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前天,杨老师出了一问题,将一3D立方体投影到2D平面上, 知道2D平面上所有点的坐标,能否恢复出3D立方体点的坐标

我的答案是:需要给定3D立方体中某一连长的长度才行

推导过程如下:

c++源码如下:

#include "AntTweakBar.h"#include 
   
    #include 
    
     #include 
     
      #include 
      
       #include 
       
        #include 
        
         #if defined(_WIN32) || defined(_WIN64)// MiniGLUT.h is provided to avoid the need of having GLUT installed to // recompile this example. Do not use it in your own programs, better// install and use the actual GLUT library SDK.//# define USE_MINI_GLUT#endif#if defined(USE_MINI_GLUT)# include "MiniGLUT.h"#elif defined(_MACOSX)# include 
         
          #else# include 
          
           #endif#include "GLM.h"#include "glm\glm.hpp"#include "glm\gtc\matrix_transform.hpp"#include "glm\gtc\type_ptr.hpp"// This example displays one of the following shapes// Shapes scalefloat g_Zoom = 1.0f;// Shape orientation (stored as a quaternion)float g_Rotation[] = { 0.0f, 0.0f, 0.0f, 1.0f };// Auto rotateint g_AutoRotate = 0;int g_RotateTime = 0;float g_RotateStart[] = { 0.0f, 0.0f, 0.0f, 1.0f };// Shapes materialfloat g_MatAmbient[] = { 0.5f, 0.0f, 0.0f, 1.0f };float g_MatDiffuse[] = { 1.0f, 1.0f, 0.0f, 1.0f };// Light parameterfloat g_LightMultiplier = 1.0f;float g_LightDirection[] = { -0.57735f, -0.57735f, -0.57735f };// Axis parameterfloat g_AxisDirection[] = {0.0f, 1.0f, 0.0f};float g_cameraAngleX = 0.0f, g_cameraAngleY = 0.0f;float g_mouseX = 0.0f, g_mouseY = 0.0f;bool g_mouseLeftDown = false;float g_screenWidth=1024;float g_screenHeight=768;glm::mat4 g_projection=glm::mat4(1);glm::mat4 g_modelview=glm::mat4(1);glm::mat4 g_world=glm::mat4(1);glm::mat4 g_view=glm::mat4(1);glm::mat4 g_mvp=glm::mat4(1);glm::mat4 Rx = glm::mat4(1);//float g_lastAngle = 0.0f;float g_accuAngle = 0.0f;float g_currentlyRotatedAngle = 0.0f;Eigen::Matrix
           
             g_3DCuboidPositionOriginal;Eigen::Matrix
            
              g_3DCuboidPositionCurrent;// Routine to set a quaternion from a rotation axis and angle// ( input axis = float[3] angle = float output: quat = float[4] )void SetQuaternionFromAxisAngle(const float *axis, float angle, float *quat){ float sina2, norm; sina2 = (float)sin(0.5f * angle); norm = (float)sqrt(axis[0]*axis[0] + axis[1]*axis[1] + axis[2]*axis[2]); quat[0] = sina2 * axis[0] / norm; quat[1] = sina2 * axis[1] / norm; quat[2] = sina2 * axis[2] / norm; quat[3] = (float)cos(0.5f * angle);}// Routine to convert a quaternion to a 4x4 matrix// ( input: quat = float[4] output: mat = float[4*4] )void ConvertQuaternionToMatrix(const float *quat, float *mat){ float yy2 = 2.0f * quat[1] * quat[1]; float xy2 = 2.0f * quat[0] * quat[1]; float xz2 = 2.0f * quat[0] * quat[2]; float yz2 = 2.0f * quat[1] * quat[2]; float zz2 = 2.0f * quat[2] * quat[2]; float wz2 = 2.0f * quat[3] * quat[2]; float wy2 = 2.0f * quat[3] * quat[1]; float wx2 = 2.0f * quat[3] * quat[0]; float xx2 = 2.0f * quat[0] * quat[0]; mat[0*4+0] = - yy2 - zz2 + 1.0f; mat[0*4+1] = xy2 + wz2; mat[0*4+2] = xz2 - wy2; mat[0*4+3] = 0; mat[1*4+0] = xy2 - wz2; mat[1*4+1] = - xx2 - zz2 + 1.0f; mat[1*4+2] = yz2 + wx2; mat[1*4+3] = 0; mat[2*4+0] = xz2 + wy2; mat[2*4+1] = yz2 - wx2; mat[2*4+2] = - xx2 - yy2 + 1.0f; mat[2*4+3] = 0; mat[3*4+0] = mat[3*4+1] = mat[3*4+2] = 0; mat[3*4+3] = 1;}// Routine to multiply 2 quaternions (ie, compose rotations)// ( input q1 = float[4] q2 = float[4] output: qout = float[4] )void MultiplyQuaternions(const float *q1, const float *q2, float *qout){ float qr[4]; qr[0] = q1[3]*q2[0] + q1[0]*q2[3] + q1[1]*q2[2] - q1[2]*q2[1]; qr[1] = q1[3]*q2[1] + q1[1]*q2[3] + q1[2]*q2[0] - q1[0]*q2[2]; qr[2] = q1[3]*q2[2] + q1[2]*q2[3] + q1[0]*q2[1] - q1[1]*q2[0]; qr[3] = q1[3]*q2[3] - (q1[0]*q2[0] + q1[1]*q2[1] + q1[2]*q2[2]); qout[0] = qr[0]; qout[1] = qr[1]; qout[2] = qr[2]; qout[3] = qr[3];}// Return elapsed time in millisecondsint GetTimeMs(){#if !defined(_WIN32) return glutGet(GLUT_ELAPSED_TIME);#else // glutGet(GLUT_ELAPSED_TIME) seems buggy on Windows return (int)GetTickCount(); #endif}void Update3DCuboidPosition(float *mat){ Eigen::Map
             
