+#include "ik.hpp"
+#include "util.hpp"
+
+using namespace glm;
+
+constexpr float tolerance = 0.3;
+
+const std::vector<glm::vec3> fabrik(const glm::vec3 t,
+ const std::vector<glm::vec3> jpsIn, // joint positions
+ const std::vector<float> jds // distances between each joint
+ ) {
+ size_t N = jpsIn.size();
+ assert(N == jds.size() + 1);
+ std::vector<glm::vec3> jps = jpsIn;
+
+ float dist = distance(jps[0], t);
+ float totalLength = 0;
+ for (int i = 0; i < N - 1; i++) totalLength += jds[i];
+ if (dist > totalLength) { // target is unreachable
+ for (int i = 0; i < N - 1; i++) {
+ float r = distance(t, jps[i]);
+ float lambda = jds[i] / r;
+ jps[i + 1] = (1.f - lambda) * jps[i] + lambda * t;
+ }
+ } else { // target is reachable
+ glm::vec3 b = jps[0];
+ // distance between end effector and target
+ float diff = distance(jps[N - 1], t);
+ while (diff > tolerance) {
+ // forward reaching
+ jps[N - 1] = t; // set end effector to target
+ for (int i = N - 2; i >= 0; i--) {
+ float r = distance(jps[i + 1], jps[i]);
+ float lambda = jds[i] / r;
+ jps[i] = (1.f - lambda) * jps[i + 1] + lambda * jps[i];
+ }
+
+ // backward reaching
+ jps[0] = b; // reset root to initial pos
+ for (int i = 0; i < N - 1; i++) {
+ float r = distance(jps[i + 1], jps[i]);
+ float lambda = jds[i] / r;
+ jps[i + 1] = (1 - lambda) * jps[i] + lambda * jps[i + 1];
+ }
+
+ float newDiff = distance(jps[N - 1], t);
+ if (newDiff == diff) abort();
+ diff = newDiff;
+ }
+ }
+ return jps;
+}
+
+std::vector<Model::Node> allNodesTo(const Model::Node &from, const Model::Node &to) {
+ if (from == to) return { to };
+ assert(to.parent != nullptr);
+ auto res = allNodesTo(from, *to.parent);
+ res.push_back(to);
+ return res;
+}
+
+mat4 getAbsTrans(const Model::Node &root, const Model::Node &n) {
+ if (root.ai.mName == n.ai.mName)
+ return mat4(1); //aiMatrixToMat4(n.ai.mTransformation);
+ assert(n.parent != nullptr);
+ return getAbsTrans(root, *n.parent) * aiMatrixToMat4(n.ai.mTransformation);
+}
+
+vec3 extractPos(mat4 trans) {
+ return vec3(trans[3]);
+}
+
+glm::mat4 absoluteToModelSpace(const Model::Node &root, const Model::Node &n, mat4 m) {
+ const Model::Node *parent = &n;
+ glm::mat4 res = m;
+ std::vector<mat4> trans;
+ while (&parent->ai != &root.ai) {
+ trans.push_back(inverse(aiMatrixToMat4(parent->ai.mTransformation)));
+ parent = parent->parent;
+ }
+ while (!trans.empty()) { res = trans.back() * res; trans.pop_back(); }
+ return res;
+}
+
+// Given points u and v on a sphere, calculate the transformation matrix
+// to bring u -> v
+// from https://math.stackexchange.com/a/2765250
+mat4 getRotationToPoint(vec3 u, vec3 v, float dist) {
+ if (distance(u, v) < 0.00001) return mat4(1);
+ vec3 n = cross(u, v) / length(cross(u, v));
+ vec3 t = cross(n, u);
+ float alpha = atan2(dot(v, t), dot(v, u));
+ mat4 T = mat4(mat3(u, t, n));
+ mat4 R = rotate(mat4(1), alpha, {0, 0, 1}); // rotation in z axis
+ mat4 res = T * R * inverse(T);
+ return res;
+}
+
+
+void inverseKinematic(Model::Node &root, Model::Node &end, vec3 target) {
+ /* float s2o2 = sqrt(2.f) / 2.f; */
+ /* assert(getRotationToPoint({1, 0, 0}, {0, s2o2, s2o2}, 1) */
+ /* == mat4({0, s2o2, s2o2, 0}, { -s2o2, 1.f/2.f, -1.f/2.f, 0}, */
+ /* {-s2o2, -1.f/2.f, 1.f/2.f, 0}, { 0, 0, 0, 1})); */
+
+ std::vector<Model::Node> chain = allNodesTo(root, end);
+ assert(!chain.empty());
+
+ std::vector<vec3> positions(chain.size()); std::vector<float> distances(chain.size() - 1);
+ for (size_t i = 0; i < chain.size(); i++) {
+ mat4 absTrans = getAbsTrans(root, chain[i]);
+ positions[i] = extractPos(absTrans);
+ if (i > 0)
+ distances[i - 1] = distance(positions[i], positions[i - 1]);
+ }
+
+ /* glm::vec3 targetPos(sin(d * 10.f), cos(d * 10.f), 0); */
+ auto newPositions = fabrik(target, positions, distances);
+
+ // Rotate all the nodes so that they are in the correct positions
+ for (size_t i = 1; i < chain.size(); i++) {
+ auto node = chain[i];
+ mat4 absTrans = getAbsTrans(root, node);
+ absTrans[3] = vec4(newPositions[i], absTrans[3][3]); // update position in transform
+
+ vec3 oldRelPos = extractPos(aiMatrixToMat4(node.ai.mTransformation));
+ vec3 newRelPos = extractPos(absoluteToModelSpace(root, *node.parent, absTrans));
+
+ mat4 rot = getRotationToPoint(oldRelPos, newRelPos, distances[i - 1]);
+ node.ai.mTransformation = mat4ToaiMatrix(rot * aiMatrixToMat4(node.ai.mTransformation));
+
+ /* std::cerr << node.ai.mName.C_Str() << ":\n"; */
+ /* printVec3(extractPos(aiMatrixToMat4(node.ai.mTransformation))); */
+ /* printVec3(newRelPos); */
+ assert(distance(extractPos(aiMatrixToMat4(node.ai.mTransformation)), newRelPos) < 0.0001);
+
+ /* absTrans[3] = vec4(newPositions[i], absTrans[3][3]); // update position in transform */
+
+ /* mat4 relTrans = absoluteToModelSpace(root, *node.parent, absTrans); */
+ /* node.ai.mTransformation = mat4ToaiMatrix(relTrans); */
+ }
+
+ // TODO: Now rotate all the nodes so that they face each other
+
+ /* for (int i = 0; i < 3; i++) { */
+ /* glm::mat4 absTrans(1); */
+ /* findNodeTrans(&sceneModel->getRoot()->ai, aiString(jointNames[i]), */
+ /* &absTrans); */
+ /* glm::mat4 newAbsTrans = absTrans; */
+ /* newAbsTrans[3] = glm::vec4(newPositions[i], newAbsTrans[3][3]); */
+
+ /* auto node = sceneModel->getRoot()->ai.FindNode(jointNames[i].c_str()); */
+
+ /* auto newTrans = worldSpaceToModelSpace(node->mParent, newAbsTrans); */
+
+ /* node->mTransformation = mat4ToaiMatrix(newTrans); */
+ /* } */
+}
+
projects / opengl.git / blobdiff