OpenGL中的旋转立方体

Question

我想要一个围绕中心旋转的立方体。这是我可以通过这个转变来做的事情：

model = glm::rotate(identity, glm::radians(-100.0f * time), glm::vec3(0.0, 1.0, 0.0)); //rotate around y-axis
model = glm::translate(model, glm::vec3(8.0, 0.0, 0.0));
model = glm::rotate(model, glm::radians(-100.0f * time), glm::vec3(1.0, 0.0, 0.0)); //self-rotation

现在我想要一个立方体，它围绕第一个立方体旋转，因为它是围绕y轴旋转的。假设第一个立方体是地球，第二个立方体是月球。我试过了，但没成功。

test = glm::rotate(test, glm::radians(-100.0f * time), glm::vec3(0.0, 1.0, 0.0));
test = glm::translate(test, glm::vec3(3.0, 0.0, 0.0));
test = glm::translate(test, glm::vec3(8.0, 0.0, 0.0));
test = glm::rotate(test, glm::radians(-100.0f * time), glm::vec3(0.0, 1.0, 0.0));
test = glm::translate(test, glm::vec3(-8.0, 0.0, 0.0));
test = glm::rotate(test, glm::radians(-100.0f * time), glm::vec3(1.0, 0.0, 0.0)); // self-rotation

知道我做错什么了吗？这是一张旋转的图片：

​

Answer 1

您的评论建议您有以下操作顺序：

mvp = m_projection*m_view*m_model
vertex' = mvp*vertex

m_view是视图的逆矩阵，m_model是实际网格的直接矩阵。

因此，您应该设置m_projection和m_view一次，然后只更新m_model。

我不使用GLM (有我自己的数学库)，但是IIRC它们模仿旧的固定流水线矩阵数学。所以当我这么做的时候(C++/VCL/OpenGL/GLSL .我知道分数应该是VBO/VAO，我只是想要快速测试)：

//---------------------------------------------------------------------------
//    ang   ,ang speed,body r,orbit r
//    [deg] ,[deg/s]   [unit],[unit]
float                  rs=1.0;          // star
float a0=0.0,da0= 50.0,r0=0.5,R0= 7.0;  // planet
float a1=0.0,da1=200.0,r1=0.2,R1= 1.0;  // moon
float a2=0.0,da2=250.0,r2=0.2,R2= 1.5;  // moon
float a3=0.0,da3= 20.0,r3=0.5,R3=10.0;  // planet
float a4=0.0,da4=150.0,r4=0.2,R4= 1.0;  // moon
float a5=0.0,da5=180.0,r5=0.2,R5= 1.5;  // moon
float b =0.0,db =50.0;                  // common self rotation
//---------------------------------------------------------------------------
void gl_draw()
    {
    GLint ix;
    GLfloat mp[16],mv[16],mm[16],m0[16];
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    float aspect=float(xs)/float(ys);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluPerspective(60.0/aspect,aspect,0.1,100.0);
    glGetFloatv(GL_PROJECTION_MATRIX,mp);
    glMatrixMode(GL_TEXTURE);
    glLoadIdentity();
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glTranslatef(0.0,0.0,-25.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mv);
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glGetFloatv(GL_MODELVIEW_MATRIX,mm);

    glDisable(GL_DEPTH_TEST);
    glDisable(GL_TEXTURE_2D);
    glDisable(GL_CULL_FACE);
//  glEnable(GL_CULL_FACE);

    // GLSL sphere shader
    glUseProgram(prog_id);
    ix=glGetUniformLocation(prog_id,"m_projection"); glUniformMatrix4fv(ix,1,false,mp);
    ix=glGetUniformLocation(prog_id,"m_view");       glUniformMatrix4fv(ix,1,false,mv);
    ix=glGetUniformLocation(prog_id,"m_model");

    // sun
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(1.0,1.0,0.0); glVertex4f(0.0,0.0,0.0,rs); glEnd();
    // planet
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glRotatef(a0,0.0,0.0,1.0);
    glTranslatef(R0,0.0,0.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,m0);
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(0.0,0.7,1.0); glVertex4f(0.0,0.0,0.0,r0); glEnd();
    // moon
    glLoadMatrixf(m0);
    glRotatef(a1,0.0,0.0,1.0);
    glTranslatef(R1,0.0,0.0);
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(0.4,0.4,0.4); glVertex4f(0.0,0.0,0.0,r1); glEnd();
    // moon
    glLoadMatrixf(m0);
    glRotatef(a2,0.0,0.0,1.0);
    glTranslatef(R2,0.0,0.0);
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(0.4,0.4,0.4); glVertex4f(0.0,0.0,0.0,r2); glEnd();
    // planet
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glRotatef(a3,0.0,0.0,1.0);
    glTranslatef(R3,0.0,0.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,m0);
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(0.0,0.7,1.0); glVertex4f(0.0,0.0,0.0,r3); glEnd();
    // moon
    glLoadMatrixf(m0);
    glRotatef(a4,0.0,0.0,1.0);
    glTranslatef(R4,0.0,0.0);
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(0.4,0.4,0.4); glVertex4f(0.0,0.0,0.0,r4); glEnd();
    // moon
    glLoadMatrixf(m0);
    glRotatef(a5,0.0,0.0,1.0);
    glTranslatef(R5,0.0,0.0);
    glRotatef(b,0.0,0.0,1.0);
    glGetFloatv(GL_MODELVIEW_MATRIX,mm); glUniformMatrix4fv(ix,1,false,mm);
    glBegin(GL_POINTS); glColor3f(0.4,0.4,0.4); glVertex4f(0.0,0.0,0.0,r5); glEnd();