              
               > mapMatrix(mat); //std::cout << mapMatrix << std::endl; g_3DCuboidPositionCurrent = mapMatrix.block<3,3>(0,0) * g_3DCuboidPositionOriginal; //std::cout << g_3DCuboidPositionCurrent << std::endl;}void Draw2DCuboid(){ glBegin(GL_LINES); for(int i = 1; i < g_3DCuboidPositionCurrent.cols(); ++i) { if( i % 4 != 0) { glVertex3f(g_3DCuboidPositionCurrent.col(i - 1)(0), g_3DCuboidPositionCurrent.col(i - 1)(1), -10); glVertex3f(g_3DCuboidPositionCurrent.col(i)(0), g_3DCuboidPositionCurrent.col(i)(1), -10); } else { glVertex3f(g_3DCuboidPositionCurrent.col(i - 4)(0), g_3DCuboidPositionCurrent.col(i - 4)(1), -10); glVertex3f(g_3DCuboidPositionCurrent.col(i - 1)(0), g_3DCuboidPositionCurrent.col(i - 1)(1), -10); } } glEnd();}void Output3DCuboidPosition(){ int order[8] = {0, 1, 2, 3, 4, 7, 6, 5}; for(int i = 0; i < 8; ++i) { std::cout << char( 'A' + order[i]) << "(3D) : " << g_3DCuboidPositionCurrent.col(i).transpose() << std::endl; } }void Output2DCuboidPosition(){ int order[8] = {0, 1, 2, 3, 4, 7, 6, 5}; for(int i = 0; i < 8; ++i) { std::cout << char( 'A' + order[i]) << "(2D) : " << g_3DCuboidPositionCurrent.col(i).head(2).transpose() << std::endl; } }void Draw3DCuboid(){ glBegin(GL_QUADS); for(int i = 0; i < g_3DCuboidPositionCurrent.cols(); ++i) { if( i % 4 == 0) { Eigen::Vector3f vec1 = g_3DCuboidPositionCurrent.col(i) - g_3DCuboidPositionCurrent.col(i + 1); Eigen::Vector3f vec2 = g_3DCuboidPositionCurrent.col(i + 2) - g_3DCuboidPositionCurrent.col(i + 1); Eigen::Vector3f nor = vec2.cross(vec1); glNormal3f(nor(0), nor(1), nor(2)); } glVertex3f(g_3DCuboidPositionCurrent.col(i)(0), g_3DCuboidPositionCurrent.col(i)(1), g_3DCuboidPositionCurrent.col(i)(2)); } glEnd();}void DrawLines(){ glDisable(GL_LIGHTING); glBegin(GL_LINES); glColor3f(1.0f, 0.0f, 0.0f); for(int i = 0; i < g_3DCuboidPositionCurrent.cols(); ++i) { glVertex3f(g_3DCuboidPositionCurrent.col(i)(0), g_3DCuboidPositionCurrent.col(i)(1), g_3DCuboidPositionCurrent.col(i)(2)); glVertex3f(g_3DCuboidPositionCurrent.col(i)(0), g_3DCuboidPositionCurrent.col(i)(1), -10); } glColor3f(1.0f, 1.0f, 1.0f); glEnd(); glEnable(GL_LIGHTING);}void SetMatrix();// Callback function called by GLUT to render screenvoid Display(void){ float v[4]; // will be used to set light parameters float mat[4*4]; // rotation matrix // Clear frame buffer glClearColor(0, 0, 0, 1); glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); glEnable(GL_DEPTH_TEST); glDisable(GL_CULL_FACE); glEnable(GL_NORMALIZE); // Set light glEnable(GL_LIGHTING); glEnable(GL_LIGHT0); v[0] = v[1] = v[2] = g_LightMultiplier*0.4f; v[3] = 1.0f; glLightfv(GL_LIGHT0, GL_AMBIENT, v); v[0] = v[1] = v[2] = g_LightMultiplier*0.8f; v[3] = 1.0f; glLightfv(GL_LIGHT0, GL_DIFFUSE, v); v[0] = -g_LightDirection[0]; v[1] = -g_LightDirection[1]; v[2] = -g_LightDirection[2]; v[3] = 0.0f; glLightfv(GL_LIGHT0, GL_POSITION, v); // Set material glMaterialfv(GL_FRONT_AND_BACK, GL_AMBIENT, g_MatAmbient); glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, g_MatDiffuse); // Set matrix SetMatrix(); // Rotate and draw shape glPushMatrix(); //glTranslatef(0.5f, -0.3f, 0.0f); if( g_AutoRotate ) {// float axis[3] = { 0, 1, 0 }; g_currentlyRotatedAngle = (float)(GetTimeMs()-g_RotateTime)/1000.0f;// float quat[4];// SetQuaternionFromAxisAngle(axis, angle, quat);// MultiplyQuaternions(g_RotateStart, quat, g_Rotation); Rx = glm::rotate(glm::mat4(1.0f), g_accuAngle + g_currentlyRotatedAngle, glm::make_vec3(g_AxisDirection)); } else { Rx = glm::rotate(glm::mat4(1.0f), g_accuAngle, glm::make_vec3(g_AxisDirection)); } Update3DCuboidPosition((float*)glm::value_ptr(Rx)); //glMultMatrixf(mat); //glScalef(g_Zoom, g_Zoom, g_Zoom); Draw3DCuboid(); if( g_AutoRotate ) Output3DCuboidPosition(); DrawLines(); Draw2DCuboid(); if( g_AutoRotate ) Output2DCuboidPosition(); //glCallList(1); glPopMatrix(); glDisable(GL_LIGHTING); glCallList(2); glEnable(GL_LIGHTING); // Draw tweak bars TwDraw(); // Present frame buffer glutSwapBuffers(); // Recall Display at next frame glutPostRedisplay();}void TransToArray(GLdouble* trans,glm::mat4 mat) //GLM->GL{ for(int i=0;i<4;i++) for(int j=0;j<4;j++) { int index=i*4+j; float temp=mat[i][j]; trans[index]=mat[i][j]; }}void SetMatrix(){ g_projection = glm::perspective(45.0f, (float)g_screenWidth / g_screenHeight, 0.1f, 50.0f); //m_view=glm::lookAt(g_camerapos,g_camerapos+glm::vec3(0,0,-1),glm::vec3(0,1,0)); glm::mat4 T = glm::translate(glm::mat4(1.0f),glm::vec3(0, 0, g_Zoom - 10)); glm::mat4 Rx = glm::rotate(T, g_cameraAngleX, glm::vec3(1.0f, 0.0f, 0.0f)); g_world = glm::rotate(Rx, g_cameraAngleY, glm::vec3(0.0f, 1.0f, 0.0f)); g_world = glm::translate(glm::mat4(1.0f),glm::vec3(0, 0, cameraDistance-5)); g_modelview=g_world; g_mvp = g_projection*g_world; glMatrixMode(GL_PROJECTION); glLoadIdentity(); GLdouble tempmat[16]; TransToArray(tempmat,g_mvp); glMultMatrixd(tempmat); glMatrixMode(GL_MODELVIEW); glLoadIdentity();}// Callback function called by GLUT when window size changesvoid Reshape(int width, int height){ if ( width != 0 && height != 0) { g_screenWidth = width; g_screenHeight = height; } SetMatrix(); // Set OpenGL viewport and camera// glViewport(0, 0, width, height);// glMatrixMode(GL_PROJECTION);// glLoadIdentity();// gluPerspective(40, (double)width/height, 1, 100);// glMatrixMode(GL_MODELVIEW);// glLoadIdentity();// gluLookAt(0,20,20, 0,0,0, 0,0,-1);// glTranslatef(0, 0.6f, -1); // Send the new window size to AntTweakBar TwWindowSize(width, height);}// Function called at exitvoid Terminate(void){ glDeleteLists(1, 2); TwTerminate();}// Callback function called when the 'AutoRotate' variable value of the tweak bar has changedvoid TW_CALL SetAutoRotateCB(const void *value, void *clientData){ (void)clientData; // unused g_AutoRotate = *(const int *)value; // copy value to g_AutoRotate if( g_AutoRotate!=0 ) { // init rotation g_RotateTime = GetTimeMs(); // make Rotation variable read-only //TwDefine(" TweakBar/ObjRotation readonly "); } else { g_accuAngle += g_currentlyRotatedAngle; // make Rotation variable read-write //TwDefine(" TweakBar/ObjRotation readwrite "); }}// Callback function called by the tweak bar to get the 'AutoRotate' valuevoid TW_CALL GetAutoRotateCB(void *value, void *clientData){ (void)clientData; // unused *(int *)value = g_AutoRotate; // copy g_AutoRotate to value}void InitCuboidPosition(){ g_3DCuboidPositionOriginal << -1.0f, -1.0f, 1.0f, 1.0f, -1.0f, 1.0f, 1.0f, -1.0f, -1.0f, -1.0f, -1.0f, -1.0f, 1.0f, 1.0f, 1.0f, 1.0f, -1.0f, 1.0f, 1.0f, -1.0f, -1.0f, -1.0f, 1.0f, 1.0f, 2.0f, -2.0f, -2.0f, 2.0f, 2.0f, 2.0f, -2.0f, -2.0f, 2.0f, 2.0f, -2.0f, -2.0f, -2.0f, -2.0f, 2.0f, 2.0f, 2.0f, 2.0f, 2.0f, 2.0f , -2.0f, -2.0f, -2.0f, -2.0f, 3.0f, 3.0f, 3.0f, 3.0f, -3.0f, -3.0f, -3.0f, -3.0f, 3.0f, -3.0f, -3.0f, 3.0f, 3.0f, -3.0f, -3.0f, 3.0f, 3.0f, 3.0f, -3.0f, -3.0f, 3.0f, -3.0f, -3.0f, 3.0f; //std::cout << g_3DCuboidPosition << std::endl;}void MouseMotionCB(int x, int y){ if (!TwEventMouseMotionGLUT(x, y)) { g_cameraAngleY += (x - g_mouseX)/100; g_cameraAngleX += (y - g_mouseY)/100; g_mouseX = x; g_mouseY = y; }}void MouseCB(int button, int state, int x, int y){ g_mouseX = x; g_mouseY = y; if (!TwEventMouseButtonGLUT(button, state, x, y)) { switch(state) { case GLUT_DOWN: if (glutGetModifiers() == GLUT_LEFT_BUTTON) { g_mouseLeftDown = true; } break; case GLUT_UP: if (glutGetModifiers() == GLUT_LEFT_BUTTON) { g_mouseLeftDown = false; } break; } }}// Mainint main(int argc, char *argv[]){ TwBar *bar; // Pointer to the tweak bar float axis[] = { 0.0f, 1.0f, 0.0f }; // initial model rotation float angle = 0.0f; // Initialize cuboid points position InitCuboidPosition(); // Initialize GLUT glutInit(&argc, argv); glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH); glutInitWindowSize(g_screenWidth, g_screenHeight); glutCreateWindow("AntTweakBar simple example using GLUT"); glutCreateMenu(NULL); // Set GLUT callbacks glutDisplayFunc(Display); glutReshapeFunc(Reshape); atexit(Terminate); // Called after glutMainLoop ends // Initialize AntTweakBar TwInit(TW_OPENGL, NULL); // Set GLUT event callbacks // - Directly redirect GLUT mouse button events to AntTweakBar //glutMouseFunc((GLUTmousebuttonfun)TwEventMouseButtonGLUT); // - Directly redirect GLUT mouse motion events to AntTweakBar //glutMotionFunc((GLUTmousemotionfun)TwEventMouseMotionGLUT); glutMouseFunc(MouseCB); glutMotionFunc(MouseMotionCB); // - Directly redirect GLUT mouse "passive" motion events to AntTweakBar (same as MouseMotion) glutPassiveMotionFunc((GLUTmousemotionfun)TwEventMouseMotionGLUT); // - Directly redirect GLUT key events to AntTweakBar glutKeyboardFunc((GLUTkeyboardfun)TwEventKeyboardGLUT); // - Directly redirect GLUT special key events to AntTweakBar glutSpecialFunc((GLUTspecialfun)TwEventSpecialGLUT); // - Send 'glutGetModifers' function pointer to AntTweakBar; // required because the GLUT key event functions do not report key modifiers states. TwGLUTModifiersFunc(glutGetModifiers); // Create some 3D objects (stored in display lists) glNewList(1, GL_COMPILE); glBegin(GL_QUADS); glNormal3d(0, 0, 1);//front glVertex3f(-1.0f, 2.0f, 3.0f);//A glVertex3f(-1.0f, -2.0f, 3.0f);//B glVertex3f(1.0f, -2.0f, 3.0f);//C glVertex3f(1.0f, 2.0f, 3.0f);//D glNormal3d(0, 0, -1);//back glVertex3f(-1.0f, 2.0f, -3.0f);//E glVertex3f(1.0f, 2.0f, -3.0f);//H glVertex3f(1.0f, -2.0f, -3.0f);//G glVertex3f(-1.0f, -2.0f, -3.0f);//F glNormal3d(-1, 0, 0);//left glVertex3f(-1.0f, 2.0f, 3.0f);//A glVertex3f(-1.0f, 2.0f, -3.0f);//E glVertex3f(-1.0f, -2.0f, -3.0f);//F glVertex3f(-1.0f, -2.0f, 3.0f);//B glNormal3d(1, 