961832164b
When multiplying two quaternions, we now implicitly copy the components of the 'a' argument so that the result can be reliably written back to the 'a' argument quaternion without conflicting with the multiplication itself. This is consistent with the cogl_matrix_multiply() api which allows the 'result' and 'a' arguments to point to the same matrix. In debug builds Cogl will assert that the 'b' and 'result' arguments don't point to the same quaternion. Reviewed-by: Neil Roberts <neil@linux.intel.com> (cherry picked from commit 207527313a8957789390069e84189254cf41e88f)
529 lines
14 KiB
C
529 lines
14 KiB
C
/*
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* Cogl
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*
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* An object oriented GL/GLES Abstraction/Utility Layer
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*
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* Copyright (C) 2010 Intel Corporation.
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the
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* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
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* Boston, MA 02111-1307, USA.
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*
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* Authors:
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* Robert Bragg <robert@linux.intel.com>
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*/
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#if !defined(__COGL_H_INSIDE__) && !defined(COGL_COMPILATION)
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#error "Only <cogl/cogl.h> can be included directly."
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#endif
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#ifndef __COGL_QUATERNION_H__
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#define __COGL_QUATERNION_H__
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#include <cogl/cogl-types.h>
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#include <cogl/cogl-vector.h>
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G_BEGIN_DECLS
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/**
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* SECTION:cogl-quaternion
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* @short_description: Functions for initializing and manipulating
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* quaternions.
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*
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* Quaternions have become a standard form for representing 3D
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* rotations and have some nice properties when compared with other
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* representation such as (roll,pitch,yaw) Euler angles. They can be
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* used to interpolate between different rotations and they don't
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* suffer from a problem called "Gimbal lock" where two of the axis of
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* rotation may become aligned and you loose a degree of freedom.
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* (<ulink url="http://en.wikipedia.org/wiki/Gimbal_lock"/>).
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*/
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#include <cogl/cogl-vector.h>
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#include <cogl/cogl-euler.h>
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/**
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* CoglQuaternion:
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*
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* A quaternion is comprised of a scalar component and a 3D vector
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* component. The scalar component is normally referred to as w and the
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* vector might either be referred to as v or a (for axis) or expanded
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* with the individual components: (x, y, z) A full quaternion would
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* then be written as <literal>[w (x, y, z)]</literal>.
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*
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* Quaternions can be considered to represent an axis and angle
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* pair although sadly these numbers are buried somewhat under some
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* maths...
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*
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* For the curious you can see here that a given axis (a) and angle (𝜃)
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* pair are represented in a quaternion as follows:
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* |[
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* [w=cos(𝜃/2) ( x=sin(𝜃/2)*a.x, y=sin(𝜃/2)*a.y, z=sin(𝜃/2)*a.x )]
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* ]|
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*
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* Unit Quaternions:
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* When using Quaternions to represent spatial orientations for 3D
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* graphics it's always assumed you have a unit quaternion. The
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* magnitude of a quaternion is defined as:
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* |[
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* sqrt (w² + x² + y² + z²)
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* ]|
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* and a unit quaternion satisfies this equation:
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* |[
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* w² + x² + y² + z² = 1
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* ]|
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*
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* Thankfully most of the time we don't actually have to worry about
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* the maths that goes on behind the scenes but if you are curious to
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* learn more here are some external references:
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*
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* <itemizedlist>
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* <listitem>
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* <ulink url="http://mathworld.wolfram.com/Quaternion.html"/>
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* </listitem>
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* <listitem>
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* <ulink url="http://www.gamedev.net/reference/articles/article1095.asp"/>
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* </listitem>
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* <listitem>
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* <ulink url="http://www.cprogramming.com/tutorial/3d/quaternions.html"/>
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* </listitem>
