File size: 6,884 Bytes
7b853a5 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 | /*
* SPDX-FileCopyrightText: Copyright (c) 2026 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
* SPDX-License-Identifier: Apache-2.0
*/
#include "InverseKinematics.h"
#include "Math/Scalar.h"
#include <iostream>
using namespace IK;
namespace
{
float getAngleWithTwoSideVectors(const Math::Vector& vecLeft, const Math::Vector& vecRight)
{
auto lNorm = vecLeft.GetNormalized3();
auto rNorm = vecRight.GetNormalized3();
float cosine = lNorm.GetDot3(rNorm);
float sine = lNorm.Cross3(rNorm).GetLength3();
return atan2f(sine, cosine); // in radian
}
float getAngleWithCosineRule (const float lSideLeft, const float lSideRight, const float lSideAcross)
{
float val =
(lSideRight * lSideRight + lSideLeft * lSideLeft - lSideAcross * lSideAcross) /
(2.0f * lSideLeft * lSideRight);
val = Math::Clamp(val, -1.0f, 1.0f); // numerical stability. also avoid impossible trangulars
return acosf(val); // in radian
}
}
void IK::TwoBoneIk(
Pose& pose,
const Math::Transform& rootTransform,
uint32_t cIdx,
float weight,
const Math::Vector& target,
const std::vector<int>& joint_parents_vec,
const Math::Vector& hintOffset
)
{
weight = Math::Clamp(weight, 0.0f, 1.0f);
if (!(weight > 0.0f))
return;
// Two bone IK: joints are represented as "a", "b", "c" in the below comments:
// 1. stage 1, bend joint a and joint b, so that |ac| = |at|, while vec_ac maintain the same direction
// 2. stage 2, rotate start joint a so that c and t are in the same place
// a a a |
// |\ |\ |\ |
// | \ | \ | \ |
// | \ (stage 1 ->) | \ (stage 2 ->) | \ |
// | b | b | b |
// | \ | | | / |
// | \ | | | / |
// t c t c t(c) |
// (a is the root joint, b is the middle joint and c is the end joint)
//
int32_t bIdx = joint_parents_vec[cIdx];
if (bIdx < 0)
{
return;
}
int32_t aIdx = joint_parents_vec[bIdx];
if (aIdx < 0)
{
return;
}
// Find the parent world transform of joint a:
Math::Transform aParentWorldTransform = Math::Transform::Identity;
int32_t idx = joint_parents_vec[aIdx];
while (idx >= 0)
{
aParentWorldTransform = aParentWorldTransform * pose[idx];
idx = joint_parents_vec[idx];
}
aParentWorldTransform = aParentWorldTransform * rootTransform;
// Compute world space transforms of a, b and c:
Math::Transform aWorld = pose[aIdx] * aParentWorldTransform;
Math::Transform bWorld = pose[bIdx] * aWorld;
Math::Transform cWorld = pose[cIdx] * bWorld;
auto a = aWorld.GetTranslation();
auto b = bWorld.GetTranslation();
auto c = cWorld.GetTranslation();
auto t = Math::Vector::Lerp(c, target, weight);
// step 1 (stage 1): extend / contract the joint chain to match the distance
float eps = 0.0001f; // numerical stability
float l_ab = (b - a).Length3().GetX();
float l_bc = (c - b).Length3().GetX();
float l_at = (a - t).Length3().GetX();
l_at = Math::Clamp(l_at, eps, (l_ab + l_bc) * 0.999f); // when not reachable, replace with maximum reachable length
// get the current angles
float theta_bac_current = getAngleWithTwoSideVectors(a - b, a - c);
float theta_abc_current = getAngleWithTwoSideVectors(b - a, b - c);
// get the desired angles
if (l_ab < eps || l_bc < eps || l_at < eps)
{
return; // the length is too small. rejecting potentially numerically unstable requests.
}
float theta_bac_desired = getAngleWithCosineRule(l_ab, l_at, l_bc);
float theta_abc_desired = getAngleWithCosineRule(l_ab, l_bc, l_at);
// in joint[0]'s parent's space
Math::Vector rotationAxis = Math::Vector::Cross3(c - a, bWorld.TransformPoint(hintOffset) - a);
float l = rotationAxis.GetLength3();
if (l == 0)
{
rotationAxis = Math::Vector(0,0,1);
}
else
{
rotationAxis /= l;
}
// get the rotation with axis in the local space of joint a and joint b
Math::Vector rotationAxisLocalInBSpace = bWorld.GetRotation().RotateVectorInverse(rotationAxis);
Math::Transform rotateInB(
Math::Quaternion(rotationAxisLocalInBSpace,
(theta_abc_desired - theta_abc_current)), Math::Vector::Zero);
pose[bIdx] = rotateInB * pose[bIdx];
Math::Vector rotationAxisLocalInASpace = aWorld.GetRotation().RotateVectorInverse(rotationAxis);
Math::Transform rotateInA(
Math::Quaternion(rotationAxisLocalInASpace,
(theta_bac_desired - theta_bac_current)), Math::Vector::Zero);
pose[aIdx] = rotateInA * pose[aIdx];
// recompute a's world space transform as we're going to need it:
aWorld = pose[aIdx] * aParentWorldTransform;
// step 2 (stage 2): rotate joint a so that the target and the end joint c matches
auto acLocal = aWorld.GetRotation().RotateVectorInverse(
c - a);
auto atLocal = aWorld.GetRotation().RotateVectorInverse(
target - a);
Math::Transform rotateStageTwo(
Math::Quaternion::FromRotationBetweenVectors(acLocal, atLocal), Math::Vector::Zero
);
pose[aIdx] = rotateStageTwo * pose[aIdx];
}
void IK::OneBoneIk(
Pose& pose,
const Math::Transform& rootTransform,
uint32_t bIdx,
float weight,
const Math::Vector& target,
const std::vector<int>& joint_parents_vec
)
{
weight = Math::Clamp(weight, 0.0f, 1.0f);
if (!(weight > 0.0f))
return;
int32_t aIdx = joint_parents_vec[bIdx];
if (aIdx < 0)
{
return;
}
// Find the parent world transform of joint a:
Math::Transform aParentWorldTransform = Math::Transform::Identity;
int32_t idx = joint_parents_vec[aIdx];
while (idx >= 0)
{
aParentWorldTransform = aParentWorldTransform * pose[idx];
idx = joint_parents_vec[idx];
}
aParentWorldTransform = aParentWorldTransform * rootTransform;
// Compute world space transforms of a, b and c:
Math::Transform aWorld = pose[aIdx] * aParentWorldTransform;
Math::Transform bWorld = pose[bIdx] * aWorld;
auto abLocal = aWorld.GetRotation().RotateVectorInverse(
bWorld.GetTranslation() - aWorld.GetTranslation());
auto atLocal = aWorld.GetRotation().RotateVectorInverse(
target - aWorld.GetTranslation());
auto deltaRLocal = Math::Quaternion::NLerp(Math::Quaternion::Identity, Math::Quaternion::FromRotationBetweenVectors(abLocal, atLocal), weight);
pose[aIdx].SetRotation(deltaRLocal * pose[aIdx].GetRotation());
}
|