0, 0);//right glVertex3f(1.0f, -2.0f, 3.0f);//C glVertex3f(1.0f, -2.0f, -3.0f);//G glVertex3f(1.0f, 2.0f, -3.0f);//H glVertex3f(1.0f, 2.0f, 3.0f);//D glNormal3d(0, 1, 0);//up glVertex3f(-1.0f, 2.0f, 3.0f);//A glVertex3f(1.0f, 2.0f, 3.0f);//D glVertex3f(1.0f, 2.0f, -3.0f);//H glVertex3f(-1.0f, 2.0f, -3.0f);//E glNormal3d(0, -1, 0);//down glVertex3f(-1.0f, -2.0f, 3.0f);//B glVertex3f(-1.0f, -2.0f, -3.0f);//F glVertex3f(1.0f, -2.0f, -3.0f);//G glVertex3f(1.0f, -2.0f, 3.0f);//C glEnd(); glEndList(); glNewList(2, GL_COMPILE); glBegin(GL_QUADS); glNormal3d(0, 0, 1);//front glVertex3f(-5.0f, 5.0f, -10.0f);//A glVertex3f(-5.0f, -5.0f, -10.0f);//B glVertex3f(5.0f, -5.0f, -10.0f);//C glVertex3f(5.0f, 5.0f, -10.0f);//D glEnd(); glEndList(); // Create a tweak bar bar = TwNewBar("TweakBar"); TwDefine(" GLOBAL help='This example shows how to integrate AntTweakBar with GLUT and OpenGL.' "); // Message added to the help bar. TwDefine(" TweakBar size='200 400' color='96 216 224' "); // change default tweak bar size and color // Add 'g_Zoom' to 'bar': this is a modifable (RW) variable of type TW_TYPE_FLOAT. Its key shortcuts are [z] and [Z]. TwAddVarRW(bar, "Zoom", TW_TYPE_FLOAT, &g_Zoom, " min=-30 max=30 step=0.01 keyIncr=z keyDecr=Z help='Scale the object (1=original size).' ");// // Add 'g_Rotation' to 'bar': this is a variable of type TW_TYPE_QUAT4F which defines the object's orientation// TwAddVarRW(bar, "ObjRotation", TW_TYPE_QUAT4F, &g_Rotation, // " label='Object rotation' opened=true help='Change the object orientation.' "); TwAddVarRW(bar, "AxisDir", TW_TYPE_DIR3F, &g_AxisDirection, " label='Axis direction' opened=true help='Change the Axis direction.' "); // Add callback to toggle auto-rotate mode (callback functions are defined above). TwAddVarCB(bar, "AutoRotate", TW_TYPE_BOOL32, SetAutoRotateCB, GetAutoRotateCB, NULL, " label='Auto-rotate' key=space help='Toggle auto-rotate mode.' "); // Add 'g_LightMultiplier' to 'bar': this is a variable of type TW_TYPE_FLOAT. Its key shortcuts are [+] and [-]. TwAddVarRW(bar, "Multiplier", TW_TYPE_FLOAT, &g_LightMultiplier, " label='Light booster' min=0.1 max=4 step=0.02 keyIncr='+' keyDecr='-' help='Increase/decrease the light power.' "); // Add 'g_LightDirection' to 'bar': this is a variable of type TW_TYPE_DIR3F which defines the light direction TwAddVarRW(bar, "LightDir", TW_TYPE_DIR3F, &g_LightDirection, " label='Light direction' opened=true help='Change the light direction.' "); // Add 'g_MatAmbient' to 'bar': this is a variable of type TW_TYPE_COLOR3F (3 floats color, alpha is ignored) // and is inserted into a group named 'Material'. TwAddVarRW(bar, "Ambient", TW_TYPE_COLOR3F, &g_MatAmbient, " group='Material' "); // Add 'g_MatDiffuse' to 'bar': this is a variable of type TW_TYPE_COLOR3F (3 floats color, alpha is ignored) // and is inserted into group 'Material'. TwAddVarRW(bar, "Diffuse", TW_TYPE_COLOR3F, &g_MatDiffuse, " group='Material' "); // Store time8ioi88uiiii g_RotateTime = GetTimeMs(); // Init rotation SetQuaternionFromAxisAngle(axis, angle, g_Rotation); SetQuaternionFromAxisAngle(axis, angle, g_RotateStart); // Call the GLUT main loop glutMainLoop(); return 0;}
              