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* <listitem>
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* <ulink url="http://www.isner.com/tutorials/quatSpells/quaternion_spells_12.htm"/>
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* </listitem>
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* <listitem>
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* 3D Maths Primer for Graphics and Game Development ISBN-10: 1556229119
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* </listitem>
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* <listitem>
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* <ulink url="http://www.cs.caltech.edu/courses/cs171/quatut.pdf"/>
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* </listitem>
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* <listitem>
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* <ulink url="http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q56"/>
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* </listitem>
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* </itemizedlist>
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*
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* @w: based on the angle of rotation it is cos(𝜃/2)
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* @x: based on the angle of rotation and x component of the axis of
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* rotation it is sin(𝜃/2)*axis.x
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* @y: based on the angle of rotation and y component of the axis of
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* rotation it is sin(𝜃/2)*axis.y
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* @z: based on the angle of rotation and z component of the axis of
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* rotation it is sin(𝜃/2)*axis.z
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*/
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struct _CoglQuaternion
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{
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float w;
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float x;
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float y;
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float z;
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/*< private >*/
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float padding0;
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float padding1;
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float padding2;
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float padding3;
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};
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COGL_STRUCT_SIZE_ASSERT (CoglQuaternion, 32);
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/**
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* cogl_quaternion_init:
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* @quaternion: An uninitialized #CoglQuaternion
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* @angle: The angle you want to rotate around the given axis
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* @x: The x component of your axis vector about which you want to
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* rotate.
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* @y: The y component of your axis vector about which you want to
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* rotate.
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* @z: The z component of your axis vector about which you want to
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* rotate.
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*
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* Initializes a quaternion that rotates @angle degrees around the
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* axis vector (@x, @y, @z). The axis vector does not need to be
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* normalized.
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*
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* Returns: A normalized, unit quaternion representing an orientation
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* rotated @angle degrees around the axis vector (@x, @y, @z)
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_init (CoglQuaternion *quaternion,
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float angle,
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float x,
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float y,
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float z);
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/**
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* cogl_quaternion_init_from_angle_vector:
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* @quaternion: An uninitialized #CoglQuaternion
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* @axis3f: your 3 component axis vector about which you want to rotate.
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*
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* Initializes a quaternion that rotates @angle degrees around the
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* given @axis vector. The axis vector does not need to be
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* normalized.
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*
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* Returns: A normalized, unit quaternion representing an orientation
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* rotated @angle degrees around the given @axis vector.
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_init_from_angle_vector (CoglQuaternion *quaternion,
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float angle,
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const float *axis3f);
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/**
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* cogl_quaternion_init_identity:
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* @quaternion: An uninitialized #CoglQuaternion
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*
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* Initializes the quaternion with the canonical quaternion identity
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* [1 (0, 0, 0)] which represents no rotation. Multiplying a
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* quaternion with this identity leaves the quaternion unchanged.
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*
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* You might also want to consider using
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* cogl_get_static_identity_quaternion().
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_init_identity (CoglQuaternion *quaternion);
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/**
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* cogl_quaternion_init_from_array:
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* @quaternion: A #CoglQuaternion
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* @array: An array of 4 floats w,(x,y,z)
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*
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* Initializes a [w (x, y,z)] quaternion directly from an array of 4
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* floats: [w,x,y,z].
