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godot/core/math/basis.h
TwistedTwigleg 5ffed49907 New and improved IK system for Skeleton3D 
This PR and commit adds a new IK system for 3D with the Skeleton3D node
that adds several new IK solvers, as well as additional changes and functionality
for making bone manipulation in Godot easier.

This work was sponsored by GSoC 2020 and TwistedTwigleg

Full list of changes:
* Adds a SkeletonModification3D resource
  * This resource is the base where all IK code is written and executed
* Adds a SkeletonModificationStack3D resource
  * This node oversees the execution of the modifications and acts as a bridge of sorts for the modifications to the Skeleton3D node
* Adds SkeletonModification3D resources for LookAt, CCDIK, FABRIK, Jiggle, and TwoBoneIK
  * Each modification is in it's own file
* Several changes to Skeletons, listed below:
  * Added local_pose_override, which acts just like global_pose_override but keeps bone-child relationships intract
    * So if you move a bone using local_pose_override, all of the bones that are children will also be moved. This is different than global_pose_override, which only affects the individual bone
  * Internally bones keep track of their children. This removes the need of a processing list, makes it possible to update just a few select bones at a time, and makes it easier to traverse down the bone chain
  * Additional functions added for converting from world transform to global poses, global poses to local poses, and all the same changes but backwards (local to global, global to world). This makes it much easier to work with bone transforms without needing to think too much about how to convert them.
  * New signal added, bone_pose_changed, that can be used to tell if a specific bone changed its transform. Needed for BoneAttachment3D
  * Added functions for getting the forward position of a bone
* BoneAttachment3D node refactored heavily
  * BoneAttachment3D node is now completely standalone in its functionality.
    * This makes the code easier and less interconnected, as well as allowing them to function properly without being direct children of Skeleton3D nodes
  * BoneAttachment3D now can be set either using the index or the bone name.
  * BoneAttachment3D nodes can now set the bone transform instead of just following it. This is disabled by default for compatibility
  * BoneAttachment3D now shows a warning when not configured correctly
* Added rotate_to_align function in Basis
* Added class reference documentation for all changes
2021-08-14 15:57:00 -04:00

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/*************************************************************************/
/* basis.h */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2021 Godot Engine contributors (cf. AUTHORS.md). */
/* */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the */
/* "Software"), to deal in the Software without restriction, including */
/* without limitation the rights to use, copy, modify, merge, publish, */
/* distribute, sublicense, and/or sell copies of the Software, and to */
/* permit persons to whom the Software is furnished to do so, subject to */
/* the following conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
/*************************************************************************/
#ifndef BASIS_H
#define BASIS_H
#include "core/math/quaternion.h"
#include "core/math/vector3.h"
class Basis {
public:
Vector3 elements[3] = {
Vector3(1, 0, 0),
Vector3(0, 1, 0),
Vector3(0, 0, 1)
};
_FORCE_INLINE_ const Vector3 &operator[](int axis) const {
return elements[axis];
}
_FORCE_INLINE_ Vector3 &operator[](int axis) {
return elements[axis];
}
void invert();
void transpose();
Basis inverse() const;
Basis transposed() const;
_FORCE_INLINE_ real_t determinant() const;
void from_z(const Vector3 &p_z);
_FORCE_INLINE_ Vector3 get_axis(int p_axis) const {
// get actual basis axis (elements is transposed for performance)
return Vector3(elements[0][p_axis], elements[1][p_axis], elements[2][p_axis]);
}
_FORCE_INLINE_ void set_axis(int p_axis, const Vector3 &p_value) {
// get actual basis axis (elements is transposed for performance)
elements[0][p_axis] = p_value.x;