    glUseProgram(0);

    glFlush();
    SwapBuffers(hdc);
    }
//---------------------------------------------------------------------------
void __fastcall TForm1::Timer1Timer(TObject *Sender)
    {
    // this is periodicaly called by timer
    gl_draw();
    float dt=0.001*float(Timer1->Interval); // timer period in seconds
    a0=fmod(a0+da0*dt,360.0);
    a1=fmod(a1+da1*dt,360.0);
    a3=fmod(a3+da3*dt,360.0);
    a4=fmod(a4+da4*dt,360.0);
    a5=fmod(a5+da5*dt,360.0);
    b =fmod(b +db *dt,360.0);
    }
//---------------------------------------------------------------------------

我得到了这个输出(使用我的球体着色器)：

​

​

该着色器只将点x,y,z,r作为球体的三维中心和半径，发出BBOX四角和渲染内接球面的法线阴影。它还使用颜色和你的3个矩阵。

所以，如果我看得对，你应该这样做：

model = identity; 
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render star
model = identity; 
model = glm::rotate(model, glm::radians(a0), glm::vec3(0.0, 1.0, 0.0));
model = glm::translate(model, glm::vec3(R0, 0.0, 0.0));
model0= model;
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render planet
model = model0;
model = glm::rotate(model, glm::radians(a1), glm::vec3(0.0, 1.0, 0.0));
model = glm::translate(model, glm::vec3(R1, 0.0, 0.0));
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render moon
model = model0;
model = glm::rotate(model, glm::radians(a2), glm::vec3(0.0, 1.0, 0.0));
model = glm::translate(model, glm::vec3(R2, 0.0, 0.0));
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render moon
model = identity; 
model = glm::rotate(model, glm::radians(a3), glm::vec3(0.0, 1.0, 0.0));
model = glm::translate(model, glm::vec3(R3, 0.0, 0.0));
model0= model;
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render planet
model = model0;
model = glm::rotate(model, glm::radians(a4), glm::vec3(0.0, 1.0, 0.0));
model = glm::translate(model, glm::vec3(R4, 0.0, 0.0));
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render moon
model = model0;
model = glm::rotate(model, glm::radians(a5), glm::vec3(0.0, 1.0, 0.0));
model = glm::translate(model, glm::vec3(R5, 0.0, 0.0));
model = glm::rotate(model, glm::radians(b), glm::vec3(0.0, 1.0, 0.0));
// render moon

如果这是不起作用的，那么你得到的矩阵顺序和使用的数学或GLM之间的其他不匹配行为与我预期的不同。我用普通的角度来做自我旋转，所以你只需要为你的身体添加索引.

另外，请注意老的GL旋转使用[deg]，所以如果GLM想要[rad]，您需要转换角度和角速度常数。

如果您想拥有更精确的/与真实世界相关的东西，或者更好地直观地看到以下内容：

• Is it possible to make realistic n-body solar system simulation in matter of size and mass?

Answer 2

对象A围绕B级旋转:A的自旋转，A到B的偏移，B的旋转，B的位置平移。因为B是太阳，我假设它在你们的世界起源，而且所有东西都在xz平面上(笛卡尔而不是OpenGL弦)，这就是：

model = glm::rotate(identity, glm::radians(-100.0f * time), glm::vec3(1.0, 0.0, 0.0)); //self-rotation
model = glm::translate(model, glm::vec3(8.0, 0.0, 0.0)); // earth is 8 away from sun, where unrotated about sun is 8 units east
model = glm::rotate(model, glm::radians(-100.0f * time), glm::vec3(0.0, 1.0, 0.0)); //rotate about sun
// no need for another translation since sun is at origin

然后，对于父为地球的对象，在解决父对象与世界的关系之前，首先解决该关系：

model = glm::rotate(identity, glm::radians(-100.0f * time), glm::vec3(1.0, 0.0, 0.0)); //self-rotation of moon
model = glm::translate(model, glm::vec3(-4.0, 0.0, 0.0)); // moon is 4 away from Earth, where unrotated about Earth is 4 units west
model = glm::rotate(model, glm::radians(-100.0f * time), glm::vec3(0.0, 1.0, 0.0)); //rotate about Earth
// translate to Earth origin, which is calculate from above code block

免责声明，我不使用glm-数学，这只是几何转换的顺序，我不知道它是否直接翻译成glm::x