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_init_from_array (CoglQuaternion *quaternion,
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const float *array);
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/**
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* cogl_quaternion_init_from_x_rotation:
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* @quaternion: An uninitialized #CoglQuaternion
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* @angle: The angle to rotate around the x axis
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*
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* XXX: check which direction this rotates
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_init_from_x_rotation (CoglQuaternion *quaternion,
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float angle);
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/**
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* cogl_quaternion_init_from_y_rotation:
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* @quaternion: An uninitialized #CoglQuaternion
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* @angle: The angle to rotate around the y axis
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*
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_init_from_y_rotation (CoglQuaternion *quaternion,
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float angle);
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/**
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* cogl_quaternion_init_from_z_rotation:
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* @quaternion: An uninitialized #CoglQuaternion
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* @angle: The angle to rotate around the z axis
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*
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_init_from_z_rotation (CoglQuaternion *quaternion,
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float angle);
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/**
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* cogl_quaternion_init_from_euler:
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* @quaternion: A #CoglQuaternion
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* @euler: A #CoglEuler with which to initialize the quaternion
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_init_from_euler (CoglQuaternion *quaternion,
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const CoglEuler *euler);
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/**
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* cogl_quaternion_init_from_quaternion:
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* @quaternion: A #CoglQuaternion
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* @src: A #CoglQuaternion with which to initialize @quaternion
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_init_from_quaternion (CoglQuaternion *quaternion,
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CoglQuaternion *src);
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/**
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* cogl_quaternion_init_from_matrix:
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* @quaternion: A Cogl Quaternion
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* @matrix: A rotation matrix with which to initialize the quaternion
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*
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* Initializes a quaternion from a rotation matrix.
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*
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* Since: 1.10
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* Stability: unstable
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*/
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void
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cogl_quaternion_init_from_matrix (CoglQuaternion *quaternion,
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const CoglMatrix *matrix);
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/**
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* cogl_quaternion_equal:
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* @v1: A #CoglQuaternion
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* @v2: A #CoglQuaternion
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*
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* Compares that all the components of quaternions @a and @b are
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* equal.
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*
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* An epsilon value is not used to compare the float components, but
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* the == operator is at least used so that 0 and -0 are considered
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* equal.
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*
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* Returns: %TRUE if the quaternions are equal else %FALSE.
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*
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* Since: 2.0
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*/
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CoglBool
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cogl_quaternion_equal (const void *v1, const void *v2);
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/**
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* cogl_quaternion_copy:
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* @src: A #CoglQuaternion
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*
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* Allocates a new #CoglQuaternion on the stack and initializes it with
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* the same values as @src.
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*
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* Returns: A newly allocated #CoglQuaternion which should be freed
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* using cogl_quaternion_free()
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*
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* Since: 2.0
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*/
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CoglQuaternion *
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cogl_quaternion_copy (const CoglQuaternion *src);
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/**
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* cogl_quaternion_free:
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* @quaternion: A #CoglQuaternion
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*
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* Frees a #CoglQuaternion that was previously allocated via
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* cogl_quaternion_copy().
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_free (CoglQuaternion *quaternion);
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/**
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* cogl_quaternion_get_rotation_angle:
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* @quaternion: A #CoglQuaternion
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*
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*
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* Since: 2.0
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*/
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float
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cogl_quaternion_get_rotation_angle (const CoglQuaternion *quaternion);
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/**
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* cogl_quaternion_get_rotation_axis:
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* @quaternion: A #CoglQuaternion
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*
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_get_rotation_axis (const CoglQuaternion *quaternion,
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float *vector3);
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/**
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* cogl_quaternion_normalize:
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* @quaternion: A #CoglQuaternion
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*
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_normalize (CoglQuaternion *quaternion);
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/**
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* cogl_quaternion_dot_product:
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* @a: A #CoglQuaternion
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* @b: A #CoglQuaternion
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*
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* Since: 2.0
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*/
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float
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cogl_quaternion_dot_product (const CoglQuaternion *a,
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const CoglQuaternion *b);
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/**
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* cogl_quaternion_invert:
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* @quaternion: A #CoglQuaternion
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*
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_invert (CoglQuaternion *quaternion);
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/**
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* cogl_quaternion_multiply:
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* @result: The destination #CoglQuaternion
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* @left: The second #CoglQuaternion rotation to apply
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* @right: The first #CoglQuaternion rotation to apply
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*
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* This combines the rotations of two quaternions into @result. The
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* operation is not commutative so the order is important because AxB
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* != BxA. Cogl follows the standard convention for quaternions here
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* so the rotations are applied @right to @left. This is similar to the
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* combining of matrices.