             
            
           
          
         
        
       
      
     
    
   

function F = Cuboid_2DTo3D(x)Data = load('2D_data_CFAB.txt');C_Prime = Data(1,:);F_Prime = Data(2,:);A_Prime = Data(3,:);B_Prime = Data(4,:);X_Prime = C_Prime - B_Prime;Y_Prime = A_Prime - B_Prime;Z_Prime = F_Prime - B_Prime;% 1 sigma_1% 2 sigma_2% 3 sigma_3% 4 axix_x% 5 axix_y% 6 axix_z% 7 cos_theta% 8 sin_thetaF(1) = x(1) * ( x(7) + ( 1 - x(7)) * x(4)^2) - X_Prime(1,1);F(2) = x(2) * ( (1 - x(7)) * x(4) * x(5) - x(8) * x(6)) - Y_Prime(1,1);F(3) = x(3) * ( (1 - x(7)) * x(4) * x(5) + x(8) * x(5)) - Z_Prime(1,1);F(4) = x(1) * ( ( 1 - x(7)) * x(4) * x(5) + x(8) * x(6)) - X_Prime(1,2);F(5) = x(2) * (  x(7) + (1 - x(7)) * x(5)^2) - Y_Prime(1,2);F(6) = x(3) * ( (1 - x(7)) * x(5) * x(6) - x(8) * x(4)) - Z_Prime(1,2);F(7) = x(7)^2 + x(8)^2 - 1;F(8) = x(1) - 2;F(9) = x(4)^2 + x(5)^2 + x(6)^2 - 1;% usage: % fun = @Cuboid_2DTo3D;% x0 =[0,0,0,0,0,0,0,0];% x = fsolve(fun, x0);

2.80175 -2.29852-1.80183 -0.8670820.129996 -0.0672071.12992 -3.23281