elements[1][p_axis] = p_value.y;
elements[2][p_axis] = p_value.z;
}
void rotate(const Vector3 &p_axis, real_t p_phi);
Basis rotated(const Vector3 &p_axis, real_t p_phi) const;
void rotate_local(const Vector3 &p_axis, real_t p_phi);
Basis rotated_local(const Vector3 &p_axis, real_t p_phi) const;
void rotate(const Vector3 &p_euler);
Basis rotated(const Vector3 &p_euler) const;
void rotate(const Quaternion &p_quaternion);
Basis rotated(const Quaternion &p_quaternion) const;
Vector3 get_rotation_euler() const;
void get_rotation_axis_angle(Vector3 &p_axis, real_t &p_angle) const;
void get_rotation_axis_angle_local(Vector3 &p_axis, real_t &p_angle) const;
Quaternion get_rotation_quaternion() const;
Vector3 get_rotation() const { return get_rotation_euler(); };
void rotate_to_align(Vector3 p_start_direction, Vector3 p_end_direction);
Vector3 rotref_posscale_decomposition(Basis &rotref) const;
Vector3 get_euler_xyz() const;
void set_euler_xyz(const Vector3 &p_euler);
Vector3 get_euler_xzy() const;
void set_euler_xzy(const Vector3 &p_euler);
Vector3 get_euler_yzx() const;
void set_euler_yzx(const Vector3 &p_euler);
Vector3 get_euler_yxz() const;
void set_euler_yxz(const Vector3 &p_euler);
Vector3 get_euler_zxy() const;
void set_euler_zxy(const Vector3 &p_euler);
Vector3 get_euler_zyx() const;
void set_euler_zyx(const Vector3 &p_euler);
Quaternion get_quaternion() const;
void set_quaternion(const Quaternion &p_quaternion);
Vector3 get_euler() const { return get_euler_yxz(); }
void set_euler(const Vector3 &p_euler) { set_euler_yxz(p_euler); }
void get_axis_angle(Vector3 &r_axis, real_t &r_angle) const;
void set_axis_angle(const Vector3 &p_axis, real_t p_phi);
void scale(const Vector3 &p_scale);
Basis scaled(const Vector3 &p_scale) const;
void scale_local(const Vector3 &p_scale);
Basis scaled_local(const Vector3 &p_scale) const;
void make_scale_uniform();
float get_uniform_scale() const;
Vector3 get_scale() const;
Vector3 get_scale_abs() const;
Vector3 get_scale_local() const;
void set_axis_angle_scale(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale);
void set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale);
void set_quaternion_scale(const Quaternion &p_quaternion, const Vector3 &p_scale);
// transposed dot products
_FORCE_INLINE_ real_t tdotx(const Vector3 &v) const {
return elements[0][0] * v[0] + elements[1][0] * v[1] + elements[2][0] * v[2];
}
_FORCE_INLINE_ real_t tdoty(const Vector3 &v) const {
return elements[0][1] * v[0] + elements[1][1] * v[1] + elements[2][1] * v[2];
}
_FORCE_INLINE_ real_t tdotz(const Vector3 &v) const {
return elements[0][2] * v[0] + elements[1][2] * v[1] + elements[2][2] * v[2];
}
bool is_equal_approx(const Basis &p_basis) const;
bool operator==(const Basis &p_matrix) const;
bool operator!=(const Basis &p_matrix) const;
_FORCE_INLINE_ Vector3 xform(const Vector3 &p_vector) const;
_FORCE_INLINE_ Vector3 xform_inv(const Vector3 &p_vector) const;
_FORCE_INLINE_ void operator*=(const Basis &p_matrix);
_FORCE_INLINE_ Basis operator*(const Basis &p_matrix) const;
_FORCE_INLINE_ void operator+=(const Basis &p_matrix);
_FORCE_INLINE_ Basis operator+(const Basis &p_matrix) const;
_FORCE_INLINE_ void operator-=(const Basis &p_matrix);
_FORCE_INLINE_ Basis operator-(const Basis &p_matrix) const;
_FORCE_INLINE_ void operator*=(const real_t p_val);
_FORCE_INLINE_ Basis operator*(const real_t p_val) const;
int get_orthogonal_index() const;
void set_orthogonal_index(int p_index);
void set_diagonal(const Vector3 &p_diag);
bool is_orthogonal() const;
bool is_diagonal() const;
bool is_rotation() const;
Basis slerp(const Basis &p_to, const real_t &p_weight) const;
void rotate_sh(real_t *p_values);
operator String() const;
/* create / set */
_FORCE_INLINE_ void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
elements[0][0] = xx;
elements[0][1] = xy;
elements[0][2] = xz;
elements[1][0] = yx;
elements[1][1] = yy;
elements[1][2] = yz;
elements[2][0] = zx;
elements[2][1] = zy;
elements[2][2] = zz;
}
_FORCE_INLINE_ void set(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z) {
set_axis(0, p_x);
set_axis(1, p_y);
set_axis(2, p_z);
}
_FORCE_INLINE_ Vector3 get_column(int i) const {
return Vector3(elements[0][i], elements[1][i], elements[2][i]);