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*
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* <note>It is possible to multiply the @a quaternion in-place, so
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* @result can be equal to @a but can't be equal to @b.</note>
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_multiply (CoglQuaternion *result,
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const CoglQuaternion *left,
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const CoglQuaternion *right);
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/**
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* cogl_quaternion_pow:
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* @quaternion: A #CoglQuaternion
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*
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_pow (CoglQuaternion *quaternion, float exponent);
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/**
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* cogl_quaternion_slerp:
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*
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* Performs a spherical linear interpolation between two quaternions.
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*
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* Noteable properties:
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* <itemizedlist>
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* <listitem>
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* commutative: No
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* </listitem>
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* <listitem>
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* constant velocity: Yes
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* </listitem>
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* <listitem>
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* torque minimal (travels along the surface of the 4-sphere): Yes
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* </listitem>
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* <listitem>
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* more expensive than cogl_quaternion_nlerp()
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* </listitem>
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* </itemizedlist>
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*/
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void
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cogl_quaternion_slerp (CoglQuaternion *result,
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const CoglQuaternion *a,
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const CoglQuaternion *b,
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float t);
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/**
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* cogl_quaternion_nlerp:
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* @result: The destination #CoglQuaternion
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* @a: The first #CoglQuaternion
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* @b: The second #CoglQuaternion
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* @t: The factor in the range [0,1] used to interpolate between
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* quaterion @a and @b.
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*
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* Performs a normalized linear interpolation between two quaternions.
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* That is it does a linear interpolation of the quaternion components
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* and then normalizes the result. This will follow the shortest arc
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* between the two orientations (just like the slerp() function) but
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* will not progress at a constant speed. Unlike slerp() nlerp is
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* commutative which is useful if you are blending animations
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* together. (I.e. nlerp (tmp, a, b) followed by nlerp (result, tmp,
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* d) is the same as nlerp (tmp, a, d) followed by nlerp (result, tmp,
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* b)). Finally nlerp is cheaper than slerp so it can be a good choice
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* if you don't need the constant speed property of the slerp() function.
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*
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* Notable properties:
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* <itemizedlist>
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* <listitem>
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* commutative: Yes
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* </listitem>
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* <listitem>
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* constant velocity: No
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* </listitem>
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* <listitem>
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* torque minimal (travels along the surface of the 4-sphere): Yes
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* </listitem>
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* <listitem>
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* faster than cogl_quaternion_slerp()
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* </listitem>
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* </itemizedlist>
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*/
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void
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cogl_quaternion_nlerp (CoglQuaternion *result,
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const CoglQuaternion *a,
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const CoglQuaternion *b,
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float t);
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/**
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* cogl_quaternion_squad:
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*
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*
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* Since: 2.0
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*/
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void
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cogl_quaternion_squad (CoglQuaternion *result,
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const CoglQuaternion *prev,
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const CoglQuaternion *a,
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const CoglQuaternion *b,
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const CoglQuaternion *next,
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float t);
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/**
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* cogl_get_static_identity_quaternion:
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*
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* Returns a pointer to a singleton quaternion constant describing the
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* canonical identity [1 (0, 0, 0)] which represents no rotation.
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*
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* If you multiply a quaternion with the identity quaternion you will
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* get back the same value as the original quaternion.
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*
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* Returns: A pointer to an identity quaternion
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|
*
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* Since: 2.0
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|
*/
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|
const CoglQuaternion *
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|
cogl_get_static_identity_quaternion (void);
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|
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|
/**
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|
* cogl_get_static_zero_quaternion:
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|
*
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|
* Returns: a pointer to a singleton quaternion constant describing a
|
|
* rotation of 180 degrees around a degenerate axis:
|
|
* [0 (0, 0, 0)]
|
|
*
|
|
* Since: 2.0
|
|
*/
|
|
const CoglQuaternion *
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|
cogl_get_static_zero_quaternion (void);
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|
|
|
G_END_DECLS
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|
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|
#endif /* __COGL_QUATERNION_H__ */
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|
|