
||||
void
|
||||
Euler<T>::simpleXYZRotation (Vec3<T> &xyzRot, const Vec3<T> &targetXyzRot)
|
||||
{
|
||||
Vec3<T> d = xyzRot - targetXyzRot;
|
||||
xyzRot[0] = targetXyzRot[0] + angleMod(d[0]);
|
||||
xyzRot[1] = targetXyzRot[1] + angleMod(d[1]);
|
||||
xyzRot[2] = targetXyzRot[2] + angleMod(d[2]);
|
||||
}
|
||||
|
||||
template <class T>
|
||||
void
|
||||
Euler<T>::nearestRotation (Vec3<T> &xyzRot, const Vec3<T> &targetXyzRot,
|
||||
Order order)
|
||||
{
|
||||
int i,j,k;
|
||||
Euler<T> e (0,0,0, order);
|
||||
e.angleOrder(i,j,k);
|
||||
|
||||
simpleXYZRotation(xyzRot, targetXyzRot);
|
||||
|
||||
Vec3<T> otherXyzRot;
|
||||
otherXyzRot[i] = M_PI+xyzRot[i];
|
||||
otherXyzRot[j] = M_PI-xyzRot[j];
|
||||
otherXyzRot[k] = M_PI+xyzRot[k];
|
||||
|
||||
simpleXYZRotation(otherXyzRot, targetXyzRot);
|
||||
|
||||
Vec3<T> d = xyzRot - targetXyzRot;
|
||||
Vec3<T> od = otherXyzRot - targetXyzRot;
|
||||
T dMag = d.dot(d);
|
||||
T odMag = od.dot(od);
|
||||
|
||||
if (odMag < dMag)
|
||||
{
|
||||
xyzRot = otherXyzRot;
|
||||
}
|
||||
}
|
||||
|
||||
template <class T>
|
||||
void
|
||||
Euler<T>::makeNear (const Euler<T> &target)
|
||||
{
|
||||
Vec3<T> xyzRot = toXYZVector();
|
||||
Vec3<T> targetXyz;
|
||||
if (order() != target.order())
|
||||
{
|
||||
Euler<T> targetSameOrder = Euler<T>(target, order());
|
||||
targetXyz = targetSameOrder.toXYZVector();
|
||||
}
|
||||
else
|
||||
{
|
||||
targetXyz = target.toXYZVector();
|
||||
}
|
||||
|
||||
nearestRotation(xyzRot, targetXyz, order());
|
||||
|
||||
setXYZVector(xyzRot);
|
||||
}
|
||||
|
||||
#if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
|
||||
#pragma warning(default:4244)
|
||||
#endif
|
||||
|
||||
IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
|
||||
|
||||
|
||||
#endif // INCLUDED_IMATHEULER_H
|
||||
Reference in New Issue
Block a user