}
_FORCE_INLINE_ Vector3 get_row(int i) const {
return Vector3(elements[i][0], elements[i][1], elements[i][2]);
}
_FORCE_INLINE_ Vector3 get_main_diagonal() const {
return Vector3(elements[0][0], elements[1][1], elements[2][2]);
}
_FORCE_INLINE_ void set_row(int i, const Vector3 &p_row) {
elements[i][0] = p_row.x;
elements[i][1] = p_row.y;
elements[i][2] = p_row.z;
}
_FORCE_INLINE_ void set_zero() {
elements[0].zero();
elements[1].zero();
elements[2].zero();
}
_FORCE_INLINE_ Basis transpose_xform(const Basis &m) const {
return Basis(
elements[0].x * m[0].x + elements[1].x * m[1].x + elements[2].x * m[2].x,
elements[0].x * m[0].y + elements[1].x * m[1].y + elements[2].x * m[2].y,
elements[0].x * m[0].z + elements[1].x * m[1].z + elements[2].x * m[2].z,
elements[0].y * m[0].x + elements[1].y * m[1].x + elements[2].y * m[2].x,
elements[0].y * m[0].y + elements[1].y * m[1].y + elements[2].y * m[2].y,
elements[0].y * m[0].z + elements[1].y * m[1].z + elements[2].y * m[2].z,
elements[0].z * m[0].x + elements[1].z * m[1].x + elements[2].z * m[2].x,
elements[0].z * m[0].y + elements[1].z * m[1].y + elements[2].z * m[2].y,
elements[0].z * m[0].z + elements[1].z * m[1].z + elements[2].z * m[2].z);
}
Basis(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
}
void orthonormalize();
Basis orthonormalized() const;
#ifdef MATH_CHECKS
bool is_symmetric() const;
#endif
Basis diagonalize();
operator Quaternion() const { return get_quaternion(); }
static Basis looking_at(const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0));
Basis(const Quaternion &p_quaternion) { set_quaternion(p_quaternion); };
Basis(const Quaternion &p_quaternion, const Vector3 &p_scale) { set_quaternion_scale(p_quaternion, p_scale); }
Basis(const Vector3 &p_euler) { set_euler(p_euler); }
Basis(const Vector3 &p_euler, const Vector3 &p_scale) { set_euler_scale(p_euler, p_scale); }
Basis(const Vector3 &p_axis, real_t p_phi) { set_axis_angle(p_axis, p_phi); }
Basis(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale) { set_axis_angle_scale(p_axis, p_phi, p_scale); }
_FORCE_INLINE_ Basis(const Vector3 &row0, const Vector3 &row1, const Vector3 &row2) {
elements[0] = row0;
elements[1] = row1;
elements[2] = row2;
}
_FORCE_INLINE_ Basis() {}
};
_FORCE_INLINE_ void Basis::operator*=(const Basis &p_matrix) {
set(
p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]));
}
_FORCE_INLINE_ Basis Basis::operator*(const Basis &p_matrix) const {
return Basis(
p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]));
}
_FORCE_INLINE_ void Basis::operator+=(const Basis &p_matrix) {
elements[0] += p_matrix.elements[0];
elements[1] += p_matrix.elements[1];
elements[2] += p_matrix.elements[2];
}
_FORCE_INLINE_ Basis Basis::operator+(const Basis &p_matrix) const {
Basis ret(*this);
ret += p_matrix;
return ret;
}
_FORCE_INLINE_ void Basis::operator-=(const Basis &p_matrix) {
elements[0] -= p_matrix.elements[0];
elements[1] -= p_matrix.elements[1];
elements[2] -= p_matrix.elements[2];
}
_FORCE_INLINE_ Basis Basis::operator-(const Basis &p_matrix) const {
Basis ret(*this);
ret -= p_matrix;
return ret;
}
_FORCE_INLINE_ void Basis::operator*=(const real_t p_val) {
elements[0] *= p_val;
elements[1] *= p_val;
elements[2] *= p_val;
}
_FORCE_INLINE_ Basis Basis::operator*(const real_t p_val) const {
Basis ret(*this);
ret *= p_val;
return ret;
}
Vector3 Basis::xform(const Vector3 &p_vector) const {
return Vector3(
elements[0].dot(p_vector),
elements[1].dot(p_vector),
elements[2].dot(p_vector));
}
Vector3 Basis::xform_inv(const Vector3 &p_vector) const {
return Vector3(
(elements[0][0] * p_vector.x) + (elements[1][0] * p_vector.y) + (elements[2][0] * p_vector.z),
(elements[0][1] * p_vector.x) + (elements[1][1] * p_vector.y) + (elements[2][1] * p_vector.z),
(elements[0][2] * p_vector.x) + (elements[1][2] * p_vector.y) + (elements[2][2] * p_vector.z));
}
real_t Basis::determinant() const {
return elements[0][0] * (elements[1][1] * elements[2][2] - elements[2][1] * elements[1][2]) -
elements[1][0] * (elements[0][1] * elements[2][2] - elements[2][1] * elements[0][2]) +
elements[2][0] * (elements[0][1] * elements[1][2] - elements[1][1] * elements[0][2]);
}
#endif // BASIS_H
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